[ { "id": "https://openalex.org/W2471190594", "doi": "10.1109/tsmc.2016.2582745", "title": "Vehicle Routing Problems for Drone Delivery", "year": 2016, "publication_date": "2016-07-14", "type": "article", "language": "en", "authors": [ "Kevin Dorling", "Jordan Heinrichs", "Geoffrey G. Messier", "Sebastian Magierowski" ], "first_author": "Kevin Dorling", "venue": "IEEE Transactions on Systems Man and Cybernetics Systems", "publisher": "Institute of Electrical and Electronics Engineers", "abstract": "Unmanned aerial vehicles, or drones, have the potential to significantly reduce the cost and time of making last-mile deliveries and responding to emergencies. Despite this potential, little work has gone into developing vehicle routing problems (VRPs) specifically for drone delivery scenarios. Existing VRPs are insufficient for planning drone deliveries: either multiple trips to the depot are not permitted, leading to solutions with excess drones, or the effect of battery and payload weight on energy consumption is not considered, leading to costly or infeasible routes. We propose two multitrip VRPs for drone delivery that address both issues. One minimizes costs subject to a delivery time limit, while the other minimizes the overall delivery time subject to a budget constraint. We mathematically derive and experimentally validate an energy consumption model for multirotor drones, demonstrating that energy consumption varies approximately linearly with payload and battery weight. We use this approximation to derive mixed integer linear programs for our VRPs. We propose a cost function that considers our energy consumption model and drone reuse, and apply it in a simulated annealing (SA) heuristic for finding suboptimal solutions to practical scenarios. To assist drone delivery practitioners with balancing cost and delivery time, the SA heuristic is used to show that the minimum cost has an inverse exponential relationship with the delivery time limit, and the minimum overall delivery time has an inverse exponential relationship with the budget. Numerical results confirm the importance of reusing drones and optimizing battery size in drone delivery VRPs.", "keywords": [ "Drone", "Payload (computing)", "Computer science", "Energy consumption", "Mathematical optimization", "Simulation", "Mathematics", "Engineering", "Computer network", "Network packet", "Electrical engineering" ], "cited_by_count": 1343, "is_retracted": false, "is_paratext": false, "open_access_url": "https://arxiv.org/pdf/1608.02305" }, { "id": "https://openalex.org/W2921047495", "doi": "10.1016/j.trb.2019.03.005", "title": "Vehicle routing problem with drones", "year": 2019, "publication_date": "2019-03-13", "type": "article", "language": "en", "authors": [ "Zheng Wang", "Jiuh‐Biing Sheu" ], "first_author": "Zheng Wang", "venue": "Transportation Research Part B Methodological", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Truck", "Vehicle routing problem", "Routing (electronic design automation)", "Integer programming", "Computer science", "Range (aeronautics)", "Transport engineering", "Key (lock)", "Operations research", "Service (business)", "Mathematical optimization" ], "cited_by_count": 556, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.trb.2019.03.005" }, { "id": "https://openalex.org/W2342478160", "doi": "10.1007/s11590-016-1035-3", "title": "The vehicle routing problem with drones: several worst-case results", "year": 2016, "publication_date": "2016-04-29", "type": "article", "language": "en", "authors": [ "Xingyin Wang", "Stefan Poikonen", "Bruce Golden" ], "first_author": "Xingyin Wang", "venue": "Optimization Letters", "publisher": "Springer Science+Business Media", "abstract": null, "keywords": [ "Drone", "Truck", "Computational intelligence", "Routing (electronic design automation)", "Computer science", "Vehicle routing problem", "Duration (music)", "Operations research", "Order (exchange)", "Transport engineering", "Business", "Engineering" ], "cited_by_count": 557, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1007/s11590-016-1035-3" }, { "id": "https://openalex.org/W2927378423", "doi": "10.1016/j.trc.2019.02.018", "title": "An adaptive large neighborhood search metaheuristic for the vehicle routing problem with drones", "year": 2019, "publication_date": "2019-03-22", "type": "article", "language": "en", "authors": [ "David Sacramento", "David Pisinger", "Stefan Røpke" ], "first_author": "David Sacramento", "venue": "Transportation Research Part C Emerging Technologies", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Travelling salesman problem", "Truck", "Vehicle routing problem", "Computer science", "Metaheuristic", "Routing (electronic design automation)", "Operations research", "2-opt", "Transport engineering", "Mathematical optimization", "Engineering" ], "cited_by_count": 566, "is_retracted": false, "is_paratext": false, "open_access_url": "https://orbit.dtu.dk/en/publications/de5c7fac-a4e0-41fc-b8e8-2f3bcb033b2b" }, { "id": "https://openalex.org/W2621937623", "doi": "10.1002/net.21746", "title": "The vehicle routing problem with drones: Extended models and connections", "year": 2017, "publication_date": "2017-06-07", "type": "article", "language": "en", "authors": [ "Stefan Poikonen", "Xingyin Wang", "Bruce Golden" ], "first_author": "Stefan Poikonen", "venue": "Networks", "publisher": "Wiley", "abstract": "The vehicle routing problem with drones (VRPD) is inspired by the increasing interest in commercial drone delivery by companies such as Amazon, Google, DHL, and Walmart. In our model, a fleet of m homogeneous trucks each carries k drones with a speed of α times that of the truck. Each drone may dispatch from the top of the truck and carry a package to a customer location. The drone then returns to the top of its truck to recharge or swap batteries (we assume instantaneously). The truck itself is allowed to move and deliver packages, but must be stationary at a delivery location or the depot when launching or retrieving drones. The goal is to minimize the completion time to deliver all packages and return all vehicles back to the central depot. In this article, we review and extend several worst‐case results from an earlier paper and we make connections with another practical variant of the vehicle routing problem and with Amdahl's Law. We find that the VRPD model offers some important practical advantages. The drones allow the truck to parallelize tasks and they are able to take advantage of crow‐fly distances. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(1), 34–43 2017", "keywords": [ "Drone", "Truck", "Computer science", "Swap (finance)", "Routing (electronic design automation)", "Vehicle routing problem", "Operations research", "Computer network", "Automotive engineering", "Engineering", "Business" ], "cited_by_count": 348, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1002/net.21746" }, { "id": "https://openalex.org/W2963624642", "doi": "10.1016/j.trc.2019.06.016", "title": "A matheuristic for the vehicle routing problem with drones and its variants", "year": 2019, "publication_date": "2019-07-22", "type": "article", "language": "en", "authors": [ "Daniel Schermer", "Mahdi Moeini", "Oliver Wendt" ], "first_author": "Daniel Schermer", "venue": "Transportation Research Part C Emerging Technologies", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Solver", "Drone", "Computer science", "Job shop scheduling", "Vehicle routing problem", "Truck", "Exploit", "Integer programming", "Mathematical optimization", "Routing (electronic design automation)", "Scheduling (production processes)", "Context (archaeology)" ], "cited_by_count": 281, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.trc.2019.06.016" }, { "id": "https://openalex.org/W2998391831", "doi": "10.1016/j.ijpe.2019.107598", "title": "Two echelon vehicle routing problem with drones in last mile delivery", "year": 2019, "publication_date": "2019-12-27", "type": "article", "language": "en", "authors": [ "Patchara Kitjacharoenchai", "Byung‐Cheol Min", "Seokcheon Lee" ], "first_author": "Patchara Kitjacharoenchai", "venue": "International Journal of Production Economics", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Truck", "Computer science", "Heuristics", "Routing (electronic design automation)", "Vehicle routing problem", "Swap (finance)", "Scheduling (production processes)", "Integer programming", "Operations research", "Mathematical optimization", "Computer network" ], "cited_by_count": 333, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.ijpe.2019.107598" }, { "id": "https://openalex.org/W1977319619", "doi": "10.1016/j.trc.2015.03.005", "title": "The flying sidekick traveling salesman problem: Optimization of drone-assisted parcel delivery", "year": 2015, "publication_date": "2015-03-25", "type": "article", "language": "en", "authors": [ "Chase C. Murray", "Amanda Chu" ], "first_author": "Chase C. Murray", "venue": "Transportation Research Part C Emerging Technologies", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Heuristics", "Truck", "Last mile (transportation)", "Computer science", "Travelling salesman problem", "Vehicle routing problem", "Operations research", "Scheduling (production processes)", "Routing (electronic design automation)", "Engineering", "Operations management" ], "cited_by_count": 1726, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.trc.2015.03.005" }, { "id": "https://openalex.org/W3010476620", "doi": "10.1111/itor.12783", "title": "Unmanned aerial vehicles/drones in vehicle routing problems: a literature review", "year": 2020, "publication_date": "2020-03-02", "type": "article", "language": "en", "authors": [ "Daniela Rojas Viloria", "Elyn Lizeth Solano Charris", "Andrés Muñoz‐Villamizar", "Jairo R. Montoya‐Torres" ], "first_author": "Daniela Rojas Viloria", "venue": "International Transactions in Operational Research", "publisher": "Wiley", "abstract": "Abstract During recent years, advances in drone technologies have made them applicable in various fields of industry, and their popularity continues to grow. In this paper, the academic contributions on drones routing problems are analyzed between 2005 and 2019 to identify the main characteristics of these types of problems, as well as the research trends and recent improvements. The literature is classified according to the objectives optimized, solution methods, applications, constraints, and whether they use a complementary vehicle or not. Finally, a discussion for trends and future research is presented.", "keywords": [ "Drone", "Popularity", "Vehicle routing problem", "Computer science", "Routing (electronic design automation)", "Operations research", "Aeronautics", "Engineering", "Computer network", "Political science" ], "cited_by_count": 265, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1111/itor.12783" }, { "id": "https://openalex.org/W3121017033", "doi": "10.1016/j.trb.2020.11.011", "title": "A branch-and-cut algorithm for the vehicle routing problem with drones", "year": 2021, "publication_date": "2021-01-13", "type": "article", "language": "en", "authors": [ "Felix Tamke", "Udo Buscher" ], "first_author": "Felix Tamke", "venue": "Transportation Research Part B Methodological", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Computer science", "Routing (electronic design automation)", "Mathematical optimization", "Branch and cut", "Linear programming", "Range (aeronautics)", "Flexibility (engineering)", "Integer programming", "Vehicle routing problem", "Lagrangian relaxation", "Linear programming relaxation" ], "cited_by_count": 201, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.trb.2020.11.011" }, { "id": "https://openalex.org/W3216846761", "doi": "10.1016/j.eswa.2021.116264", "title": "Vehicle routing problem with drones considering time windows", "year": 2021, "publication_date": "2021-11-27", "type": "article", "language": "en", "authors": [ "R.J. Kuo", "Shih‐Hao Lu", "Pei-Yu Lai", "Setyo Tri Windras Mara" ], "first_author": "R.J. Kuo", "venue": "Expert Systems with Applications", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Computer science", "Truck", "Vehicle routing problem", "Solver", "Variable neighborhood search", "Routing (electronic design automation)", "Rendezvous", "Service (business)", "Node (physics)", "Integer programming", "Operations research" ], "cited_by_count": 193, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.eswa.2021.116264" }, { "id": "https://openalex.org/W2935841433", "doi": "10.1016/j.apenergy.2019.03.117", "title": "Impact of drone delivery on sustainability and cost: Realizing the UAV potential through vehicle routing optimization", "year": 2019, "publication_date": "2019-03-22", "type": "article", "language": "en", "authors": [ "Wen‐Chyuan Chiang", "Yuyu Li", "Jennifer S. Shang", "Timothy L. Urban" ], "first_author": "Wen‐Chyuan Chiang", "venue": "Applied Energy", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Carbon footprint", "Greenhouse gas", "Sustainability", "Flexibility (engineering)", "Vehicle routing problem", "Energy consumption", "Exploit", "Routing (electronic design automation)", "Truck", "Computer science", "Integer programming" ], "cited_by_count": 394, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.apenergy.2019.03.117" }, { "id": "https://openalex.org/W2973603239", "doi": "10.1016/j.cor.2019.104802", "title": "Multi-visit drone routing problem", "year": 2019, "publication_date": "2019-09-17", "type": "article", "language": "en", "authors": [ "Stefan Poikonen", "Bruce Golden" ], "first_author": "Stefan Poikonen", "venue": "Computers & Operations Research", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Routing (electronic design automation)", "Computer science", "Swap (finance)", "Truck", "Heuristic", "Set (abstract data type)", "Operations research", "Computer network", "Artificial intelligence", "Engineering", "Automotive engineering" ], "cited_by_count": 302, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.cor.2019.104802" }, { "id": "https://openalex.org/W2943166133", "doi": "10.1016/j.cor.2019.04.021", "title": "A hybrid VNS/Tabu search algorithm for solving the vehicle routing problem with drones and en route operations", "year": 2019, "publication_date": "2019-05-01", "type": "article", "language": "en", "authors": [ "Daniel Schermer", "Mahdi Moeini", "Oliver Wendt" ], "first_author": "Daniel Schermer", "venue": "Computers & Operations Research", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Tabu search", "Computer science", "Variable neighborhood search", "Solver", "Drone", "Vehicle routing problem", "Mathematical optimization", "Integer programming", "Routing (electronic design automation)", "Heuristic", "Job shop scheduling", "Local search (optimization)" ], "cited_by_count": 271, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.cor.2019.04.021" }, { "id": "https://openalex.org/W3182067109", "doi": "10.1016/j.ejor.2021.07.008", "title": "The min-cost parallel drone scheduling vehicle routing problem", "year": 2021, "publication_date": "2021-07-10", "type": "article", "language": "en", "authors": [ "Minh Anh Nguyen", "Giang Thi-Huong Dang", "Minh Hoàng Hà", "Minh-Trien Pham" ], "first_author": "Minh Anh Nguyen", "venue": "European Journal of Operational Research", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Travelling salesman problem", "Computer science", "Vehicle routing problem", "Scheduling (production processes)", "Mathematical optimization", "Truck", "Job shop scheduling", "Routing (electronic design automation)", "Heuristic", "Integer programming", "Operations research" ], "cited_by_count": 157, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.ejor.2021.07.008" }, { "id": "https://openalex.org/W4313593040", "doi": "10.1016/j.trb.2023.01.002", "title": "An exact algorithm for the two-echelon vehicle routing problem with drones", "year": 2023, "publication_date": "2023-01-04", "type": "article", "language": "en", "authors": [ "Hang Zhou", "Hu Qin", "Chun Cheng", "Louis-Martin Rousseau" ], "first_author": "Hang Zhou", "venue": "Transportation Research Part B Methodological", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Vehicle routing problem", "Drone", "Computer science", "Routing (electronic design automation)", "Mathematical optimization", "Algorithm", "Mathematics", "Computer network" ], "cited_by_count": 147, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.trb.2023.01.002" }, { "id": "https://openalex.org/W3215148040", "doi": "10.1016/j.cor.2022.106112", "title": "The vehicle routing problem with drones and drone speed selection", "year": 2022, "publication_date": "2022-12-05", "type": "article", "language": "en", "authors": [ "Felix Tamke", "Udo Buscher" ], "first_author": "Felix Tamke", "venue": "Computers & Operations Research", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Truck", "Computer science", "Energy consumption", "Fuel efficiency", "Routing (electronic design automation)", "Operations research", "Automotive engineering", "Engineering" ], "cited_by_count": 94, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.cor.2022.106112" }, { "id": "https://openalex.org/W4210344377", "doi": "10.1016/j.aei.2022.101536", "title": "Solving the vehicle routing problem with drone for delivery services using an ant colony optimization algorithm", "year": 2022, "publication_date": "2022-01-01", "type": "article", "language": "en", "authors": [ "Shan-Huen Huang", "Ying‐Hua Huang", "Carola Alejandra Blazquez", "Chia-Yi Chen" ], "first_author": "Shan-Huen Huang", "venue": "Advanced Engineering Informatics", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Truck", "Ant colony optimization algorithms", "Vehicle routing problem", "Computer science", "Routing (electronic design automation)", "Service (business)", "Integer programming", "Ant colony", "Operations research", "Engineering", "Mathematical optimization" ], "cited_by_count": 175, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.aei.2022.101536" }, { "id": "https://openalex.org/W2928814937", "doi": "10.1016/j.trc.2019.03.021", "title": "The hybrid vehicle-drone routing problem for pick-up and delivery services", "year": 2019, "publication_date": "2019-03-28", "type": "article", "language": "en", "authors": [ "Aline Karak", "Khaled F. Abdelghany" ], "first_author": "Aline Karak", "venue": "Transportation Research Part C Emerging Technologies", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Heuristics", "Vehicle routing problem", "Routing (electronic design automation)", "Heuristic", "Computer science", "Mathematical optimization", "Operations research", "Engineering", "Computer network", "Artificial intelligence", "Mathematics" ], "cited_by_count": 297, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.trc.2019.03.021" }, { "id": "https://openalex.org/W3097170600", "doi": "10.1016/j.phycom.2020.101236", "title": "Hybrid genetic-sweep algorithm to solve the vehicle routing problem with drones", "year": 2020, "publication_date": "2020-11-07", "type": "article", "language": "en", "authors": [ "Jalel Euchi", "Abdeljawed Sadok" ], "first_author": "Jalel Euchi", "venue": "Physical Communication", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Computer science", "Vehicle routing problem", "Genetic algorithm", "Routing (electronic design automation)", "Mathematical optimization", "Embedded system", "Machine learning", "Mathematics" ], "cited_by_count": 131, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.phycom.2020.101236" }, { "id": "https://openalex.org/W3084064394", "doi": "10.1016/j.trc.2020.102762", "title": "Drone-aided routing: A literature review", "year": 2020, "publication_date": "2020-09-07", "type": "article", "language": "en", "authors": [ "Giusy Macrina", "Luigi Di Puglia Pugliese", "Francesca Guerriero", "Gilbert Laporte" ], "first_author": "Giusy Macrina", "venue": "Transportation Research Part C Emerging Technologies", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Context (archaeology)", "Routing (electronic design automation)", "Computer science", "Focus (optics)", "Work (physics)", "Engineering", "Transport engineering", "Geography", "Computer network" ], "cited_by_count": 524, "is_retracted": false, "is_paratext": false, "open_access_url": "https://purehost.bath.ac.uk/ws/files/221385593/4._Survey_VRP_D_Copy_1_.pdf" }, { "id": "https://openalex.org/W4283784116", "doi": "10.1016/j.tre.2022.102757", "title": "Vehicle routing problems with drones equipped with multi-package payload compartments", "year": 2022, "publication_date": "2022-07-03", "type": "article", "language": "en", "authors": [ "Mohamed Amine Masmoudi", "Simona Mancini", "Roberto Baldacci", "Yong‐Hong Kuo" ], "first_author": "Mohamed Amine Masmoudi", "venue": "Transportation Research Part E Logistics and Transportation Review", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Truck", "Vehicle routing problem", "Computer science", "Payload (computing)", "Fuel efficiency", "Automotive engineering", "Routing (electronic design automation)", "Engineering", "Computer network", "Network packet" ], "cited_by_count": 127, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.sciencedirect.com/science/article/abs/pii/S136655452200148X" }, { "id": "https://openalex.org/W2986975079", "doi": "10.1287/ijoc.2018.0879", "title": "The Mothership and Drone Routing Problem", "year": 2019, "publication_date": "2019-11-11", "type": "article", "language": "en", "authors": [ "Stefan Poikonen", "Bruce Golden" ], "first_author": "Stefan Poikonen", "venue": "INFORMS journal on computing", "publisher": "Institute for Operations Research and the Management Sciences", "abstract": "The mothership and drone routing problem (MDRP) considers the routing of a two-vehicle tandem. The larger vehicle, which may be a ship or an airplane, is called the mothership; the smaller vehicle, which may be a small boat or unmanned aerial vehicle, is called the drone. We assume that there exists a set of target locations T. For each t in T, the drone must launch from the mothership, visit t, and then return to the mothership to refuel. The drone has a limited range of R time units. In the MDRP, we assume that both mothership and drone operate in the “open seas” (i.e., using the Euclidean metric). We also introduce the mothership and infinite-capacity drone routing problem (MDRP-IC), where a drone launches from the mothership and visits one or more targets consecutively before returning to the mothership. Our exact approach uses branch and bound, where each node of the branch-and-bound tree corresponds to a potential subsequence of the order of target visits. A lower bound at each node is given by solving a second-order cone program, which optimally chooses a launch point and landing point for each target in the subsequence. A set of heuristics that also uses a second-order cone program as an embedded procedure is presented. We show that our schemes are flexible to accommodate a variety of additional constraints and/or objective functions. Computational results and interesting variants of the MDRP and MDRP-IC are also presented.", "keywords": [ "Drone", "Computer science", "Heuristics", "Routing (electronic design automation)", "Real-time computing", "Mathematical optimization", "Mathematics", "Embedded system" ], "cited_by_count": 161, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1287/ijoc.2018.0879" }, { "id": "https://openalex.org/W4381949822", "doi": "10.1016/j.ejor.2023.06.021", "title": "A multi-visit flexible-docking vehicle routing problem with drones for simultaneous pickup and delivery services", "year": 2023, "publication_date": "2023-06-25", "type": "article", "language": "en", "authors": [ "Jie Jiang", "Ying Dai", "Fei Yang", "Zujun Ma" ], "first_author": "Jie Jiang", "venue": "European Journal of Operational Research", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Truck", "Vehicle routing problem", "Pickup", "Computer science", "Integer programming", "Interdependence", "Metaheuristic", "Routing (electronic design automation)", "Operations research", "Transport engineering", "Simulation" ], "cited_by_count": 156, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.ejor.2023.06.021" }, { "id": "https://openalex.org/W4220774469", "doi": "10.1016/j.clscn.2022.100041", "title": "The electric vehicle routing problem with drones: An energy minimization approach for aerial deliveries", "year": 2022, "publication_date": "2022-03-15", "type": "article", "language": "en", "authors": [ "Nikolaos A. Kyriakakis", "Themistoklis Stamadianos", "Magdalene Marinaki", "Yannis Marinakis" ], "first_author": "Nikolaos A. Kyriakakis", "venue": "Cleaner Logistics and Supply Chain", "publisher": "Elsevier BV", "abstract": "This paper introduces the Electric Vehicle Routing Problem with Drones (EVRPD), the first VRP combining electric ground vehicles (EVs) with unmanned aerial vehicles (UAVs), also known as drones, in order to deliver packages to customers. The problem’s objective is to minimize the total energy consumption, focusing on the main non-constant and controllable factor of energy consumption on a delivery vehicle, the payload weight. The problem considers same-sized packages, belonging to different weight classes. EVs serve as motherships, from which drones are deployed to deliver the packages. Drones can carry multiple packages, up to a certain weight limit and their range is depended on their payload weight. For solving the EVRPD, four algorithms of the Ant Colony Optimization framework are implemented, two versions of the Ant Colony System and the Min–Max Ant System. A Variable Neighborhood Descent algorithm is utilized in all variants as a local search procedure. Instances for the EVRPD are created based on the two-echelon VRP literature and are used to test the proposed algorithms. Their computational results are compared and discussed. Practical, real-life scenarios of the EVRPD application are also presented and solved.", "keywords": [ "Drone", "Payload (computing)", "Ant colony optimization algorithms", "Minification", "Vehicle routing problem", "Computer science", "Energy consumption", "Routing (electronic design automation)", "Electric vehicle", "Mathematical optimization", "Range (aeronautics)", "Ant colony" ], "cited_by_count": 100, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.sciencedirect.com/science/article/pii/S2772390922000142/pdf" }, { "id": "https://openalex.org/W3210226161", "doi": "10.1016/j.engappai.2021.104510", "title": "A dynamical artificial bee colony for vehicle routing problem with drones", "year": 2021, "publication_date": "2021-11-03", "type": "article", "language": "en", "authors": [ "Deming Lei", "Zhengzhi Cui", "Ming Li" ], "first_author": "Deming Lei", "venue": "Engineering Applications of Artificial Intelligence", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Computer science", "Swarm behaviour", "Truck", "Vehicle routing problem", "Artificial bee colony algorithm", "Descent (aeronautics)", "Routing (electronic design automation)", "Honey bee", "Variable (mathematics)", "Process (computing)", "Mathematical optimization" ], "cited_by_count": 84, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.engappai.2021.104510" }, { "id": "https://openalex.org/W2792734736", "doi": "10.1007/978-3-319-75417-8_33", "title": "Algorithms for Solving the Vehicle Routing Problem with Drones", "year": 2018, "publication_date": "2018-01-01", "type": "conference-paper", "language": "en", "authors": [ "Daniel Schermer", "Mahdi Moeini", "Oliver Wendt" ], "first_author": "Daniel Schermer", "venue": "Lecture notes in computer science", "publisher": "Springer Science+Business Media", "abstract": null, "keywords": [ "Drone", "Heuristics", "Vehicle routing problem", "Computer science", "Routing (electronic design automation)", "Heuristic", "Focus (optics)", "Mathematical optimization", "Operations research", "Artificial intelligence", "Computer network", "Mathematics" ], "cited_by_count": 66, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1007/978-3-319-75417-8_33" }, { "id": "https://openalex.org/W4328051498", "doi": "10.1016/j.trb.2023.03.003", "title": "A branch-and-price-and-cut algorithm for the vehicle routing problem with load-dependent drones", "year": 2023, "publication_date": "2023-03-21", "type": "article", "language": "en", "authors": [ "Yang Xia", "Wenjia Zeng", "Canrong Zhang", "Hai Long Yang" ], "first_author": "Yang Xia", "venue": "Transportation Research Part B Methodological", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Computer science", "Mathematical optimization", "Truck", "Energy consumption", "Routing (electronic design automation)", "Vehicle routing problem", "Integer programming", "Nonlinear programming", "Nonlinear system", "Algorithm", "Engineering" ], "cited_by_count": 96, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.trb.2023.03.003" }, { "id": "https://openalex.org/W2947601823", "doi": "10.1016/j.cor.2019.05.024", "title": "An optimization-driven dynamic vehicle routing algorithm for on-demand meal delivery using drones", "year": 2019, "publication_date": "2019-05-28", "type": "article", "language": "en", "authors": [ "Yanchao Liu" ], "first_author": "Yanchao Liu", "venue": "Computers & Operations Research", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Computer science", "Vehicle routing problem", "Drone", "Pickup", "Integer programming", "Mathematical optimization", "Routing (electronic design automation)", "Operations research", "Simulation", "Algorithm", "Engineering", "Mathematics" ], "cited_by_count": 204, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.cor.2019.05.024" }, { "id": "https://openalex.org/W4297109112", "doi": "10.1016/j.trc.2022.103901", "title": "Truck–drone hybrid routing problem with time-dependent road travel time", "year": 2022, "publication_date": "2022-09-26", "type": "article", "language": "en", "authors": [ "Yong Wang", "Zheng Wang", "Xiangpei Hu", "Guiqin Xue", "Xiangyang Guan" ], "first_author": "Yong Wang", "venue": "Transportation Research Part C Emerging Technologies", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Truck", "Vehicle routing problem", "Routing (electronic design automation)", "Time travel", "Computer science", "Travel time", "Transport engineering", "Automotive engineering", "Engineering", "Computer network", "Artificial intelligence" ], "cited_by_count": 207, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.trc.2022.103901" }, { "id": "https://openalex.org/W2892159790", "doi": "10.3390/su10093344", "title": "Sizing of the Drone Delivery Fleet Considering Energy Autonomy", "year": 2018, "publication_date": "2018-09-19", "type": "article", "language": "en", "authors": [ "Asma Troudi", "Sid-Ali Addouche", "Sofiène Dellagi", "Abderrahman El Mhamedi" ], "first_author": "Asma Troudi", "venue": "Sustainability", "publisher": "Multidisciplinary Digital Publishing Institute", "abstract": "One of the most innovative solutions treated in the literature in order to reduce the environmental impact of urban parcel delivery logistics is the use of drones for delivery on the last kilometer. Consequently, nowadays, the primary challenge is essentially related to the drones’ fleet sizing according to its means of support for the urban delivery of parcels. In this paper, we will discuss the issue of dimensioning from a forecast of deliveries of an urban perimeter, the size of the fleet, the stock of battery to dispose of and the strategy of battery charging. We will present an analytical model expressing the proposed problem of the optimal drones’ delivery mission taking into account the issues of autonomy and energy consumption related to the drone’s technical specification. According to the developed analytical model, two optimization policies will be proposed. The first policy consists of planning missions under reducing distance. The second policy tries to make a compromise between the distance and the number of drones. A case study will be presented in order to compare the two policies based on the overall cost of a plan. The main objective of the study is to create a decision-making tool for the design of a drone fleet in the case of forecast deliveries over a time horizon under operational constraints.", "keywords": [ "Drone", "Dimensioning", "Dispose pattern", "Operations research", "Sizing", "Computer science", "Profit (economics)", "Transport engineering", "Engineering", "Economics" ], "cited_by_count": 109, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.mdpi.com/2071-1050/10/9/3344/pdf?version=1537338292" }, { "id": "https://openalex.org/W3122711124", "doi": "10.1109/tsmc.2020.2968839", "title": "Two-Echelon Routing Problem for Parcel Delivery by Cooperated Truck and Drone", "year": 2020, "publication_date": "2020-02-10", "type": "article", "language": "en", "authors": [ "Yao Liu", "Zhong Liu", "Jianmai Shi", "Guohua Wu", "Witold Pedrycz" ], "first_author": "Yao Liu", "venue": "IEEE Transactions on Systems Man and Cybernetics Systems", "publisher": "Institute of Electrical and Electronics Engineers", "abstract": "A new variant of the two-echelon routing problem is investigated, where the truck and the drone are used to cooperatively complete the deliveries of all parcels. The truck not only acts as a tool for parcel delivery but also serves as a moving depot for the drone. The drone can carry several parcels and take off from the truck, while returning to the truck after completing the delivery. The energy consumption model for the routing process of the drone is analyzed, when it is utilized to deliver multiple parcels. A two-stage route-based modeling approach is proposed to optimize both the truck’s main route and the drone’s adjoint flying routes. A hybrid heuristic integrating nearest neighbor and cost saving strategies is developed to quickly construct a feasible solution. The simulated annealing algorithm is integrated with Tabu search, to improve the quality of the solution as well as the search efficiency. Random instances at different scales are used to test the performance of the proposed algorithm. A case study based on the practical road network in Changsha, China, is presented, through which the sensitivity analysis is conducted with respect to some critical factors.", "keywords": [ "Drone", "Truck", "Routing (electronic design automation)", "Vehicle routing problem", "Computer science", "Operations research", "Business", "Engineering", "Computer network", "Automotive engineering" ], "cited_by_count": 176, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1109/tsmc.2020.2968839" }, { "id": "https://openalex.org/W4285089687", "doi": "10.1007/s10479-022-04816-y", "title": "A multi-objective humanitarian pickup and delivery vehicle routing problem with drones", "year": 2022, "publication_date": "2022-07-12", "type": "article", "language": "en", "authors": [ "Yichen Lu", "Chao Yang", "Jun Yang" ], "first_author": "Yichen Lu", "venue": "Annals of Operations Research", "publisher": "Springer Science+Business Media", "abstract": null, "keywords": [ "Drone", "Vehicle routing problem", "Routing (electronic design automation)", "Pickup", "Computer science", "Ant colony optimization algorithms", "Mathematical optimization", "Truck", "Integer programming", "Theory of computation", "Operations research", "Engineering" ], "cited_by_count": 77, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1007/s10479-022-04816-y" }, { "id": "https://openalex.org/W4286321718", "doi": "10.1016/j.trc.2022.103733", "title": "A hierarchical solution evaluation method and a hybrid algorithm for the vehicle routing problem with drones and multiple visits", "year": 2022, "publication_date": "2022-06-06", "type": "article", "language": "en", "authors": [ "Ruixue Gu", "Mark Poon", "Zhihao Luo", "Yang Liu", "Zhong Liu" ], "first_author": "Ruixue Gu", "venue": "Transportation Research Part C Emerging Technologies", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Travelling salesman problem", "Computer science", "Payload (computing)", "Truck", "Vehicle routing problem", "Heuristic", "Mathematical optimization", "Algorithm", "Routing (electronic design automation)", "Network packet", "Engineering" ], "cited_by_count": 99, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.trc.2022.103733" }, { "id": "https://openalex.org/W4323275682", "doi": "10.1016/j.eswa.2023.119777", "title": "Applying NSGA-II to vehicle routing problem with drones considering makespan and carbon emission", "year": 2023, "publication_date": "2023-03-05", "type": "article", "language": "en", "authors": [ "R.J. Kuo", "Evan Edbert", "Ferani Eva Zulvia", "Shih‐Hao Lu" ], "first_author": "R.J. Kuo", "venue": "Expert Systems with Applications", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Sorting", "Computer science", "Job shop scheduling", "Genetic algorithm", "Routing (electronic design automation)", "Mathematical optimization", "Vehicle routing problem", "Operator (biology)", "Operations research", "Algorithm", "Mathematics" ], "cited_by_count": 84, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.eswa.2023.119777" }, { "id": "https://openalex.org/W4390226701", "doi": "10.1016/j.cor.2023.106514", "title": "Parallel drone scheduling vehicle routing problems with collective drones", "year": 2023, "publication_date": "2023-12-26", "type": "article", "language": "en", "authors": [ "Roberto Montemanni", "Mauro Dell’Amico", "Andrea Corsini" ], "first_author": "Roberto Montemanni", "venue": "Computers & Operations Research", "publisher": "Elsevier BV", "abstract": "We study last-mile delivery problems where trucks and drones collaborate to deliver goods to final customers. In particular, we focus on problem settings where either a single truck or a fleet with several homogeneous trucks work in parallel to drones, and drones have the capability of collaborating for delivering missions. This cooperative behaviour of the drones, which are able to connect to each other and work together for some delivery tasks, enhance their potential, since connected drone has increased lifting capabilities and can fly at higher speed, overcoming the main limitations of the setting where the drones can only work independently. In this work, we contribute a Constraint Programming model and a valid inequality for the version of the problem with one truck, namely the Parallel Drone Scheduling Traveling Salesman Problem with Collective Drones and we introduce for the first time the variant with multiple trucks, called the Parallel Drone Scheduling Vehicle Routing Problem with Collective Drones. For the latter version of the problem, we propose two Constraint Programming models and a Mixed Integer Linear Programming model. An extensive experimental campaign leads to state-of-the-art results for the problem with one truck and some understanding of the presented models’ behaviour on the version with multiple trucks. Some insights about future research are finally discussed.", "keywords": [ "Drone", "Truck", "Travelling salesman problem", "Computer science", "Vehicle routing problem", "Scheduling (production processes)", "Integer programming", "Constraint programming", "Operations research", "Routing (electronic design automation)", "Mathematical optimization", "Computer network" ], "cited_by_count": 47, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.cor.2023.106514" }, { "id": "https://openalex.org/W2784102161", "doi": "10.1049/iet-its.2017.0227", "title": "En route truck–drone parcel delivery for optimal vehicle routing strategies", "year": 2018, "publication_date": "2018-01-12", "type": "article", "language": "en", "authors": [ "Mario Marinelli", "Leonardo Caggiani", "Michele Ottomanelli", "Mauro Dell’Orco" ], "first_author": "Mario Marinelli", "venue": "IET Intelligent Transport Systems", "publisher": "Institution of Engineering and Technology", "abstract": "Recently, several prominent logistic companies in Europe and the USA are seriously considering the idea of using drones launched from trucks and working in parallel to deliver packages. In the relevant literature, a novel problem formulation called travelling salesman problem with drone has been introduced, and some modelling and solution approaches have been presented. Existing approaches are based on the main assumption that the truck can dispatch and pick up a drone only at a node, i.e. the depot or a customer location. Here, the authors present a novel approach aimed to maximise the drone usage in parcel delivering. The authors consider that a truck can deliver and pick a drone up not only at a node but also along a route arc ( en route ). In this way, the operations of a drone are not strictly related to the customers’ position, but it can serve a wider area along the route. The authors tested the proposed heuristic on benchmark instances and analysed the benefits introduced with the en route approach.", "keywords": [ "Drone", "Truck", "Vehicle routing problem", "Routing (electronic design automation)", "Computer science", "Transport engineering", "Automotive engineering", "Engineering", "Computer network" ], "cited_by_count": 161, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1049/iet-its.2017.0227" }, { "id": "https://openalex.org/W3000737138", "doi": "10.1287/trsc.2019.0944", "title": "Same-Day Delivery with Drone Resupply", "year": 2020, "publication_date": "2020-01-01", "type": "article", "language": "en", "authors": [ "Iman Dayarian", "Martin W. P. Savelsbergh", "John-Paul Clarke" ], "first_author": "Iman Dayarian", "venue": "Transportation Science", "publisher": "Institute for Operations Research and the Management Sciences", "abstract": "Unmanned aerial vehicles, commonly referred to as drones, have recently seen an increased level of interest as their potential use in same-day home delivery has been promoted and advocated by large retailers and courier delivery companies. We introduce a novel way to exploit drones in same-day home delivery settings: drone resupply. We consider a home delivery system in which delivery trucks are regularly resupplied by drones. Resupply can take place whenever a delivery truck is stationary and a drone can land on the truck’s roof. We introduce the vehicle routing problem with drone resupply to capture and investigate this setting. We develop different algorithms and compare their performance. Finally, we quantify the potential benefits of drone resupply and generate valuable insights for advancing this concept.", "keywords": [ "Drone", "Truck", "Exploit", "Aeronautics", "Computer science", "Engineering", "Computer security", "Aerospace engineering" ], "cited_by_count": 246, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1287/trsc.2019.0944" }, { "id": "https://openalex.org/W4312059606", "doi": "10.1016/j.tre.2022.102990", "title": "The multi-visit drone routing problem for pickup and delivery services", "year": 2022, "publication_date": "2022-12-21", "type": "article", "language": "en", "authors": [ "Shanshan Meng", "Xiuping Guo", "Dong Li", "Guoquan Liu" ], "first_author": "Shanshan Meng", "venue": "Transportation Research Part E Logistics and Transportation Review", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Heuristics", "Computer science", "Pickup", "Truck", "Payload (computing)", "Routing (electronic design automation)", "Vehicle routing problem", "Benchmark (surveying)", "Mathematical optimization", "Integer programming", "Simulated annealing" ], "cited_by_count": 131, "is_retracted": false, "is_paratext": false, "open_access_url": "https://figshare.com/articles/journal_contribution/The_multi-visit_drone_routing_problem_for_pickup_and_delivery_services/21740627" }, { "id": "https://openalex.org/W3137336600", "doi": "10.1016/j.eswa.2021.114854", "title": "Applications and Research avenues for drone-based models in logistics: A classification and review", "year": 2021, "publication_date": "2021-03-14", "type": "article", "language": "en", "authors": [ "Mohammad Moshref‐Javadi", "Matthias Winkenbach" ], "first_author": "Mohammad Moshref‐Javadi", "venue": "Expert Systems with Applications", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Computer science", "Extant taxon", "Variety (cybernetics)", "Scalability", "Data science", "Operations research", "Systems engineering", "Management science", "Process management", "Artificial intelligence", "Business" ], "cited_by_count": 396, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.eswa.2021.114854" }, { "id": "https://openalex.org/W3193644409", "doi": "10.1287/trsc.2021.1055", "title": "An Exact Algorithm for Heterogeneous Drone-Truck Routing Problem", "year": 2021, "publication_date": "2021-08-18", "type": "article", "language": "en", "authors": [ "Munjeong Kang", "Chungmok Lee" ], "first_author": "Munjeong Kang", "venue": "Transportation Science", "publisher": "Institute for Operations Research and the Management Sciences", "abstract": "Recently, there are attempts to utilize drones in the logistic application. We consider the case in which there are multiple drones with different characteristics, such as speed and battery capacity. The truck and drone collaborate the delivery to serve all customers, while the drones are carried by and dispatched from the truck. The multiple drones can be deployed simultaneously; however, the truck must wait until all drones return. Therefore, the goal is to minimize the total sum of truck travel and waiting times for drones to return after deliveries. We call the proposed model a heterogeneous drone-truck routing problem (HDTRP), and a mixed-integer programming formulation for the problem is presented. We develop an exact algorithm based on the logic-based Benders decomposition approach, which outperforms the state-of-the-art solvers.", "keywords": [ "Drone", "Truck", "Routing (electronic design automation)", "Computer science", "Integer programming", "Vehicle routing problem", "Benders' decomposition", "Mathematical optimization", "Engineering", "Algorithm", "Mathematics", "Computer network" ], "cited_by_count": 112, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1287/trsc.2021.1055" }, { "id": "https://openalex.org/W2609088824", "doi": "10.1016/j.cor.2017.04.011", "title": "A multi-objective green UAV routing problem", "year": 2017, "publication_date": "2017-04-29", "type": "article", "language": "en", "authors": [ "Bruno N. Coelho", "Vitor N. Coelho", "Igor Machado Coelho", "Luiz Satoru Ochi", "Roozbeh Haghnazar K.", "Demetrius Zuidema", "Milton Sérgio Fernandes de Lima", "Adilson Rodrigues da Costa" ], "first_author": "Bruno N. Coelho", "venue": "Computers & Operations Research", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Computer science", "Routing (electronic design automation)", "Mathematical optimization", "Deliverable", "Range (aeronautics)", "Branch and bound", "Integer programming", "Linear programming", "Operations research", "Systems engineering", "Mathematics" ], "cited_by_count": 193, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.cor.2017.04.011" }, { "id": "https://openalex.org/W3035279594", "doi": "10.1016/j.trb.2020.05.010", "title": "Two-echelon vehicle routing problem with time windows and mobile satellites", "year": 2020, "publication_date": "2020-06-10", "type": "article", "language": "en", "authors": [ "Hongqi Li", "Haotian Wang", "Jun Chen", "Ming Bai" ], "first_author": "Hongqi Li", "venue": "Transportation Research Part B Methodological", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Vehicle routing problem", "Heuristic", "Cruise", "Computer science", "Operations research", "Routing (electronic design automation)", "Real-time computing", "Engineering", "Computer network", "Artificial intelligence", "Aerospace engineering" ], "cited_by_count": 170, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.trb.2020.05.010" }, { "id": "https://openalex.org/W3027940156", "doi": "10.1109/tits.2020.2992549", "title": "Synchronized Truck and Drone Routing in Package Delivery Logistics", "year": 2020, "publication_date": "2020-05-22", "type": "article", "language": "en", "authors": [ "D DAS", "Rohan Sewani", "Junwei Wang", "Manoj Kumar Tiwari" ], "first_author": "D DAS", "venue": "IEEE Transactions on Intelligent Transportation Systems", "publisher": "Institute of Electrical and Electronics Engineers", "abstract": "The use of Unmanned Aerial Vehicles (UAVs) in delivery logistics has become an efficient solution with the advancement of autonomous robotics. This paper proposes a novel mechanism that synchronizes drones and delivery trucks; particularly the case where trucks can work as mobile launching and retrieval sites. The problem is a Vehicle Routing Problem with Time Windows and Synchronized Drones. A multi-objective optimization model is developed with two conflicting objectives, minimizing the travel costs and maximizing the customer service level in terms of timely deliveries. A novel Collaborative Pareto Ant Colony Optimization algorithm is proposed to solve the model and Non-dominated Sorting Genetic Algorithm II (NSGA-II) is used to compare and validate the proposed algorithm. The experimental results indicate that the proposed mechanism is an efficient solution to parcel delivery logistics.", "keywords": [ "Drone", "Truck", "Ant colony optimization algorithms", "Genetic algorithm", "Computer science", "Sorting", "Vehicle routing problem", "Routing (electronic design automation)", "Pareto principle", "Service (business)", "Multi-objective optimization", "Operations research" ], "cited_by_count": 231, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1109/tits.2020.2992549" }, { "id": "https://openalex.org/W4386997203", "doi": "10.1016/j.eswa.2023.121741", "title": "The drone-assisted vehicle routing problem with robot stations", "year": 2023, "publication_date": "2023-09-24", "type": "article", "language": "en", "authors": [ "André Morim", "Giovanni Campuzano", "Pedro Amorim", "Martijn Mes", "Eduardo Lalla‐Ruiz" ], "first_author": "André Morim", "venue": "Expert Systems with Applications", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Solver", "Drone", "Computer science", "Job shop scheduling", "Metaheuristic", "Simulated annealing", "Truck", "Vehicle routing problem", "Mathematical optimization", "Robot", "Routing (electronic design automation)", "Integer programming" ], "cited_by_count": 41, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.sciencedirect.com/science/article/pii/S0957417423022431" }, { "id": "https://openalex.org/W4296935095", "doi": "10.1016/j.cie.2022.108679", "title": "A novel multi-objective optimization model for the vehicle routing problem with drone delivery and dynamic flight endurance", "year": 2022, "publication_date": "2022-09-24", "type": "article", "language": "en", "authors": [ "Shuai Zhang", "Siliang Liu", "Weibo Xu", "Wanru Wang" ], "first_author": "Shuai Zhang", "venue": "Computers & Industrial Engineering", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Vehicle routing problem", "Engineering", "Computer science", "Routing (electronic design automation)", "Aeronautics", "Simulation", "Operations research", "Automotive engineering", "Embedded system" ], "cited_by_count": 77, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.cie.2022.108679" }, { "id": "https://openalex.org/W2898315333", "doi": "10.1002/net.21858", "title": "Drone arc routing problems", "year": 2018, "publication_date": "2018-10-24", "type": "article", "language": "en", "authors": [ "James F. Campbell", "Ángel Corberán", "Isaac Plana", "José María Sanchis" ], "first_author": "James F. Campbell", "venue": "Networks", "publisher": "Wiley", "abstract": "Abstract In this article, we present some drone arc routing problems (Drone ARPs) and study their relation with well‐known postman ARPs. Applications for Drone ARPs include traffic monitoring by flying over roadways, infrastructure inspection such as by flying along power transmission lines, pipelines or fences, and surveillance along linear features such as coastlines or territorial borders. Unlike the postmen in traditional ARPs, drones can travel directly between any two points in the plane without following the edges of the network. As a consequence, a drone route may service only part of an edge, with multiple routes being used to cover the entire edge. Thus the Drone ARPs are continuous optimization problems with an infinite number of feasible solutions. In order to solve them as a discrete optimization problem, we approximate each curve in the plane by a polygonal chain, thus allowing the vehicle to enter and leave each curve only at the points of the polygonal chain. If the capacity of the vehicles is unlimited, the resulting problem is a rural postman problem (RPP). We propose an algorithm that iteratively solves RPP instances with an increasing number of points of the polygonal chain and present results on several sets of instances. We also briefly discuss the case in which the drones have limited capacity and several drones are needed.", "keywords": [ "Drone", "Arc routing", "Computer science", "Routing (electronic design automation)", "Enhanced Data Rates for GSM Evolution", "Relation (database)", "Mathematical optimization", "Plane (geometry)", "Topology (electrical circuits)", "Mathematics", "Computer network", "Artificial intelligence" ], "cited_by_count": 68, "is_retracted": false, "is_paratext": false, "open_access_url": "https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/net.21858" }, { "id": "https://openalex.org/W3134157502", "doi": "10.1016/j.trc.2022.103645", "title": "Nested vehicle routing problem: Optimizing drone-truck surveillance operations", "year": 2022, "publication_date": "2022-04-12", "type": "article", "language": "en", "authors": [ "Fanruiqi Zeng", "Zaiwei Chen", "John-Paul Clarke", "David M. Goldsman" ], "first_author": "Fanruiqi Zeng", "venue": "Transportation Research Part C Emerging Technologies", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Computer science", "Heuristic", "Rendezvous", "Routing (electronic design automation)", "Vehicle routing problem", "Integer programming", "Mathematical optimization", "Truck", "Linear programming", "Linearization", "Mathematics" ], "cited_by_count": 52, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.trc.2022.103645" }, { "id": "https://openalex.org/W2890722280", "doi": "10.1016/j.ijpe.2019.01.010", "title": "Truck-drone hybrid delivery routing: Payload-energy dependency and No-Fly zones", "year": 2019, "publication_date": "2019-01-09", "type": "article", "language": "en", "authors": [ "Ho Young Jeong", "Byung Duk Song", "Seokcheon Lee" ], "first_author": "Ho Young Jeong", "venue": "International Journal of Production Economics", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Payload (computing)", "Truck", "Computer science", "Routing (electronic design automation)", "Heuristic", "Energy consumption", "Aviation", "Automotive engineering", "Simulation", "Aerospace engineering", "Computer network" ], "cited_by_count": 351, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.ijpe.2019.01.010" }, { "id": "https://openalex.org/W2898326709", "doi": "10.1002/net.21855", "title": "Same‐day delivery with heterogeneous fleets of drones and vehicles", "year": 2018, "publication_date": "2018-10-25", "type": "article", "language": "en", "authors": [ "Marlin Wolf Ulmer", "Barrett W. Thomas" ], "first_author": "Marlin Wolf Ulmer", "venue": "Networks", "publisher": "Wiley", "abstract": "In this paper, we analyze how drones can be combined with regular delivery vehicles to improve same‐day delivery performance. To this end, we present a dynamic vehicle routing problem with heterogeneous fleets. Customers order goods over the course of the day. These goods are delivered either by a drone or by a regular transportation vehicle within a delivery deadline. Drones are faster, but have a limited capacity as well as require charging after use. In the same‐day context, vehicle capacity is not a constraint, but vehicles are slow due to urban traffic. To decide whether an order is delivered by a drone or by a vehicle, we present a policy function approximation based on geographical districting. Our computational study reveals two major implications. First, geographical districting is highly effective increasing the expected number of same‐day deliveries. Second, a combination of drone and vehicle fleets may significantly reduce the required delivery resources.", "keywords": [ "Drone", "Context (archaeology)", "Vehicle routing problem", "Computer science", "Constraint (computer-aided design)", "Order (exchange)", "Routing (electronic design automation)", "Operations research", "Function (biology)", "Transport engineering", "Business", "Computer network" ], "cited_by_count": 239, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1002/net.21855" }, { "id": "https://openalex.org/W2969952159", "doi": "10.3390/drones3030066", "title": "A Survey of Recent Extended Variants of the Traveling Salesman and Vehicle Routing Problems for Unmanned Aerial Vehicles", "year": 2019, "publication_date": "2019-08-24", "type": "article", "language": "en", "authors": [ "Ines Khoufi", "Anis Laouiti", "Cédric Adjih" ], "first_author": "Ines Khoufi", "venue": "Drones", "publisher": "Multidisciplinary Digital Publishing Institute", "abstract": "The use of Unmanned Aerial Vehicles (UAVs) is rapidly growing in popularity. Initially introduced for military purposes, over the past few years, UAVs and related technologies have successfully transitioned to a whole new range of civilian applications such as delivery, logistics, surveillance, entertainment, and so forth. They have opened new possibilities such as allowing operation in otherwise difficult or hazardous areas, for instance. For all applications, one foremost concern is the selection of the paths and trajectories of UAVs, and at the same time, UAVs control comes with many challenges, as they have limited energy, limited load capacity and are vulnerable to difficult weather conditions. Generally, efficiently operating a drone can be mathematically formalized as a path optimization problem under some constraints. This shares some commonalities with similar problems that have been extensively studied in the context of urban vehicles and it is only natural that the recent literature has extended the latter to fit aerial vehicle constraints. The knowledge of such problems, their formulation, the resolution methods proposed—through the variants induced specifically by UAVs features—are of interest for practitioners for any UAV application. Hence, in this study, we propose a review of existing literature devoted to such UAV path optimization problems, focusing specifically on the sub-class of problems that consider the mobility on a macroscopic scale. These are related to the two existing general classic ones—the Traveling Salesman Problem and the Vehicle Routing Problem. We analyze the recent literature that adapted the problems to the UAV context, provide an extensive classification and taxonomy of their problems and their formulation and also give a synthetic overview of the resolution techniques, performance metrics and obtained numerical results.", "keywords": [ "Travelling salesman problem", "Drone", "Computer science", "Context (archaeology)", "Vehicle routing problem", "Routing (electronic design automation)", "Class (philosophy)", "Range (aeronautics)", "Operations research", "Popularity", "Artificial intelligence", "Engineering" ], "cited_by_count": 165, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.mdpi.com/2504-446X/3/3/66/pdf?version=1567042939" }, { "id": "https://openalex.org/W4386295464", "doi": "10.1016/j.cie.2023.109563", "title": "A humanitarian vehicle routing problem synchronized with drones in time-varying weather conditions", "year": 2023, "publication_date": "2023-08-30", "type": "article", "language": "en", "authors": [ "Yichen Lu", "Jun Yang", "Chao Yang" ], "first_author": "Yichen Lu", "venue": "Computers & Industrial Engineering", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Computer science", "Duration (music)", "Routing (electronic design automation)", "Truck", "Operations research", "Genetic algorithm", "Resilience (materials science)", "Set (abstract data type)", "Extreme weather", "Mathematical optimization", "Engineering" ], "cited_by_count": 54, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.cie.2023.109563" }, { "id": "https://openalex.org/W3041611419", "doi": "10.1016/j.trb.2020.06.011", "title": "Drone routing with energy function: Formulation and exact algorithm", "year": 2020, "publication_date": "2020-07-11", "type": "article", "language": "en", "authors": [ "Chun Cheng", "Yossiri Adulyasak", "Louis-Martin Rousseau" ], "first_author": "Chun Cheng", "venue": "Transportation Research Part B Methodological", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Mathematical optimization", "Energy consumption", "Computer science", "Drone", "Routing (electronic design automation)", "Subgradient method", "Nonlinear system", "Benchmark (surveying)", "Energy (signal processing)", "Mathematics", "Engineering" ], "cited_by_count": 232, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.trb.2020.06.011" }, { "id": "https://openalex.org/W4283518432", "doi": "10.1016/j.trc.2022.103763", "title": "Heterogeneous multi-drone routing problem for parcel delivery", "year": 2022, "publication_date": "2022-06-25", "type": "article", "language": "en", "authors": [ "Xupeng Wen", "Guohua Wu" ], "first_author": "Xupeng Wen", "venue": "Transportation Research Part C Emerging Technologies", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Payload (computing)", "Computer science", "Real-time computing", "Computer network" ], "cited_by_count": 88, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.trc.2022.103763" }, { "id": "https://openalex.org/W4321457416", "doi": "10.1016/j.ejor.2023.02.030", "title": "A branch-and-price-and-cut algorithm for the truck-based drone delivery routing problem with time windows", "year": 2023, "publication_date": "2023-02-21", "type": "article", "language": "en", "authors": [ "Yunqiang Yin", "Dongwei Li", "Dujuan Wang", "Joshua Ignatius", "T.C.E. Cheng", "Sutong Wang" ], "first_author": "Yunqiang Yin", "venue": "European Journal of Operational Research", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Truck", "Drone", "Computer science", "Vehicle routing problem", "Leverage (statistics)", "Routing (electronic design automation)", "Node (physics)", "Operations research", "Mathematical optimization", "Computer network", "Engineering", "Mathematics" ], "cited_by_count": 139, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.ejor.2023.02.030" }, { "id": "https://openalex.org/W3023508804", "doi": "10.1177/1729881420920031", "title": "Metaheuristic algorithm for solving the multi-objective vehicle routing problem with time window and drones", "year": 2020, "publication_date": "2020-03-01", "type": "article", "language": "en", "authors": [ "Yunqi Han", "Junqing Li", "Zhengmin Liu", "Chuang Liu", "Jie Tian" ], "first_author": "Yunqi Han", "venue": "International Journal of Advanced Robotic Systems", "publisher": "SAGE Publishing", "abstract": "In some special rescue scenarios, the needed goods should be transported by drones because of the landform. Therefore, in this study, we investigate a multi-objective vehicle routing problem with time window and drone transportation constraints. The vehicles are used to transport the goods and drones to customer locations, while the drones are used to transport goods vertically and timely to the customer. Three types of objectives are considered simultaneously, including minimization of the total energy consumption of the trucks, total energy consumption of the drones, and the total number of trucks. An improved artificial bee colony algorithm is designed to solve the problem. In the proposed algorithm, each solution is represented by a two-dimensional vector, and the initialization method based on the Push-Forward Insertion Heuristic is embedded. To enhance the exploitation abilities, an improved employed heuristic is developed to perform detailed local search. Meanwhile, a novel scout bee strategy is presented to improve the global search abilities of the proposed algorithm. Several instances extended from the Solomon instances are used to test the performance of the proposed improved artificial bee colony algorithm. Experimental comparisons with the other efficient algorithms in the literature verify the competitive performance of the proposed algorithm.", "keywords": [ "Computer science", "Drone", "Heuristic", "Initialization", "Truck", "Algorithm", "Energy consumption", "Mathematical optimization", "Vehicle routing problem", "Artificial bee colony algorithm", "Minification", "Routing (electronic design automation)" ], "cited_by_count": 56, "is_retracted": false, "is_paratext": false, "open_access_url": "https://journals.sagepub.com/doi/pdf/10.1177/1729881420920031" }, { "id": "https://openalex.org/W4382656934", "doi": "10.1016/j.trb.2023.102781", "title": "Robust vehicle routing with drones under uncertain demands and truck travel times in humanitarian logistics", "year": 2023, "publication_date": "2023-06-30", "type": "article", "language": "en", "authors": [ "Yunqiang Yin", "Yongjian Yang", "Yugang Yu", "Dujuan Wang", "T.C.E. Cheng" ], "first_author": "Yunqiang Yin", "venue": "Transportation Research Part B Methodological", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Truck", "Drone", "Robustness (evolution)", "Vehicle routing problem", "Computer science", "Operations research", "Routing (electronic design automation)", "Robust optimization", "Resource (disambiguation)", "Transport engineering", "Mathematical optimization", "Engineering" ], "cited_by_count": 119, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.trb.2023.102781" }, { "id": "https://openalex.org/W4382584167", "doi": "10.1016/j.aei.2023.102071", "title": "The time-dependent electric vehicle routing problem with drone and synchronized mobile battery swapping", "year": 2023, "publication_date": "2023-06-28", "type": "article", "language": "en", "authors": [ "Xiaoxue Ren", "Houming Fan", "Houming Fan", "Ming-Xin Bao", "Hao Fan", "Hao Fan" ], "first_author": "Xiaoxue Ren", "venue": "Advanced Engineering Informatics", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Battery (electricity)", "Lagrangian relaxation", "Computer science", "Charging station", "Electric vehicle", "Energy consumption", "Real-time computing", "Engineering", "Automotive engineering", "Mathematical optimization", "Electrical engineering" ], "cited_by_count": 51, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.aei.2023.102071" }, { "id": "https://openalex.org/W4394783593", "doi": "10.1016/j.trc.2024.104611", "title": "Dynamic vehicle routing problem with drone resupply for same-day delivery", "year": 2024, "publication_date": "2024-04-13", "type": "article", "language": "en", "authors": [ "Juan C. Pina-Pardo", "Daniel F. Silva", "Alice E. Smith", "Ricardo A. Gatica" ], "first_author": "Juan C. Pina-Pardo", "venue": "Transportation Research Part C Emerging Technologies", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Markov decision process", "Truck", "Operations research", "Vehicle routing problem", "Computer science", "Service (business)", "Routing (electronic design automation)", "Process (computing)", "Markov chain", "Partially observable Markov decision process", "Real-time computing" ], "cited_by_count": 43, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.trc.2024.104611" }, { "id": "https://openalex.org/W4224309848", "doi": "10.1007/s40305-021-00383-4", "title": "A Survey of Truck–Drone Routing Problem: Literature Review and Research Prospects", "year": 2022, "publication_date": "2022-04-06", "type": "article", "language": "en", "authors": [ "Yijing Liang", "Zhixing Luo" ], "first_author": "Yijing Liang", "venue": "Journal of the Operations Research Society of China", "publisher": "Springer Science+Business Media", "abstract": null, "keywords": [ "Drone", "Truck", "Vehicle routing problem", "Travelling salesman problem", "Routing (electronic design automation)", "Computer science", "Operations research", "Transport engineering", "Engineering", "Computer network" ], "cited_by_count": 90, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1007/s40305-021-00383-4" }, { "id": "https://openalex.org/W4388766824", "doi": "10.1016/j.eswa.2023.122483", "title": "Multi-Depot Vehicle Routing Problem with Drones: Mathematical formulation, solution algorithm and experiments", "year": 2023, "publication_date": "2023-11-17", "type": "article", "language": "en", "authors": [ "Petr Stodola", "Libor Kutěj" ], "first_author": "Petr Stodola", "venue": "Expert Systems with Applications", "publisher": "Elsevier BV", "abstract": "The use of Unmanned Aerial Vehicles (UAVs) is expected to grow rapidly in the coming years, driven by technological advancements, cost-effectiveness, and the increasing demand for faster and more efficient delivery solutions. This article deals with the mathematical formulation of the Multi-Depot Vehicle Routing Problem with Drones (MDVRP-D), whereby a set of heterogeneous trucks, each paired with a UAV, are located in different depots. Both types of vehicles deliver goods to customers; UAVs are dispatched from trucks while en route to make the last-mile delivery. A metaheuristic algorithm based on the Ant Colony Optimization (ACO) principle is proposed as the solution. This algorithm has been adapted for this newly proposed problem; the novel mechanics include the probabilistic decision to dispatch an UAV, the selection of a customer to be served, and local search optimization. Extensive computational experiments are performed to verify the proposed algorithm. First, its performance is compared with Adaptive Large Neighborhood Search (ALNS) metaheuristics on a set of Vehicle Routing Problem with Drones (VRP-D) benchmarks. A set of various benchmark instances are subsequently proposed for the newly formulated MDVRP-D (differing in complexity and graph topology). Finally, the behavior of the proposed algorithm is thoroughly analyzed, especially in respect of features connected with UAVs. The findings presented in this article provide valuable contributions to the NP-hard models related to the Travelling Salesman Problem (TSP) and to the very popular ACO-based algorithms.", "keywords": [ "Vehicle routing problem", "Computer science", "Travelling salesman problem", "Ant colony optimization algorithms", "Metaheuristic", "Mathematical optimization", "Drone", "Benchmark (surveying)", "Truck", "Set (abstract data type)", "Algorithm", "Probabilistic logic" ], "cited_by_count": 47, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.eswa.2023.122483" }, { "id": "https://openalex.org/W4210509311", "doi": "10.1016/j.eswa.2022.116604", "title": "A multi-agent approach to the truck multi-drone routing problem", "year": 2022, "publication_date": "2022-01-31", "type": "article", "language": "en", "authors": [ "Jose Miguel Leon-Blanco", "P.L. Gonzalez-R", "José Luis Andrade-Pineda", "David Canca", "M. Calle" ], "first_author": "Jose Miguel Leon-Blanco", "venue": "Expert Systems with Applications", "publisher": "Elsevier BV", "abstract": "In this work, we address the Truck-multi-Drone Team Logistics Problem (TmDTL), devoted to visit a set of points with a truck helped by a team of unmanned aerial vehicles (UAVs) or drones in the minimum time, starting at a certain location and ending at a different one. It is an enhanced version of the multiple Flying Sidekicks Traveling Salesman Problem (mFSTSP) presented in Murray and Raj (2020) wherein drones are allowed to visit several customers per trip. In order to cope with large instances of the complex TmDTL, we have developed a novel agent-based method where agents represent the points that are going to be visited by vehicles. Agents evolve by means of movement inside a grid (locations vs. vehicles) according to a set of rules in the seek of better objective function values. Each agent needs to explore only a fraction of the complete problem, sharing its progress with the rest of the agents which are coordinated by one central agent which helps to maintain an asynchronous memory of solutions – e.g. on the control of the mechanism to escape from local minima. Our agent-based approach is firstly tested using the largest instances of the single TDTL problem reported in the literature, which additionally serves as upper bounds to the TmDTL problem. Secondly, we have solved instances up to 500 locations with up to 6 drones in the fleet. Thirdly, we have tested the behavior of our approach in 500 locations problems with up to 8 drones in order to test the fleet size sensitivity. Our experiments demonstrate the ability of the proposed agent-based system to obtain good quality solutions for complex optimization problems that arise. Further, the abstraction in solutions coding applied makes the agent-based approach scalable and flexible enough to be applied to a wide range of other optimization problems.", "keywords": [ "Drone", "Travelling salesman problem", "Computer science", "Truck", "Set (abstract data type)", "Maxima and minima", "Grid", "Order (exchange)", "Asynchronous communication", "Operations research", "Function (biology)", "Computer network" ], "cited_by_count": 77, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.sciencedirect.com/science/article/pii/S0957417422000975/pdf" }, { "id": "https://openalex.org/W2605251097", "doi": "10.1007/s10846-017-0548-z", "title": "Drone-Aided Healthcare Services for Patients with Chronic Diseases in Rural Areas", "year": 2017, "publication_date": "2017-04-04", "type": "article", "language": "en", "authors": [ "Seonjin Kim", "Gino J. Lim", "Jaeyoung Cho", "Murray J. Côté" ], "first_author": "Seonjin Kim", "venue": "Journal of Intelligent & Robotic Systems", "publisher": "Springer Science+Business Media", "abstract": null, "keywords": [ "Drone", "Preprocessor", "Computer science", "Health care", "Pickup", "Lagrangian relaxation", "Service (business)", "Healthcare service", "Routing (electronic design automation)", "Work (physics)", "Standardization", "Operations research" ], "cited_by_count": 235, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1007/s10846-017-0548-z" }, { "id": "https://openalex.org/W3011794261", "doi": "10.1016/j.trc.2020.02.030", "title": "Truck-drone team logistics: A heuristic approach to multi-drop route planning", "year": 2020, "publication_date": "2020-03-13", "type": "article", "language": "en", "authors": [ "Pedro Luis González Rodríguez", "David Canca", "José Luis Andrade-Pineda", "Marcos Calle Suárez", "Jose Miguel Leon-Blanco" ], "first_author": "Pedro Luis González Rodríguez", "venue": "Transportation Research Part C Emerging Technologies", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Computer science", "Vehicle routing problem", "Routing (electronic design automation)", "Simulated annealing", "Truck", "Heuristic", "Operations research", "Mathematical optimization", "Engineering", "Artificial intelligence", "Algorithm" ], "cited_by_count": 247, "is_retracted": false, "is_paratext": false, "open_access_url": "https://hdl.handle.net/11441/167149" }, { "id": "https://openalex.org/W3180394329", "doi": "10.1016/j.cor.2021.105445", "title": "Coordinating drones with mothership vehicles: The mothership and drone routing problem with graphs", "year": 2021, "publication_date": "2021-07-10", "type": "article", "language": "en", "authors": [ "Lavinia Amorosi", "Justo Puerto", "Carlos Valverde" ], "first_author": "Lavinia Amorosi", "venue": "Computers & Operations Research", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Computer science", "Testbed", "Mathematical optimization", "Graph", "Vehicle routing problem", "Routing (electronic design automation)", "Integer programming", "Algorithm", "Mathematics", "Theoretical computer science", "Computer network" ], "cited_by_count": 59, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.cor.2021.105445" }, { "id": "https://openalex.org/W3176761908", "doi": "10.1109/tsmc.2021.3088776", "title": "Unmanned-Aerial-Vehicle Routing Problem With Mobile Charging Stations for Assisting Search and Rescue Missions in Postdisaster Scenarios", "year": 2021, "publication_date": "2021-06-22", "type": "article", "language": "en", "authors": [ "Roberto Gomes Ribeiro", "Luciano Perdig�ão Cota", "Thiago A. M. Euzébio", "Jaime Arturo Ramírez", "Frederico Gadelha Guimarães" ], "first_author": "Roberto Gomes Ribeiro", "venue": "IEEE Transactions on Systems Man and Cybernetics Systems", "publisher": "Institute of Electrical and Electronics Engineers", "abstract": "Recent technological breakthroughs have allowed unmanned aerial vehicles (UAVs) to be utilized in a broad range of new operations. Among these various applications, herein, we focus on the use of UAVs for search and rescue missions in emergency and postdisaster scenarios. In this context, self-charging technologies for drones create new challenges in the routing of UAVs with charging stations. We present a variant of the vehicle routing problem (VRP) to address the integrated use of UAVs and mobile charging stations and define the VRP with synchronized networks (VRPSN), a new class of VRPs involving the routing of UAVs whose recharge platforms can travel to different locations during an operation. This leads to two networks within the VRP that must be integrated and synchronized. This research develops a mixed-integer linear program model for the VRPSN that considers the use of UAVs and mobile charging stations in a synchronized manner. To overcome the computational limits of the MILP model, this research presents a construct-and-adjust heuristic method integrated with a genetic algorithm. As a numerical example, we test the proposed model on the Córrego do Feijão Mine located in Minas Gerais, Brazil, where a dam recently collapsed, killing many workers. Numerical tests show that the new methodology is an attractive planning method for providing efficient and rapid responses in search and rescue missions.", "keywords": [ "Search and rescue", "Vehicle routing problem", "Routing (electronic design automation)", "Drone", "Computer science", "Heuristic", "Context (archaeology)", "Genetic algorithm", "Real-time computing", "Computer network", "Geography", "Robot" ], "cited_by_count": 145, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1109/tsmc.2021.3088776" }, { "id": "https://openalex.org/W3037622630", "doi": "10.3390/app10134504", "title": "Unmanned Aerial Vehicle Routing Problems: A Literature Review", "year": 2020, "publication_date": "2020-06-29", "type": "article", "language": "en", "authors": [ "Amila Thibbotuwawa", "Grzegorz Bocewicz", "Peter Nielsen", "Zbigniew Antoni Banaszak" ], "first_author": "Amila Thibbotuwawa", "venue": "Applied Sciences", "publisher": "Multidisciplinary Digital Publishing Institute", "abstract": "Unmanned aerial vehicle (UAV) routing is transitioning from an emerging topic to a growing research area as the 3D flexible utilization of airspace, promogulated by UAVs, is a potential game changer in solving the urban air mobility challenge by allowing to reshape transportation and logistics in the future. This has revealed a need to classify different types of research and examine the general characteristics of the research area. This research aims to assist in identifying the main topics and emerging research streams and provides a published overview of the current state and contributions to the area of the UAV routing problem (UAVRP) and a general categorization of the vehicle routing problem (VRP) followed by a UAVRP classification with a graphical taxonomy based on the analysis of UAVRP current status. To achieve this, an analysis of the existing research contributions promulgated in this domain is conducted. This analysis is used to identify the current state of UAVRP and the gaps related to the UAVs’ flight dynamics and weather conditions, which significantly influence the fuel consumption of the UAV when modeling the UAVRP.", "keywords": [ "Computer science" ], "cited_by_count": 88, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.3390/app10134504" }, { "id": "https://openalex.org/W2316555489", "doi": "10.2514/6.2007-2839", "title": "UAV Scheduling via the Vehicle Routing Problem with Time Windows", "year": 2007, "publication_date": "2007-05-07", "type": "conference-paper", "language": "en", "authors": [ "Amanda Weinstein", "Corey J. Schumacher" ], "first_author": "Amanda Weinstein", "venue": "AIAA Infotech@Aerospace 2007 Conference and Exhibit", "publisher": null, "abstract": "In an urban environment, multiple small unmanned aerial vehicles (UAVs) may be utilized to locate, surveil, or attack various targets. Whatever the task, the air vehicles must cooperate by efficiently communicating with each other and optimally assigning each UAV to the appropriate task at the appropriate target and at the appropriate time. In this paper, a vehicle assignment algorithm is developed using a mixed integer linear program (MILP) to find the global optimal scheduling solution. The MILP can accommodate both binary and continuous decision variables as well as a variety of constraints and objective functions; however, the NP-hard nature of the problem implies a dramatic increase in the computing complexity as the number of variables and constraints increase. This formulation accounts for an assortment of scenarios focused on the military necessity for precise intelligence, surveillance, and reconnaissance (ISR) by modifying the vehicle routing problem with time windows (VRPTW) formulation. The VRPTW is a type of capacitated vehicle routing problem which optimally assigns a designated number of delivery vehicles originating at a single depot to a known number of customers. Specifically, the VRPTW and network flow techniques account for various scenarios as well as operator imposed timing constraints such as precedence constraints. For example, certain targets may take precedence or require simultaneous arrival times where the targets are first hierarchically clustered according to their proximity to each other. Thus, this paper also focuses on methods of clustering targets and implements this information into the MILP to optimally assign UAVs to targets. Clustering targets that are near enough to alert each other of an attack will allow UAVs to recognize this potential and hence surveil these targets simultaneously to avoid early detection. This technique will also prevent targets from being further camouflaged or moved once alerted to a nearby attack. Finally, this paper will directly compare the computation times and solutions for the min makespan objective, the minimum total time objective, and the total distance minimization.", "keywords": [ "Vehicle routing problem", "Computer science", "Scheduling (production processes)", "Cluster analysis", "Routing (electronic design automation)", "Mathematical optimization", "Task (project management)", "Job shop scheduling", "Integer programming", "Linear programming", "Distributed computing", "Artificial intelligence" ], "cited_by_count": 59, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.2514/6.2007-2839" }, { "id": "https://openalex.org/W2053083032", "doi": "10.1016/j.apm.2013.07.002", "title": "A multi-objective approach for unmanned aerial vehicle routing problem with soft time windows constraints", "year": 2013, "publication_date": "2013-07-19", "type": "article", "language": "en", "authors": [ "Francesca Guerriero", "Rosario Surace", "Valéria Loscrì", "Enrico Natalizio" ], "first_author": "Francesca Guerriero", "venue": "Applied Mathematical Modelling", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Computer science", "Scheduling (production processes)", "Robotics", "Vehicle routing problem", "Drone", "Point (geometry)", "Artificial intelligence", "Real-time computing", "Time horizon", "Travelling salesman problem", "Distributed computing", "Routing (electronic design automation)" ], "cited_by_count": 139, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.sciencedirect.com/science/article/pii/S0307904X13004460/pdf" }, { "id": "https://openalex.org/W3129292331", "doi": "10.1016/j.ejor.2021.02.022", "title": "Ground-vehicle and unmanned-aerial-vehicle routing problems from two-echelon scheme perspective: A review", "year": 2021, "publication_date": "2021-02-16", "type": "article", "language": "en", "authors": [ "Hongqi Li", "Jun Chen", "Feilong Wang", "Ming Bai" ], "first_author": "Hongqi Li", "venue": "European Journal of Operational Research", "publisher": "Elsevier BV", "abstract": "More and more studies have aimed to optimize the ground vehicle (GV) and unmanned aerial vehicle (UAV) system in which GVs function as mobile satellites and UAVs are dispatched from GVs for last-mile deliveries. From the two-echelon scheme perspective, GV routes originating at the depot are on one echelon, and UAV routes originating at satellites are on the other echelon. A change in a GV route may affect some UAV routes, which indicates the satellite synchronization. In the past decade, the optimization of vehicle routes in two-echelon networks has attracted increasing attention in the operations research community. We classify routing problems of two-echelon networks based on the modeling mechanism connecting the two echelons. Different formulations for describing connection mechanisms of the two-echelon scheme, especially constraints on capacitated satellites, satellite synchronization, vehicle coupling/decoupling at satellites, etc., are briefly introduced. There are several modeling challenges of optimizing delivery routes for a fleet of GV–UAV combinations that include new connection mechanisms between the two echelons. Some important variants, especially those involving mobile satellite synchronization, and GV–UAV flexibly coupling/decoupling, require new mathematical formulations and algorithms catering to more general and practical situations.", "keywords": [ "Computer science", "Decoupling (probability)", "Synchronization (alternating current)", "Scheme (mathematics)", "Perspective (graphical)", "Real-time computing", "Operations research", "Distributed computing", "Computer network", "Engineering", "Artificial intelligence", "Control engineering" ], "cited_by_count": 147, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.sciencedirect.com/science/article/pii/S0377221721001156/pdf" }, { "id": "https://openalex.org/W2110579257", "doi": "10.1109/cdc.2008.4739366", "title": "Vehicle Routing Problem with Metric Temporal Logic Specifications", "year": 2008, "publication_date": "2008-01-01", "type": "conference-paper", "language": "en", "authors": [ "Sertaç Karaman", "Emilio Frazzoli" ], "first_author": "Sertaç Karaman", "venue": null, "publisher": null, "abstract": "This paper proposes a novel version of the vehicle routing problem (VRP). Instead of servicing all the customers, feasible solutions of the VRP instance are forced to satisfy a set of complex high-level tasks given as a metric temporal logic (MTL) specification, which allows complex quantitative timing constraints to be incorporated into the problem. For the resulting vehicle routing problem with metric temporal logic specifications (VRPMTL), a mixed-integer linear programming (MILP) based algorithm is provided that solves the problem to optimality. Examples for optimal multi-UAV mission planning are provided where MTL is used as a high level language to specify complex mission tasks.", "keywords": [ "Metric (unit)", "Integer programming", "Temporal logic", "Computer science", "Routing (electronic design automation)", "Set (abstract data type)", "Vehicle routing problem", "Linear temporal logic", "Mathematical optimization", "Linear programming", "Theoretical computer science", "Algorithm" ], "cited_by_count": 88, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1109/cdc.2008.4739366" }, { "id": "https://openalex.org/W3006984451", "doi": "10.1016/j.promfg.2020.01.338", "title": "Vehicle Routing Problem with Drones for Last Mile Delivery", "year": 2019, "publication_date": "2019-01-01", "type": "article", "language": "en", "authors": [ "Patchara Kitjacharoenchai", "Seokcheon Lee" ], "first_author": "Patchara Kitjacharoenchai", "venue": "Procedia Manufacturing", "publisher": "Elsevier BV", "abstract": "E-commerce and retail companies are seeking ways to cut delivery times and costs by exploring opportunities to use drones for making last mile delivery deliveries. In recent years, drone routing and scheduling has become a highly active area of research. This research addresses the delivery concept of a truck-drone combination along with the idea of allowing autonomous drones to fly from delivery trucks, make deliveries, and fly to delivery trucks nearby. The proposed model considers the synchronized truck drone routing model by allowing multiple drones to fly from a truck, serve customers and immediately return to the same truck for the battery swap and package retrieval. The model also takes into account both trucks and drones capacities to ensure that the amount of loads carried by each drone must not exceed its capacity and the total amount of loads in each delivery route must be less than truck’s capacity. The goal is to find the optimal routes of both trucks and drones which minimize the total arrival time of both trucks and drones at the depot after completing the deliveries. The problem can be solved by the formulated mixed integer programming (MIP) for the small size problem. Numerical results in the case study and benchmark problems are presented to show the delivery time improvement over the delivery time from other delivery types.", "keywords": [ "Drone", "Truck", "Routing (electronic design automation)", "Swap (finance)", "Computer science", "Scheduling (production processes)", "Integer programming", "Vehicle routing problem", "Transport engineering", "Mile", "Last mile (transportation)", "Operations research" ], "cited_by_count": 28, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.sciencedirect.com/science/article/pii/S2351978920304054/pdf" }, { "id": "https://openalex.org/W2160179157", "doi": "10.1109/case.2011.6042503", "title": "Multi-robot persistent surveillance planning as a Vehicle Routing Problem", "year": 2011, "publication_date": "2011-08-01", "type": "conference-paper", "language": "en", "authors": [ "Ethan Stump", "Nathan Michael" ], "first_author": "Ethan Stump", "venue": null, "publisher": null, "abstract": "We consider a persistent surveillance problem as one of finding sequences of visits to discrete sites in a periodic fashion, cast it as a Vehicle Routing Problem with Time Windows, and solve it using exact methods developed in the operations research community. The work is a successful application of recent advances in combinatorial optimization for logistics problems but in the context of a robotics application taking place in continuous time. We apply these methods to the task of surveying a building using multiple UAVs and perform a long-term simulation developed to mimic a hardware testbed currently under development.", "keywords": [ "Testbed", "Vehicle routing problem", "Robotics", "Computer science", "Task (project management)", "Context (archaeology)", "Routing (electronic design automation)", "Robot", "Artificial intelligence", "Real-time computing", "Systems engineering", "Embedded system" ], "cited_by_count": 96, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1109/case.2011.6042503" }, { "id": "https://openalex.org/W4404820955", "doi": "10.1287/trsc.2024.0544", "title": "Exact Solution of the Vehicle Routing Problem with Drones", "year": 2024, "publication_date": "2024-11-28", "type": "article", "language": "en", "authors": [ "Jeanette Schmidt", "Christian Tilk", "Stefan Irnich" ], "first_author": "Jeanette Schmidt", "venue": "Transportation Science", "publisher": "Institute for Operations Research and the Management Sciences", "abstract": "The vehicle routing problem with drones (VRP-D) that we consider is an extension of the capacitated vehicle routing problem in which the fleet consists of trucks equipped with one drone each. A truck and its drone can either move together or separately. A truck can release its drone at the depot or at a customer location and must pick it up later at another customer or the depot location. In this way, both trucks and drones deliver goods to customers working together as synchronized working units. A feasible route has to satisfy the capacity constraints of both the truck and the drone. A feasible solution to the VRP-D is a set of feasible routes such that each customer is served exactly once by either a truck or a drone. We investigate two standard objectives considered in the literature, that is, the minimization of the total routing cost and the sum of the routes’ durations. To solve the VRP-D exactly, we develop a branch-price-and-cut (BPC) algorithm. In particular, we present a new forward and implicit bidirectional labeling algorithm defined over an artificial network to solve the column-generation subproblems. The new bidirectional labeling algorithm substantially accelerates the solution process compared with its monodirectional counterpart. The time needed to solve the pricing problems is reduced by 55% on average when minimizing routing costs and by 30% when minimizing the sum of the routes’ durations. In further computational experiments, we analyze algorithmic components of the BPC algorithm, compare the cost and duration objectives, and highlight the impact of the drones’ speed on the structure of VRP-D solutions. For the routing-cost minimization objective, our BPC algorithm is able to solve several VRP-D instances with 50 vertices to proven optimality within one hour of computation time. The same instances with duration minimization are more difficult, and the BPC algorithm provides only heuristic solutions with an average gap not exceeding 3%. Funding: This work was supported by Deutsche Forschungsgemeinschaft [Project 418727865, Grant IR 122/10-1]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2024.0544 .", "keywords": [ "Drone", "Vehicle routing problem", "Routing (electronic design automation)", "Computer science", "Transport engineering", "Engineering", "Mathematical optimization", "Operations research", "Computer network", "Mathematics" ], "cited_by_count": 24, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1287/trsc.2024.0544" }, { "id": "https://openalex.org/W3200703255", "doi": "10.1016/j.ejor.2021.08.014", "title": "The parallel drone scheduling problem with multiple drones and vehicles", "year": 2021, "publication_date": "2021-09-20", "type": "article", "language": "en", "authors": [ "Raïssa G. Mbiadou Saleu", "Laurent Deroussi", "Dominique Feillet", "Nathalie Grangeon", "Alain Quilliot" ], "first_author": "Raïssa G. Mbiadou Saleu", "venue": "European Journal of Operational Research", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Travelling salesman problem", "Computer science", "Scheduling (production processes)", "Vehicle routing problem", "Metaheuristic", "Integer programming", "TRIPS architecture", "Operations research", "Job shop scheduling", "Mathematical optimization", "Routing (electronic design automation)" ], "cited_by_count": 100, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.ejor.2021.08.014" }, { "id": "https://openalex.org/W3197006902", "doi": "10.1111/itor.13052", "title": "The two‐echelon routing problem with truck and drones", "year": 2021, "publication_date": "2021-08-29", "type": "article", "language": "en", "authors": [ "Lam Vu", "Duy Manh Vu", "Minh Hoàng Hà", "Viet‐Phuong Nguyen" ], "first_author": "Lam Vu", "venue": "International Transactions in Operational Research", "publisher": "Wiley", "abstract": "Abstract In this paper, we study novel variants of the well‐known two‐echelon vehicle routing problem in which a truck works on the first echelon to transport parcels and a fleet of drones to intermediate depots while in the second echelon, the drones are used to deliver parcels from intermediate depots to customers. The objective is to minimize the completion time instead of the transportation cost as in classical two‐echelon vehicle routing problems. Depending on the context, a drone can be launched from the truck at an intermediate depot once (single‐trip drone) or several times (multiple‐trip drone). Mixed‐integer linear programming models are first proposed to formulate mathematically the problems and solve to optimality small‐sized instances. To handle larger instances, a metaheuristic based on the idea of greedy randomized adaptive search procedure is introduced. The main novel feature of our metaheuristic lies in the design of initial solution construction and local search operators, which can cover all the decision layers of the problems and run in using additional data structures. Experimental results obtained on instances of different contexts are reported and analyzed.", "keywords": [ "Drone", "Truck", "Vehicle routing problem", "Context (archaeology)", "Computer science", "Metaheuristic", "Mathematical optimization", "Integer programming", "Routing (electronic design automation)", "Linear programming", "Operations research", "Mathematics" ], "cited_by_count": 51, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1111/itor.13052" }, { "id": "https://openalex.org/W4407275006", "doi": "10.1016/j.trc.2025.105026", "title": "The multi-visit vehicle routing problem with multiple heterogeneous drones", "year": 2025, "publication_date": "2025-02-08", "type": "article", "language": "en", "authors": [ "Yu Jiang", "Mengmeng Liu", "Xibei Jia", "Qingwen Xue" ], "first_author": "Yu Jiang", "venue": "Transportation Research Part C Emerging Technologies", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Vehicle routing problem", "Routing (electronic design automation)", "Computer science", "Transport engineering", "Engineering", "Aeronautics", "Operations research", "Computer network", "Biology" ], "cited_by_count": 28, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.trc.2025.105026" }, { "id": "https://openalex.org/W2971057457", "doi": "10.1007/978-3-030-28377-3_42", "title": "An Integer Programming Model for the Capacitated Vehicle Routing Problem with Drones", "year": 2019, "publication_date": "2019-01-01", "type": "conference-paper", "language": "en", "authors": [ "Jarosław Wikarek", "Paweł Sitek", "Lukasz Zawarczynski" ], "first_author": "Jarosław Wikarek", "venue": "Lecture notes in computer science", "publisher": "Springer Science+Business Media", "abstract": null, "keywords": [ "Drone", "Computer science", "Truck", "Payload (computing)", "Integer programming", "Routing (electronic design automation)", "Operations research", "Mathematical optimization", "Linear programming", "Computer network", "Network packet", "Engineering" ], "cited_by_count": 27, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1007/978-3-030-28377-3_42" }, { "id": "https://openalex.org/W2792465044", "doi": "10.1016/j.eswa.2018.03.032", "title": "Optimal delivery routing with wider drone-delivery areas along a shorter truck-route", "year": 2018, "publication_date": "2018-03-19", "type": "article", "language": "en", "authors": [ "Yong Sik Chang", "Hyun Jung Lee" ], "first_author": "Yong Sik Chang", "venue": "Expert Systems with Applications", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Travelling salesman problem", "Cluster analysis", "Truck", "Computer science", "Routing (electronic design automation)", "Vehicle routing problem", "Mathematical optimization", "Operations research", "Computer network", "Mathematics", "Artificial intelligence" ], "cited_by_count": 237, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.eswa.2018.03.032" }, { "id": "https://openalex.org/W3134942149", "doi": "10.1016/j.ejor.2021.06.021", "title": "Deep Q-learning for same-day delivery with vehicles and drones", "year": 2021, "publication_date": "2021-06-17", "type": "article", "language": "en", "authors": [ "Xinwei Chen", "Marlin Wolf Ulmer", "Barrett W. Thomas" ], "first_author": "Xinwei Chen", "venue": "European Journal of Operational Research", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Exploit", "Computer science", "Benchmark (surveying)", "Service (business)", "Deep learning", "Operations research", "Artificial intelligence", "Computer security", "Engineering", "Business" ], "cited_by_count": 172, "is_retracted": false, "is_paratext": false, "open_access_url": "https://arxiv.org/pdf/1910.11901" }, { "id": "https://openalex.org/W4293433710", "doi": "10.1016/j.trc.2022.103791", "title": "Collaborative truck-and-drone delivery for inventory-routing problems", "year": 2022, "publication_date": "2022-08-29", "type": "article", "language": "en", "authors": [ "Waleed Najy", "Claudia Archetti", "Ali H. Diabat" ], "first_author": "Waleed Najy", "venue": "Transportation Research Part C Emerging Technologies", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Truck", "Travelling salesman problem", "Vehicle routing problem", "Computer science", "Supply chain", "Operations research", "Toll", "Routing (electronic design automation)", "Profit (economics)", "Last mile (transportation)", "Heuristic" ], "cited_by_count": 50, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.trc.2022.103791" }, { "id": "https://openalex.org/W2998354188", "doi": "10.1287/opre.2019.1874", "title": "An Exact Solution Framework for Multitrip Vehicle-Routing Problems with Time Windows", "year": 2020, "publication_date": "2020-01-01", "type": "article", "language": "en", "authors": [ "Rosario Paradiso", "Roberto Roberti", "Demetrio Laganà", "Wout E. H. Dullaert" ], "first_author": "Rosario Paradiso", "venue": "Operations Research", "publisher": "Institute for Operations Research and the Management Sciences", "abstract": "The need to reduce pollution and traffic in city centers requires the use of small vans, electric vehicles, and drones to distribute goods. Because of autonomy and capacity issues, these vehicles need to perform multiple trips from/to the depot during the day. The category of decision-making problems modeling such distribution problems are known as multitrip vehicle-routing problems (MTVRPs), which generalize the well-known vehicle-routing problem by allowing vehicles to perform multiple trips per day. Several MTVRPs are solved in the literature with different mathematical models and algorithms. In “An Exact Solution Framework for Multitrip Vehicle-Routing Problems with Time Windows,” R. Paradiso, R. Roberti, D. Laganà, and W. Dullaert propose a single algorithm that can solve, to optimality, the MTVRP with capacity and time windows constraints and four variants of this problem featuring additional operational constraints. The proposed framework significantly outperforms the state-of-the-art algorithms from the literature.", "keywords": [ "Vehicle routing problem", "TRIPS architecture", "Computer science", "Routing (electronic design automation)", "Mathematical optimization", "Operations research", "Drone", "State (computer science)", "Computer network", "Algorithm", "Mathematics" ], "cited_by_count": 84, "is_retracted": false, "is_paratext": false, "open_access_url": "https://hdl.handle.net/1871.1/e1a3027f-e7fb-4a58-b3f7-53a12df75b81" }, { "id": "https://openalex.org/W2615695563", "doi": "10.48550/arxiv.1705.06431", "title": "Vehicle Routing with Drones", "year": 2017, "publication_date": "2017-05-18", "type": "preprint", "language": "en", "authors": [ "Rami Daknama", "Elisabeth Kraus" ], "first_author": "Rami Daknama", "venue": "arXiv (Cornell University)", "publisher": "Cornell University", "abstract": "We introduce a package service model where trucks as well as drones can deliver packages. Drones can travel on trucks or fly; but while flying, drones can only carry one package at a time and have to return to a truck to charge after each delivery. We present a heuristic algorithm to solve the problem of finding a good schedule for all drones and trucks. The algorithm is based on two nested local searches, thus the definition of suitable neighbourhoods of solutions is crucial for the algorithm. Empirical tests show that our algorithm performs significantly better than a natural Greedy algorithm. Moreover, the savings compared to solutions without drones turn out to be substantial, suggesting that delivery systems might considerably benefit from using drones in addition to trucks.", "keywords": [ "Drone", "Routing (electronic design automation)", "Computer science", "Business", "Computer network", "Biology" ], "cited_by_count": 30, "is_retracted": false, "is_paratext": false, "open_access_url": "https://arxiv.org/pdf/1705.06431" }, { "id": "https://openalex.org/W3015829695", "doi": "10.1016/j.promfg.2020.02.043", "title": "Using drones for parcels delivery process", "year": 2020, "publication_date": "2020-01-01", "type": "article", "language": "en", "authors": [ "Luigi Di Puglia Pugliese", "Francesca Guerriero", "Giusy Macrina" ], "first_author": "Luigi Di Puglia Pugliese", "venue": "Procedia Manufacturing", "publisher": "Elsevier BV", "abstract": "Parcels delivery is the most expensive phase of the distribution logistics. Everyday, several vehicles, usually internal combustion engine vehicles, have to serve a high number of customers spatially distributed in an urban area. Their presence generates several negative externalities, such as, noise, congestion and pollutant emissions. Drones have become a valid alternative to support the delivery process and several big companies, such as, Amazon and DHL, have started to use them for parcels deliveries. On the one hand, drones drastically reduce negative externalities, allowing a more sustainable delivery process. On the other hand, several technical aspects must be carefully taken into account. In particular, they have a limited flight endurance and capacity. In addition, several restrictions related to safety and flight area must be considered. Indeed, not all countries allow the use of drones in the urban area. In this work, we provide a qualitative and quantitative analysis on benefits and drawbacks in using drones in the parcels delivery process. We analyze three different transportation systems with incremental use of drones for the delivery. In particular, we address the problem of delivering parcels without drone, known as vehicle routing problem, the problem in which the deliveries are performed by a fleet of drones starting from the central depot, and a hybrid transportation system where the classical vehicles are equipped with drones. In the latter case, the classical vehicles perform the deliveries and the drones can get in charge some deliveries. The drone takes off from the vehicle, carries out the delivery, and lands to the same vehicle at a randevouz-location. During the drone delivery, the classical vehicle continues its work. The three transportation systems are formalized via mathematical programming models. The solutions obtained by solving the models via a general-purpose solver are compared and insights on the use of drones in the urban area are provided.", "keywords": [ "Drone", "Process (computing)", "Externality", "Work (physics)", "Transport engineering", "Vehicle routing problem", "Computer science", "Routing (electronic design automation)", "Engineering", "Economics" ], "cited_by_count": 118, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.sciencedirect.com/science/article/pii/S2351978920305928/pdf" }, { "id": "https://openalex.org/W4404905432", "doi": "10.1016/j.ejor.2024.11.036", "title": "Truck–drone routing problem with stochastic demand", "year": 2024, "publication_date": "2024-12-02", "type": "article", "language": "en", "authors": [ "Feilong Wang", "Hongqi Li", "Hanxi Xiong" ], "first_author": "Feilong Wang", "venue": "European Journal of Operational Research", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Truck", "Vehicle routing problem", "Computer science", "Routing (electronic design automation)", "Mathematical optimization", "Operations research", "Mathematics", "Computer network", "Engineering", "Automotive engineering" ], "cited_by_count": 47, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.ejor.2024.11.036" }, { "id": "https://openalex.org/W3015958418", "doi": "10.1111/itor.12796", "title": "Agile optimization of a two‐echelon vehicle routing problem with pickup and delivery", "year": 2020, "publication_date": "2020-04-09", "type": "article", "language": "en", "authors": [ "Leandro do C. Martins", "Patrick Hirsch", "Angel Alejandro Juan" ], "first_author": "Leandro do C. Martins", "venue": "International Transactions in Operational Research", "publisher": "Wiley", "abstract": "Abstract In this paper, we consider a vehicle routing problem in which a fleet of homogeneous vehicles, initially located at a depot, has to satisfy customers' demands in a two‐echelon network: first, the vehicles have to visit intermediate nodes (e.g., a retail center or a consolidation center), where they deliver raw materials or bulk products and collect a number of processed items requested by the customers in their route; then, the vehicles proceed to complete their assigned routes, thus delivering the processed items to the final customers before returning to the depot. During this stage, vehicles might visit other intermediate nodes for reloading new items. In some real‐life scenarios, this problem needs to be solved in just a few seconds or even milliseconds, which leads to the concept of “agile optimization.” This might be the case in some rescue operations using drones in humanitarian logistics, where every second can be decisive to save lives. In order to deal with this real‐time two‐echelon vehicle routing problem with pickup and delivery, an original constructive heuristic is proposed. This heuristic is able to provide a feasible and reasonably good solution in just a few milliseconds. The constructive heuristic is extended into a biased‐randomized algorithm using a skewed probability distribution to modify its greedy behavior. This way, parallel runs of the algorithm are able to generate even better results without violating the real‐time constraint. Results show that the proposed methodology generates competitive results in milliseconds, being able to outperform other heuristics from the literature.", "keywords": [ "Computer science", "Heuristics", "Vehicle routing problem", "Heuristic", "Agile software development", "Mathematical optimization", "Routing (electronic design automation)", "Operations research", "Constructive", "Computer network", "Mathematics", "Process (computing)" ], "cited_by_count": 82, "is_retracted": false, "is_paratext": false, "open_access_url": "https://onlinelibrary.wiley.com/doi/pdfdirect/10.1111/itor.12796" }, { "id": "https://openalex.org/W4362635965", "doi": "10.1016/j.swevo.2023.101295", "title": "Solving electric vehicle–drone routing problem using memetic algorithm", "year": 2023, "publication_date": "2023-04-05", "type": "article", "language": "en", "authors": [ "Setyo Tri Windras Mara", "Ruhul Amin Sarker", "Daryl Essam", "Saber Mohammed Elsayed" ], "first_author": "Setyo Tri Windras Mara", "venue": "Swarm and Evolutionary Computation", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Memetic algorithm", "Computer science", "Routing (electronic design automation)", "Set (abstract data type)", "Electric vehicle", "Vehicle routing problem", "Integer programming", "Mathematical optimization", "Battery (electricity)", "Algorithm", "Local search (optimization)" ], "cited_by_count": 64, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.swevo.2023.101295" }, { "id": "https://openalex.org/W3089258357", "doi": "10.1002/net.21982", "title": "Future directions in drone routing research", "year": 2020, "publication_date": "2020-09-07", "type": "article", "language": "en", "authors": [ "Stefan Poikonen", "James F. Campbell" ], "first_author": "Stefan Poikonen", "venue": "Networks", "publisher": "Wiley", "abstract": "Abstract Optimization of routing problems using drones (unmanned aerial vehicles or UAVs) has become an important area of academic research. The purpose of this article is to look to the future and help stimulate drone routing research in directions we hope will prove interesting and fruitful. We discuss opportunities for better modeling of (1) drone capabilities for both existing drones and those likely to be used in the future, (2) constraints on drone performance and operations, (3) different objectives for various drone services, and (4) alternative delivery modes, as well as some areas for methodological advances and some possible new applications. While much of the research to date has leveraged existing TSP (traveling salesman problem), VRP (vehicle routing problem), and arc routing models, we look forward to new contributions from drone research that use better models of more realistic drone types and new drone applications.", "keywords": [ "Drone", "Routing (electronic design automation)", "Computer science", "Travelling salesman problem", "Vehicle routing problem", "Arc routing", "Operations research", "Computer network", "Engineering" ], "cited_by_count": 95, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1002/net.21982" }, { "id": "https://openalex.org/W4224118409", "doi": "10.1038/s41598-022-10408-4", "title": "Drone routing problem model for last-mile delivery using the public transportation capacity as moving charging stations", "year": 2022, "publication_date": "2022-04-15", "type": "article", "language": "en", "authors": [ "Amirhossein Moadab", "Fatemeh Farajzadeh", "Omid Fatahi Valilai" ], "first_author": "Amirhossein Moadab", "venue": "Scientific Reports", "publisher": "Nature Portfolio", "abstract": "The fast and cost-efficient delivery of goods ordered online is logistically a challenging problem. Many firms are looking for ways to cut delivery times and costs by exploring opportunities to take advantage of drone technology. Deploying drones as a promising technology is more efficient from both environmental and economic perspectives in last-mile delivery. This paper considers a last-mile delivery system in which a set of drones are operated in coordination with public transportation system to deliver a set of orders to customer locations. A mathematical model based on Vehicle routing Problem (VRP) is extended to solve this problem. A real-world case inspired by Bremen 2025 transportation paradigm is also developed to validate the developed mathematical formulation. Results show that the sequence of visiting customers and public transport stations highly impacts the remaining charge and efficiency of drone tour planning. Also, using public transport vehicles, which enables drones to charge their battery or to approach customers, can reduce the number of drones required for satisfying the demands in a service area. The results show that there are high potentials to save energy for drone-enabled last-mile delivery by using the public transportation network.", "keywords": [ "Drone", "Last mile (transportation)", "Mile", "Computer science", "Routing (electronic design automation)", "Transport engineering", "Public transport", "Set (abstract data type)", "Operations research", "Computer network", "Engineering" ], "cited_by_count": 89, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.nature.com/articles/s41598-022-10408-4.pdf" }, { "id": "https://openalex.org/W4293765590", "doi": "10.1109/tits.2021.3119080", "title": "Hybrid Multi-Objective Optimization Approach With Pareto Local Search for Collaborative Truck-Drone Routing Problems Considering Flexible Time Windows", "year": 2021, "publication_date": "2021-10-20", "type": "article", "language": "en", "authors": [ "Qizhang Luo", "Guohua Wu", "Bin Ji", "Ling Wang", "Ponnuthurai Nagaratnam Suganthan" ], "first_author": "Qizhang Luo", "venue": "IEEE Transactions on Intelligent Transportation Systems", "publisher": "Institute of Electrical and Electronics Engineers", "abstract": "The collaboration of drones and trucks for last-mile delivery has attracted much attention. In this paper, we address a collaborative routing problem of the truck-drone system, in which a truck collaborates with multiple drones to perform parcel deliveries and each customer can be served earlier and later than the required time with a given tolerance. To meet the practical demands of logistics companies, we build a multi-objective optimization model that minimizes total distribution cost and maximizes overall customer satisfaction simultaneously. We propose a hybrid multi-objective genetic optimization approach incorporated with a Pareto local search algorithm to solve the problem. Particularly, we develop a greedy-based heuristic method to create initial solutions and introduce a problem-specific solution representation, genetic operations, as well as six heuristic neighborhood strategies for the hybrid algorithm. Besides, an adaptive strategy is adopted to further balance the convergence and the diversity of the hybrid algorithm. The performance of the proposed algorithm is evaluated by using a set of benchmark instances. The experimental results show that the proposed algorithm outperforms three competitors. Furthermore, we investigate the sensitivity of the proposed model and hybrid algorithm based on a real-world case in Changsha city, China.", "keywords": [ "Vehicle routing problem", "Pareto principle", "Truck", "Computer science", "Mathematical optimization", "Hybrid algorithm (constraint satisfaction)", "Genetic algorithm", "Drone", "Local search (optimization)", "Heuristic", "Greedy algorithm", "Multi-objective optimization" ], "cited_by_count": 122, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1109/tits.2021.3119080" }, { "id": "https://openalex.org/W4214683918", "doi": "10.1002/nav.22053", "title": "Truck and drone routing problem with synchronization on arcs", "year": 2022, "publication_date": "2022-02-26", "type": "article", "language": "en", "authors": [ "Hongqi Li", "Jun Chen", "Feilong Wang", "Yibin Zhao" ], "first_author": "Hongqi Li", "venue": "Naval Research Logistics (NRL)", "publisher": "Wiley", "abstract": "Abstract Truck–drone technology that enables drones to launch from or land on a moving truck without the need for the truck to stop is the focus of this study. We define the truck and drone routing problem with synchronization on arcs (TDRP‐SA). The TDRP‐SA is characterized by synchronization on arcs, time windows, classified customers, direct delivery, multiple trucks, and multiple drones carried by each truck. The TDRP‐SA involves synchronization on arcs to permit trucks to dispatch and retrieve drones at suitable moving‐LRLs (drone launch/retrieval locations) on arcs of truck routes. A moving‐LRL is essentially a drone launch/retrieval location with a moving truck, and the drone launch/retrieval operations do not need special parking for the trucks. We develop a mixed integer nonlinear programming model to address the TDRP‐SA. We propose a mathematical analysis method to locate moving‐LRLs and to estimate the drone's arrival time at the customers. We develop boundary models through introducing linear piecewise functions to locate moving‐LRLs. We provide an adaptive large neighborhood search (ALNS) heuristic. Through computational experiments, the effectiveness of the boundary models, the TDRP‐SA model and ALNS‐based heuristic are evaluated.", "keywords": [ "Drone", "Truck", "Computer science", "Heuristic", "Routing (electronic design automation)", "Synchronization (alternating current)", "Real-time computing", "Operations research", "Artificial intelligence", "Engineering", "Computer network", "Automotive engineering" ], "cited_by_count": 43, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1002/nav.22053" }, { "id": "https://openalex.org/W4366132000", "doi": "10.1016/j.trc.2023.104139", "title": "Dynamic truck–drone routing problem for scheduled deliveries and on-demand pickups with time-related constraints", "year": 2023, "publication_date": "2023-04-17", "type": "article", "language": "en", "authors": [ "Ruixue Gu", "Yang Liu", "Mark Poon" ], "first_author": "Ruixue Gu", "venue": "Transportation Research Part C Emerging Technologies", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Truck", "Vehicle routing problem", "Routing (electronic design automation)", "Computer science", "Transport engineering", "Engineering", "Operations research", "Automotive engineering", "Computer network" ], "cited_by_count": 80, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.trc.2023.104139" }, { "id": "https://openalex.org/W4386839006", "doi": "10.1016/j.trc.2023.104322", "title": "The drone latency location routing problem under uncertainty", "year": 2023, "publication_date": "2023-09-15", "type": "article", "language": "en", "authors": [ "Maria Elena Bruni", "Sara Khodaparasti", "Guido Perboli" ], "first_author": "Maria Elena Bruni", "venue": "Transportation Research Part C Emerging Technologies", "publisher": "Elsevier BV", "abstract": "This paper addresses a location routing problem arising in the last-mile drone delivery context, where drones are used to deliver small packages to a set of customers. Each drone is launched from a fulfillment center to serve multiple customers on a single trip. The goal is to find the optimal subset of fulfillment centers to use as drone launching and landing platforms and the optimal drone routes with the aim of minimizing the sum of customers’ waiting times. We study the problem under two realistic assumptions. First, the drone energy consumption is a nonlinear function of the drone load that varies along the route, as parcels are delivered. Second, the drone flight time is not deterministically known. To hedge against drone flight time uncertainty, we adopt a robust optimization approach. Due to the complex nature of the problem, which turns out to be a nonlinear mixed-integer problem, we design an exact method based on a tailored efficient Branch & Check algorithm that uses customized no-good cuts. The computational experiments show the validity of the proposed model and the promising performance of the exact method. Moreover, we present a case study on last-mile parcel delivery in Turin, Italy, providing insights into the advantages of a drone-based delivery system.", "keywords": [ "Drone", "Computer science", "Context (archaeology)", "Mathematical optimization", "Routing (electronic design automation)", "Operations research", "Real-time computing", "Engineering", "Computer network", "Mathematics", "Geography" ], "cited_by_count": 48, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.trc.2023.104322" }, { "id": "https://openalex.org/W1980088782", "doi": "10.1002/rnc.1715", "title": "Linear temporal logic vehicle routing with applications to multi‐UAV mission planning", "year": 2011, "publication_date": "2011-05-10", "type": "article", "language": "en", "authors": [ "Sertaç Karaman", "Emilio Frazzoli" ], "first_author": "Sertaç Karaman", "venue": "International Journal of Robust and Nonlinear Control", "publisher": "Wiley", "abstract": "Abstract Missions with high combinatorial complexity involving several logical and temporal constraints often arise in cooperative control of multiple Uninhabited Aerial Vehicles. In this paper, we propose a new class of problems that generalizes the standard Vehicle Routing Problem (VRP) by addressing complex tasks and constraints on the mission, called the ‘mission specifications’, expressed in a high‐level specification language. In the generalized problem setup, these mission specifications are naturally specified using the Linear Temporal Logic language LTL−X. Using a novel systematic procedure, the LTL−Xspecification is converted to a set of constraints suitable to a Mixed‐Integer Linear Programming (MILP) formulation, which in turn can be incorporated into two widely‐used MILP formulations of the standard VRP. Solving the resulting MILP provides an optimal plan that satisfies the given mission specification. The paper also presents two mission planning applications. Copyright © 2011 John Wiley & Sons, Ltd.", "keywords": [ "Integer programming", "Linear programming", "Linear temporal logic", "Class (philosophy)", "Set (abstract data type)", "Routing (electronic design automation)", "Computer science", "Vehicle routing problem", "Temporal logic", "Plan (archaeology)", "Mathematical optimization", "Theoretical computer science" ], "cited_by_count": 129, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1002/rnc.1715" }, { "id": "https://openalex.org/W4390862194", "doi": "10.1016/j.ejor.2024.05.031", "title": "A competitive heuristic algorithm for vehicle routing problems with drones", "year": 2024, "publication_date": "2024-05-19", "type": "article", "language": "en", "authors": [ "Xuan Ren", "Aurélien Froger", "Ola Jabali", "Gongqian Liang" ], "first_author": "Xuan Ren", "venue": "European Journal of Operational Research", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Vehicle routing problem", "Drone", "Computer science", "Heuristic", "Routing (electronic design automation)", "Mathematical optimization", "Algorithm", "Operations research", "Artificial intelligence", "Mathematics", "Computer network" ], "cited_by_count": 20, "is_retracted": false, "is_paratext": false, "open_access_url": "https://inria.hal.science/hal-04010250/document" }, { "id": "https://openalex.org/W2910778520", "doi": "10.1016/j.cor.2019.01.001", "title": "A vehicle routing problem arising in unmanned aerial monitoring", "year": 2019, "publication_date": "2019-01-08", "type": "article", "language": "en", "authors": [ "Lu Zhen", "Miao Li", "Gilbert Laporte", "Wencheng Wang" ], "first_author": "Lu Zhen", "venue": "Computers & Operations Research", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Tabu search", "Computer science", "Metaheuristic", "Vehicle routing problem", "Integer programming", "Routing (electronic design automation)", "Set (abstract data type)", "Heuristic", "Route planning", "Mathematical optimization", "Real-time computing", "Operations research" ], "cited_by_count": 60, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.cor.2019.01.001" }, { "id": "https://openalex.org/W4399986805", "doi": "10.1016/j.cie.2024.110330", "title": "Time-dependent hydrogen fuel cell vehicle routing problem with drones and variable drone speeds", "year": 2024, "publication_date": "2024-06-24", "type": "article", "language": "en", "authors": [ "Xiaoxue Ren", "Houming Fan", "Houming Fan", "Mengzhi Ma", "Hao Fan", "Hao Fan", "Lijun Yue" ], "first_author": "Xiaoxue Ren", "venue": "Computers & Industrial Engineering", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Variable (mathematics)", "Vehicle routing problem", "Fuel cells", "Routing (electronic design automation)", "Computer science", "Engineering", "Aeronautics", "Automotive engineering", "Environmental science", "Aerospace engineering", "Biology" ], "cited_by_count": 20, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.cie.2024.110330" }, { "id": "https://openalex.org/W2147611175", "doi": "10.2514/6.2010-8435", "title": "Vehicle Routing Problem Instances: Application to Multi-UAV Mission Planning", "year": 2010, "publication_date": "2010-06-26", "type": "conference-paper", "language": "en", "authors": [ "Mariam Adbelhafiz", "Ahmed Mostafa", "Anouck Girard" ], "first_author": "Mariam Adbelhafiz", "venue": null, "publisher": null, "abstract": "variants have been studied and found applications in the real world. This paper briey surveys VRP instances with applications to multi-objective Unmanned Aerial Vehicle (UAV) operations. Focusing on multi-objective multi-UAV mission planning problems, we try to take advantage of the literature in the VRP and its variants. We show that each military multi-UAV mission has its corresponding VRP variant. We present a novel algorithm that relies on an enhanced tree search algorithm to solve complex multi-UAV mission planning problems with complex constraints. In simulation, we introduce examples for practical problem sizes in military UAV applications.", "keywords": [ "Computer science", "Vehicle routing problem", "Routing (electronic design automation)", "Route planning", "Real-time computing", "Computer network", "Engineering", "Transport engineering" ], "cited_by_count": 42, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.2514/6.2010-8435" }, { "id": "https://openalex.org/W2989768175", "doi": "10.3390/s19235164", "title": "Traffic Patrolling Routing Problem with Drones in an Urban Road System", "year": 2019, "publication_date": "2019-11-25", "type": "article", "language": "en", "authors": [ "He Luo", "Peng Zhang", "Jiajie Wang", "Guoqiang Wang", "Fanhe Meng" ], "first_author": "He Luo", "venue": "Sensors", "publisher": "Multidisciplinary Digital Publishing Institute", "abstract": "The remarkable development of various sensor equipment and communication technologies has stimulated many application platforms of automation. A drone is a sensing platform with strong environmental adaptability and expandability, which is widely used in aerial photography, transmission line inspection, remote sensing mapping, auxiliary communication, traffic patrolling, and other fields. A drone is an effective supplement to the current patrolling business in road traffic patrolling with complex urban buildings and road conditions and a limited ground perspective. However, the limited endurance of patrol drones can be directly solved by vehicles that cooperate with drones on patrolling missions. In this paper, we first proposed and studied the traffic patrolling routing problem with drones (TPRP-D) in an urban road system. Considering road network equations and the heterogeneity of patrolling tasks in the actual patrolling process, we modeled the problem as a double-layer arc routing problem (DL-ARP). Based on graph theory and related research work, we present the mixed integer linear programming formulations and two-stage heuristic solution approaches to solve practical-sized problems. Through analysis of numerical experiments, the solution method proposed in this paper can quickly provide an optimal path planning scheme for different test sets, which can save 9%-16% of time compared with traditional vehicle patrol. At the same time, we analyze several relevant parameters of the patrol process to determine the effect of coordinated traffic patrol. Finally, a case study was completed to verify the practicability of the algorithm.", "keywords": [ "Patrolling", "Drone", "Routing (electronic design automation)", "Computer science", "Transport engineering", "Computer network", "Computer security", "Engineering", "Geography" ], "cited_by_count": 49, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.mdpi.com/1424-8220/19/23/5164/pdf?version=1575440742" }, { "id": "https://openalex.org/W2938352754", "doi": "10.1016/j.trpro.2020.03.160", "title": "A vehicle routing problem with movement synchronization of drones, sidewalk robots, or foot-walkers", "year": 2020, "publication_date": "2020-01-01", "type": "article", "language": "en", "authors": [ "Puyuan Deng", "Glareh Amirjamshidi", "Matthew J. Roorda" ], "first_author": "Puyuan Deng", "venue": "Transportation research procedia", "publisher": "Elsevier BV", "abstract": "The vehicle routing problem (VRP) and its variants have many city logistics applications, such as goods delivery. The VRP extension with movement synchronization (VRPMS) has potential applications of drone and robot technologies to assist with the delivery of parcels. VRPMS seeks the optimal route for a set of composite resources, e.g. delivery van with drones, or delivery van with sidewalk robots. This paper proposes an exact formulation of the problem, and a metaheuristic approach to solve larger instances of the VRPMS in order to assess the economic benefits of the different technologies. It is shown that with the current physical constraints of drone technology, assisted delivery with drones has some challenges because of its capacity. Sidewalk robots and walkers, however, do contribute a cost savings compared to truck deliveries. As the technology matures, the presented metaheuristic approach can be used to evaluate improved economic benefits and cost benefit ratios.", "keywords": [ "Drone", "Robot", "Vehicle routing problem", "Metaheuristic", "Routing (electronic design automation)", "Computer science", "Synchronization (alternating current)", "Truck", "Transport engineering", "Set (abstract data type)", "Operations research", "Simulation" ], "cited_by_count": 25, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.sciencedirect.com/science/article/pii/S2352146520303604/pdf" }, { "id": "https://openalex.org/W2548903816", "doi": "10.1016/j.cie.2016.10.029", "title": "Solving location and routing problem for UAVs", "year": 2016, "publication_date": "2016-11-03", "type": "article", "language": "en", "authors": [ "Ertan Yakıcı" ], "first_author": "Ertan Yakıcı", "venue": "Computers & Industrial Engineering", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Metaheuristic", "Solver", "Mathematical optimization", "Maximization", "Heuristic", "Ant colony optimization algorithms", "Integer programming", "Computer science", "Routing (electronic design automation)", "Vehicle routing problem", "Ant colony", "Integer (computer science)" ], "cited_by_count": 82, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.cie.2016.10.029" }, { "id": "https://openalex.org/W3200869038", "doi": "10.1016/j.ejor.2021.09.008", "title": "A cumulative unmanned aerial vehicle routing problem approach for humanitarian coverage path planning", "year": 2021, "publication_date": "2021-09-15", "type": "article", "language": "en", "authors": [ "Nikolaos A. Kyriakakis", "Magdalene Marinaki", "Nikolaos F. Matsatsinis", "Yannis Marinakis" ], "first_author": "Nikolaos A. Kyriakakis", "venue": "European Journal of Operational Research", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Motion planning", "Computer science", "Routing (electronic design automation)", "Mathematical optimization", "Vehicle routing problem", "GRASP", "Computer network", "Mathematics", "Artificial intelligence", "Robot" ], "cited_by_count": 78, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.ejor.2021.09.008" }, { "id": "https://openalex.org/W3185199585", "doi": "10.1016/j.tre.2021.102417", "title": "Humanitarian relief network assessment using collaborative truck-and-drone system", "year": 2021, "publication_date": "2021-07-18", "type": "article", "language": "en", "authors": [ "Guowei Zhang", "Ning Yan Zhu", "Shoufeng Ma", "Jun Zhong Xia" ], "first_author": "Guowei Zhang", "venue": "Transportation Research Part E Logistics and Transportation Review", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Truck", "Aeronautics", "Engineering", "Transport engineering", "Humanitarian Logistics", "Computer science", "Computer security", "Operations research", "Operations management", "Automotive engineering" ], "cited_by_count": 145, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.tre.2021.102417" }, { "id": "https://openalex.org/W4389432372", "doi": "10.3390/app132413086", "title": "Vehicle Routing Problem with Drones Considering Time Windows and Dynamic Demand", "year": 2023, "publication_date": "2023-12-07", "type": "article", "language": "en", "authors": [ "Jing Han", "Yanqiu Liu", "李岩 Li Yan" ], "first_author": "Jing Han", "venue": "Applied Sciences", "publisher": "Multidisciplinary Digital Publishing Institute", "abstract": "As a new delivery mode, the collaborative delivery of packages using trucks and drones has been proven to reduce delivery costs and delivery time. To cope with the huge cost challenges brought by strict time constraints and ever-changing customer orders in the actual delivery process, we established a two-stage optimization model based on different demand response strategies with the goal of minimizing delivery costs. To solve this problem, we designed a simulated annealing chimp optimization algorithm with a sine–cosine operator. The performance of this algorithm is improved by designing a variable-dimensional matrix encode to generate an initial solution, incorporating a sine–cosine operator and a simulated annealing mechanism to avoid falling into a local optimum. Numerical experiments verify the effectiveness of the proposed algorithm and strategy. Finally, we analyze the impact of dynamic degree on delivery cost. The proposed model and algorithm extend the theory of the vehicle routing problem with drones and also provide a feasible solution for route planning, taking into account dynamic demands and time windows.", "keywords": [ "Simulated annealing", "Mathematical optimization", "Computer science", "Vehicle routing problem", "Operator (biology)", "Routing (electronic design automation)", "Drone", "Dynamic programming", "Truck", "Algorithm", "Engineering", "Mathematics" ], "cited_by_count": 20, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.mdpi.com/2076-3417/13/24/13086/pdf?version=1701963451" }, { "id": "https://openalex.org/W2765355161", "doi": "10.1007/978-3-319-67308-0_56", "title": "Last-Mile Deliveries by Using Drones and Classical Vehicles", "year": 2017, "publication_date": "2017-01-01", "type": "conference-paper", "language": "en", "authors": [ "Luigi Di Puglia Pugliese", "Francesca Guerriero" ], "first_author": "Luigi Di Puglia Pugliese", "venue": "Springer proceedings in mathematics & statistics", "publisher": "Springer International Publishing", "abstract": null, "keywords": [ "Drone", "Truck", "Last mile (transportation)", "Computer science", "Process (computing)", "Operations research", "Service (business)", "Aeronautics", "Mile", "Transport engineering", "Engineering", "Real-time computing" ], "cited_by_count": 106, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1007/978-3-319-67308-0_56" }, { "id": "https://openalex.org/W3197830882", "doi": "10.2139/ssrn.3879710", "title": "A branch-and-price approach for the parallel drone scheduling vehicle routing problem", "year": 2021, "publication_date": "2021-01-01", "type": "preprint", "language": "en", "authors": [ "Ritwik Raj", "Dowon Lee", "Seunghan Lee", "Jose L. Walteros", "Chase C. Murray" ], "first_author": "Ritwik Raj", "venue": "SSRN Electronic Journal", "publisher": "RELX Group (Netherlands)", "abstract": null, "keywords": [ "Drone", "Scheduling (production processes)", "Computer science", "Vehicle routing problem", "Branch and price", "Operations research", "Mathematical optimization", "Computer network", "Routing (electronic design automation)", "Integer programming", "Engineering", "Mathematics" ], "cited_by_count": 18, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.2139/ssrn.3879710" }, { "id": "https://openalex.org/W4313678757", "doi": "10.1016/j.trc.2022.103981", "title": "A deep reinforcement learning approach for solving the Traveling Salesman Problem with Drone", "year": 2023, "publication_date": "2023-01-07", "type": "article", "language": "en", "authors": [ "Aigerim Bogyrbayeva", "Taehyun Yoon", "Hanbum Ko", "Sungbin Lim", "Hyokun Yun", "Changhyun Kwon" ], "first_author": "Aigerim Bogyrbayeva", "venue": "Transportation Research Part C Emerging Technologies", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Travelling salesman problem", "Computer science", "Reinforcement learning", "Drone", "Routing (electronic design automation)", "Vehicle routing problem", "Node (physics)", "2-opt", "Mathematical optimization", "Artificial intelligence", "Computer network", "Engineering" ], "cited_by_count": 115, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.trc.2022.103981" }, { "id": "https://openalex.org/W4405663184", "doi": "10.1016/j.swevo.2024.101825", "title": "Approaches to the truck-drone routing problem: A systematic review", "year": 2024, "publication_date": "2024-12-21", "type": "review", "language": "en", "authors": [ "Jie Duan", "He Luo", "Guoqiang Wang" ], "first_author": "Jie Duan", "venue": "Swarm and Evolutionary Computation", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Computer science", "Drone", "Truck", "Routing (electronic design automation)", "Operations research", "Computer network", "Automotive engineering" ], "cited_by_count": 34, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.swevo.2024.101825" }, { "id": "https://openalex.org/W4243401736", "doi": "10.1016/j.swevo.2013.12.003", "title": "A Bumble Bees Mating Optimization algorithm for the Open Vehicle Routing Problem", "year": 2013, "publication_date": "2013-12-20", "type": "article", "language": "en", "authors": [ "Yannis Marinakis", "Magdalene Marinaki" ], "first_author": "Yannis Marinakis", "venue": "Swarm and Evolutionary Computation", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Computer science", "Vehicle routing problem", "Bees algorithm", "Benchmark (surveying)", "Mathematical optimization", "Metaheuristic", "Swarm intelligence", "Algorithm", "Swarm behaviour", "Bat algorithm", "Routing (electronic design automation)", "Local search (optimization)" ], "cited_by_count": 57, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.swevo.2013.12.003" }, { "id": "https://openalex.org/W3160013986", "doi": "10.1016/j.omega.2021.102482", "title": "Managing price and fleet size for courier service with shared drones", "year": 2021, "publication_date": "2021-05-08", "type": "article", "language": "en", "authors": [ "Zhi Pei", "Xu Dai", "Yilun Yuan", "Rui Du", "Changchun Liu" ], "first_author": "Zhi Pei", "venue": "Omega", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Service (business)", "Quality of service", "Service provider", "Revenue", "Computer science", "Operations research", "Queueing theory", "Abandonment (legal)", "Business", "Operations management", "Marketing" ], "cited_by_count": 31, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.omega.2021.102482" }, { "id": "https://openalex.org/W3175039752", "doi": "10.1016/j.cie.2021.107495", "title": "Drone routing and optimization for post-disaster inspection", "year": 2021, "publication_date": "2021-06-22", "type": "article", "language": "en", "authors": [ "Sudipta Chowdhury", "Omid Shahvari", "Mohammad Marufuzzaman", "Xiaopeng Li", "Linkan Bian" ], "first_author": "Sudipta Chowdhury", "venue": "Computers & Industrial Engineering", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Routing (electronic design automation)", "Vehicle routing problem", "Computer science", "Aeronautics", "Operations research", "Engineering", "Computer network", "Biology" ], "cited_by_count": 94, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.cie.2021.107495" }, { "id": "https://openalex.org/W4404087519", "doi": "10.1007/s10586-024-04809-5", "title": "Multi-depot vehicle routing problem with drones in emergency logistics", "year": 2024, "publication_date": "2024-11-04", "type": "article", "language": "en", "authors": [ "Xun Weng", "Wenke She", "Hong-Qiang Fan", "Jingtian Zhang", "Lifen Yun" ], "first_author": "Xun Weng", "venue": "Cluster Computing", "publisher": "Springer Science+Business Media", "abstract": null, "keywords": [ "Computer science", "Vehicle routing problem", "Depot", "Drone", "Routing (electronic design automation)", "Operations research", "Computer network" ], "cited_by_count": 16, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1007/s10586-024-04809-5" }, { "id": "https://openalex.org/W4285296730", "doi": "10.1109/tits.2022.3181282", "title": "Collaborative Truck-Drone Routing for Contactless Parcel Delivery During the Epidemic", "year": 2022, "publication_date": "2022-06-20", "type": "article", "language": "en", "authors": [ "Guohua Wu", "Ni Mao", "Qizhang Luo", "Binjie Xu", "Jianmai Shi", "Ponnuthurai Nagaratnam Suganthan" ], "first_author": "Guohua Wu", "venue": "IEEE Transactions on Intelligent Transportation Systems", "publisher": "Institute of Electrical and Electronics Engineers", "abstract": "The COVID-19 pandemic calls for contactless deliveries. To prevent the further spread of the disease and ensure the timely delivery of supplies, this paper investigates a collaborative truck-drone routing problem for contactless parcel delivery (CRP-T&D), which allows multiple trucks and multiple drones to deliver parcels cooperatively in epidemic areas. We formulate a mixed-integer programming model that minimizes the delivery time, with the consideration of the energy consumption model of drones. To solve CRP-T&D, we develop an improved variable neighborhood descent (IVND) that combines the Metropolis acceptance criterion of Simulated Annealing (SA) and the tabu list of Tabu Search (TS). Meanwhile, the integration of K-means clustering and Nearest neighbor strategy is applied to generate the initial solution. To evaluate the performance of IVND, experiments are conducted by comparing IVND with VND, SA, TS, variants of VND, and large neighborhood search (LNS) on instances with different scales. Several critical factors are tested to verify the robustness of IVND. Moreover, the experimental results on a practical instance further demonstrate the superior performance of IVND.", "keywords": [ "Drone", "Tabu search", "Robustness (evolution)", "Computer science", "Simulated annealing", "Truck", "Vehicle routing problem", "Routing (electronic design automation)", "Cluster analysis", "Integer programming", "Computer network", "Engineering" ], "cited_by_count": 122, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1109/tits.2022.3181282" }, { "id": "https://openalex.org/W4367185959", "doi": "10.1016/j.eswa.2023.120260", "title": "Drone routing problem with truck: Optimization and quantitative analysis", "year": 2023, "publication_date": "2023-04-27", "type": "article", "language": "en", "authors": [ "Ho Young Jeong", "Seokcheon Lee" ], "first_author": "Ho Young Jeong", "venue": "Expert Systems with Applications", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Truck", "Computer science", "Heuristic", "Routing (electronic design automation)", "Vehicle routing problem", "Operations research", "Computer network", "Engineering", "Artificial intelligence", "Automotive engineering" ], "cited_by_count": 32, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.eswa.2023.120260" }, { "id": "https://openalex.org/W4386053882", "doi": "10.1155/2023/1183764", "title": "Multivisit Drone-Vehicle Routing Problem with Simultaneous Pickup and Delivery considering No-Fly Zones", "year": 2023, "publication_date": "2023-08-22", "type": "article", "language": "en", "authors": [ "Yanqiu Liu", "Jing Han", "Ying Zhang", "Yan Li", "Tao Jiang" ], "first_author": "Yanqiu Liu", "venue": "Discrete Dynamics in Nature and Society", "publisher": "Hindawi Publishing Corporation", "abstract": "The employment of drones for the distribution of goods represents a significant avenue for addressing logistical challenges at the end of the supply chain. The truck-drone cooperative delivery model overcomes drone limitations such as limited capacity and endurance and has emerged as a crucial mode of drone participation in logistics delivery. This delivery model effectively reduces delivery costs and shortens delivery times. Herein, we examine a variant of the truck-drone routing problem, which encompasses the strategic deployment and routing of multiple fleets of trucks, each equipped with an auxiliary drone. The objective is to fulfill all the pickup and delivery demands of a designated customer base while minimizing the overall route cost. Within this problem domain, drones are authorized to serve multiple customers within their capacity and endurance limits, providing both pickup and delivery services during each trip. However, the utilization of drones for servicing all customers is impeded by the existence of no-fly zones that have been implemented in numerous cities worldwide. These prescribed no-fly zones cause significant challenges when attempting to optimize the routing of truck-drone operations. Thus, this study constructs a mixed integer linear programming (MILP) model for the path optimization problem of joint service of trucks and drones considering no-fly zones and simultaneous pickup and delivery. Given the intricacy of the MILP model, we propose a two-stage heuristic algorithm based on a simulated annealing approach, combined with strategies for rectifying infeasible solutions and expediting algorithmic processes. During the phase of computational experimentation, we explore the advantages derived from enabling drones to serve multiple customers and assess the effectiveness of the proposed model and two-stage heuristic algorithm. Finally, sensitivity analysis is conducted on two key parameters.", "keywords": [ "Drone", "Truck", "Computer science", "Pickup", "Routing (electronic design automation)", "Vehicle routing problem", "Heuristic", "Integer programming", "Supply chain", "Operations research", "Transport engineering", "Business" ], "cited_by_count": 21, "is_retracted": false, "is_paratext": false, "open_access_url": "https://downloads.hindawi.com/journals/ddns/2023/1183764.pdf" }, { "id": "https://openalex.org/W3120782450", "doi": "10.1109/access.2021.3050658", "title": "A New Truck-Drone Routing Problem for Parcel Delivery Services Aided by Parking Lots", "year": 2021, "publication_date": "2021-01-01", "type": "article", "language": "en", "authors": [ "Javier E. Gómez-Lagos", "Alfredo Candia-Véjar", "Flavio Encina" ], "first_author": "Javier E. Gómez-Lagos", "venue": "IEEE Access", "publisher": "Institute of Electrical and Electronics Engineers", "abstract": "Collaborative routing aided by drones in last-mile delivery (LMD) has been an extensively studied topic in recent years. In this article, a new optimization problem for collaborative routing with a truck and a fleet of drones in LMD is introduced. The problem proposes a new strategy to coordinate a truck and a fleet of drones to serve a given set of customers. The plan is based on identifying the locations where the truck can park and where the drones fly to serve the customers. A procedure to locate these parking lots conveniently is given. For the transportation network, which includes these points, a mixed linear integer programming formulation is provided, which aims to minimize the makespan of serving all the customers. Computational experiments on a set of problem instances were conducted to analyze the model solutions' characteristics and find their computational limits. The experiments showed that the proposed model could significantly improve the results obtained when only the truck delivers. Additionally, we propose a GRASP metaheuristic to solve instances of greater size. Its computational performance was studied when applied to a set of instances with different characteristics. The paper discusses some insights obtained from the computational experimentation and presents future research directions.", "keywords": [ "Truck", "Drone", "Computer science", "Routing (electronic design automation)", "Metaheuristic", "GRASP", "Integer programming", "Vehicle routing problem", "Set (abstract data type)", "Plan (archaeology)", "Job shop scheduling", "Operations research" ], "cited_by_count": 50, "is_retracted": false, "is_paratext": false, "open_access_url": "https://ieeexplore.ieee.org/ielx7/6287639/9312710/09319131.pdf" }, { "id": "https://openalex.org/W4294724298", "doi": "10.1016/j.cie.2022.108632", "title": "On a Pickup to Delivery Drone Routing Problem: Models and algorithms", "year": 2022, "publication_date": "2022-09-06", "type": "article", "language": "en", "authors": [ "Javier E. Gómez-Lagos", "Benjamín Rojas-Espinoza", "Alfredo Candia-Véjar" ], "first_author": "Javier E. Gómez-Lagos", "venue": "Computers & Industrial Engineering", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Pickup", "Routing (electronic design automation)", "Vehicle routing problem", "Computer science", "Algorithm", "Mathematical optimization", "Engineering", "Distributed computing", "Mathematics", "Computer network", "Artificial intelligence" ], "cited_by_count": 32, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.cie.2022.108632" }, { "id": "https://openalex.org/W2802948916", "doi": "10.1016/j.cie.2018.04.037", "title": "The unmanned aerial vehicle routing and trajectory optimisation problem, a taxonomic review", "year": 2018, "publication_date": "2018-04-22", "type": "article", "language": "en", "authors": [ "Walton Pereira Coutinho", "Maria Battarra", "Jörg Fliege" ], "first_author": "Walton Pereira Coutinho", "venue": "Computers & Industrial Engineering", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Trajectory", "Vehicle routing problem", "Computer science", "Routing (electronic design automation)", "Taxonomy (biology)", "Identification (biology)", "Operations research", "Engineering", "Computer network", "Ecology", "Biology" ], "cited_by_count": 191, "is_retracted": false, "is_paratext": false, "open_access_url": "https://researchportal.bath.ac.uk/files/169821880/UAVRTOP_manuscript_7_.pdf" }, { "id": "https://openalex.org/W4293791090", "doi": "10.3390/app12168255", "title": "A Proactive Approach to Extended Vehicle Routing Problem with Drones (EVRPD)", "year": 2022, "publication_date": "2022-08-18", "type": "article", "language": "en", "authors": [ "Paweł Sitek", "Jarosław Wikarek", "Mieczysław Jagodziński" ], "first_author": "Paweł Sitek", "venue": "Applied Sciences", "publisher": "Multidisciplinary Digital Publishing Institute", "abstract": "Unmanned aerial vehicles (UAVs), also known as drones, are increasingly common and popular due to their relatively low prices and high mobility. The number of areas for their practical applications is rapidly growing. The most promising are: last-mile delivery, emergency response, the inspection of technical devices and installations, etc. In these applications, it is often necessary to solve vehicle routing problems, formulated as a variant of the vehicle routing problems with drones (VRPD). This study presents a proactive approach to a modified and extended VRPD, including: the dynamic selection of drone take-off points, bidirectional delivery (delivery and pick up), various types of shipments, allocation of shipments to drones and drones to vehicles, the selection of the optimal number of drones, etc. Moreover, a formal model of constraints and questions for the extended vehicle routing problem with drones (EVRPD) and exact and approximate methods for solving it have been proposed. The proposed model can be the basis for supporting proactive and reactive decisions regarding last-mile delivery, particularly the selection of the necessary fleet, starting points, the identification of specific shipments that prevent delivery with available resources, etc. The study also includes the results of numerous computational experiments verifying the effectiveness of the implementation methods. The time to obtain a solution is at least 20 times shorter for the proposed DGA (dedicated genetic algorithm) than for the mathematical programming solvers such as Gurobi or LINGO. Moreover, for larger-sized data instances, these solvers do not allow obtaining any solution in an acceptable time, or they obtain worse solutions.", "keywords": [ "Drone", "Computer science", "Vehicle routing problem", "Routing (electronic design automation)", "Selection (genetic algorithm)", "Operations research", "Identification (biology)", "Last mile (transportation)", "Mathematical optimization", "Mile", "Computer network", "Engineering" ], "cited_by_count": 14, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.mdpi.com/2076-3417/12/16/8255/pdf?version=1660824443" }, { "id": "https://openalex.org/W4411225498", "doi": "10.1016/j.eswa.2025.128503", "title": "Multi-objective optimization for time-dependent vehicle routing problem with drones", "year": 2025, "publication_date": "2025-06-12", "type": "article", "language": "en", "authors": [ "Yong Peng", "Chengxi Zhang", "Ajinkya N. Tanksale", "Dennis Z. Yu" ], "first_author": "Yong Peng", "venue": "Expert Systems with Applications", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Vehicle routing problem", "Computer science", "Mathematical optimization", "Routing (electronic design automation)", "Mathematics", "Computer network" ], "cited_by_count": 16, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.eswa.2025.128503" }, { "id": "https://openalex.org/W2616938768", "doi": "10.1007/978-3-319-59513-9_9", "title": "Logistics Support Approach for Drone Delivery Fleet", "year": 2017, "publication_date": "2017-01-01", "type": "conference-paper", "language": "en", "authors": [ "Asma Troudi", "Sid-Ali Addouche", "Sofiène Dellagi", "Abderrahman El Mhamedi" ], "first_author": "Asma Troudi", "venue": "Lecture notes in computer science", "publisher": "Springer Science+Business Media", "abstract": null, "keywords": [ "Drone", "Computer science", "Last mile (transportation)", "City logistics", "Cover (algebra)", "Aeronautics", "Operations research", "Transport engineering", "Mile", "Engineering", "Geography" ], "cited_by_count": 20, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1007/978-3-319-59513-9_9" }, { "id": "https://openalex.org/W3184846191", "doi": "10.1109/tai.2021.3087666", "title": "Reinforcement Learning Based Truck-and-Drone Coordinated Delivery", "year": 2021, "publication_date": "2021-07-01", "type": "article", "language": "en", "authors": [ "Guohua Wu", "Mingfeng Fan", "Jianmai Shi", "Yanghe Feng" ], "first_author": "Guohua Wu", "venue": "IEEE Transactions on Artificial Intelligence", "publisher": "Institute of Electrical and Electronics Engineers", "abstract": "Coronavirus disease 2019 has brought a great challenge to the supply of daily necessities and medical items for home-quarantined people. Considering the unmanned operation, agility, and use of clean energy of drones, we propose a novel truck-and-drone coordinated delivery system that does not require direct human contact during the delivery process. All final deliveries are completed by the drone while the truck acts as a movable charging station and a carrier, so that the contagion risks are reduced. Moreover, we spilt the whole delivery problem into the customer-clustering problem and the routing problems of both the truck and the drone. An encoder–decoder framework combined with reinforcement learning is created to solve the routing problems without handcrafted designed heuristics. We design the different problem contexts specific to the truck routing problem and the drone routing problem. The experimental results show that the proposed approach has good generality and can consequently be applied to problems of different scales with high time efficiency.", "keywords": [ "Drone", "Reinforcement learning", "Routing (electronic design automation)", "Heuristics", "Truck", "Computer science", "Generality", "Cluster analysis", "Vehicle routing problem", "Operations research", "Engineering", "Artificial intelligence" ], "cited_by_count": 85, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1109/tai.2021.3087666" }, { "id": "https://openalex.org/W4406064016", "doi": "10.1016/j.cor.2024.106963", "title": "Transportation and carbon emissions costs minimization for time-dependent vehicle routing problem with drones", "year": 2025, "publication_date": "2025-01-04", "type": "article", "language": "en", "authors": [ "Yong Peng", "Zhi Ren", "Dennis Z. Yu", "Yonghui Zhang" ], "first_author": "Yong Peng", "venue": "Computers & Operations Research", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Vehicle routing problem", "Minification", "Computer science", "Routing (electronic design automation)", "Operations research", "Mathematical optimization", "Environmental science", "Transport engineering", "Mathematics", "Computer network", "Engineering" ], "cited_by_count": 18, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.cor.2024.106963" }, { "id": "https://openalex.org/W4281672706", "doi": "10.1080/24725854.2022.2060535", "title": "Branch-price-and-cut for trucks and drones cooperative delivery", "year": 2022, "publication_date": "2022-05-13", "type": "article", "language": "en", "authors": [ "Lu Zhen", "Jiajing Gao", "Zheyi Tan", "Shuaian Wang", "Roberto Baldacci" ], "first_author": "Lu Zhen", "venue": "IISE Transactions", "publisher": "Taylor & Francis", "abstract": "The truck and drone-based cooperative model of delivery can improve the efficiency of last mile delivery, and has thus increasingly attracted attention in academia and from practitioners. In this study, we examine a vehicle routing problem and apply a cooperative form of delivery involving trucks and drones. We propose a mixed-integer programming model and a branch-price-and-cut-based exact algorithm to address this problem. To reduce the computation time, we design several acceleration strategies, including a combination of dynamic programming and calculus-based approximation for the pricing problem, and various effective inequalities for the restricted master problem. Numerical experiments are conducted to validate the effectiveness and efficiency of the proposed solution.", "keywords": [ "Truck", "Drone", "Computer science", "Aeronautics", "Business", "Automotive engineering", "Engineering", "Biology" ], "cited_by_count": 78, "is_retracted": false, "is_paratext": false, "open_access_url": "http://ira.lib.polyu.edu.hk/bitstream/10397/99079/1/trucks%20and%20drones.pdf" }, { "id": "https://openalex.org/W2746990488", "doi": "10.1109/dasc.2017.8101984", "title": "Security, privacy and safety evaluation of dynamic and static fleets of drones", "year": 2017, "publication_date": "2017-09-01", "type": "conference-paper", "language": "en", "authors": [ "Raja Naeem Akram", "Konstantinos Markantonakis", "Keith E. Mayes", "Oussama Habachi", "Damien Sauveron", "Andreas Steyven", "Serge Chaumette" ], "first_author": "Raja Naeem Akram", "venue": null, "publisher": null, "abstract": "Interconnected everyday objects, either via public or private networks, are gradually becoming reality in modern life — often referred to as the Internet of Things (IoT) or Cyber-Physical Systems (CPS). One stand-out example are those systems based on Unmanned Aerial Vehicles (UAVs). Fleets of such vehicles (drones) are prophesied to assume multiple roles from mundane to high-sensitive applications, such as prompt pizza or shopping deliveries to the home, or to deployment on battlefields for battlefield and combat missions. Drones, which we refer to as UAVs in this paper, can operate either individually (solo missions) or as part of a fleet (group missions), with and without constant connection with a base station. The base station acts as the command centre to manage the drones' activities; however, an independent, localised and effective fleet control is necessary, potentially based on swarm intelligence, for several reasons: 1) an increase in the number of drone fleets; 2) fleet size might reach tens of UAVs; 3) making time-critical decisions by such fleets in the wild; 4) potential communication congestion and latency; and 5) in some cases, working in challenging terrains that hinders or mandates limited communication with a control centre, e.g. operations spanning long period of times or military usage of fleets in enemy territory. This self-aware, mission-focused and independent fleet of drones may utilise swarm intelligence for a), air-traffic or flight control management, b) obstacle avoidance, c) self-preservation (while maintaining the mission criteria), d) autonomous collaboration with other fleets in the wild, and e) assuring the security, privacy and safety of physical (drones itself) and virtual (data, software) assets. In this paper, we investigate the challenges faced by fleet of drones and propose a potential course of action on how to overcome them.", "keywords": [ "Drone", "Software deployment", "Computer security", "Adversary", "Computer science", "Obstacle", "Control (management)", "Aeronautics", "Operations research", "Engineering", "Geography", "Artificial intelligence" ], "cited_by_count": 87, "is_retracted": false, "is_paratext": false, "open_access_url": "https://arxiv.org/pdf/1708.05732" }, { "id": "https://openalex.org/W4386969711", "doi": "10.1016/j.ejco.2023.100078", "title": "Constraint programming models for the parallel drone scheduling vehicle routing problem", "year": 2023, "publication_date": "2023-01-01", "type": "article", "language": "en", "authors": [ "Roberto Montemanni", "Mauro Dell’Amico" ], "first_author": "Roberto Montemanni", "venue": "EURO Journal on Computational Optimization", "publisher": "Springer Science+Business Media", "abstract": "Drones are currently seen as a viable way for improving the distribution of parcels in urban and rural environments, while working in coordination with traditional vehicles like trucks. In this paper we consider the parallel drone scheduling vehicle routing problem, where the service of a set of customers requiring a delivery is split between a fleet of trucks and a fleet of drones. We consider two variations of the problem. In the first one, the problem is more theoretical, and the target is the minimization of the time required to complete the service and have all the vehicles back to the depot. In the second variant, more realistic constraints involving operating costs, capacity limitation and workload balance, are considered, and the target is to minimize the total operational costs. We propose different constraint programming models to deal with the two problems. An experimental champaign on the instances previously adopted in the literature is presented to validate the new solving methods. The results show that, on top of being a viable way to solve problems to optimality, the models can also be used to derive effective heuristic solutions and high-quality lower bounds for the optimal cost, if the execution is interrupted before its natural end.", "keywords": [ "Computer science", "Vehicle routing problem", "Drone", "Truck", "Scheduling (production processes)", "Mathematical optimization", "Workload", "Constraint programming", "Job shop scheduling", "Operations research", "Routing (electronic design automation)", "Heuristic" ], "cited_by_count": 15, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.ejco.2023.100078" }, { "id": "https://openalex.org/W4283716732", "doi": "10.1016/j.cie.2022.108389", "title": "A bi-objective optimization model for the medical supplies' simultaneous pickup and delivery with drones", "year": 2022, "publication_date": "2022-06-30", "type": "article", "language": "en", "authors": [ "Yuhe Shi", "Yun Jung Lin", "Bo Li", "Rita Yi Man Li" ], "first_author": "Yuhe Shi", "venue": "Computers & Industrial Engineering", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "SAFER", "Pickup", "Sorting", "Computer science", "Genetic algorithm", "Integer programming", "Routing (electronic design automation)", "Operations research", "Engineering", "Simulation", "Computer network" ], "cited_by_count": 122, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.ncbi.nlm.nih.gov/pmc/articles/9245375" }, { "id": "https://openalex.org/W2618465491", "doi": "10.1109/syscon.2017.7934790", "title": "Optimization of a modular drone delivery system", "year": 2017, "publication_date": "2017-04-01", "type": "conference-paper", "language": "en", "authors": [ "Jaihyun Lee" ], "first_author": "Jaihyun Lee", "venue": "2017 Annual IEEE International Systems Conference (SysCon)", "publisher": null, "abstract": "Drones have recently become a promising solution for rapid parcel delivery due to advances in battery technology and navigation systems. Drones have inherited limitations in battery capacity and payload, which make their efficient operation and management a critical problem for a successful delivery system. Adopting modularity in the drone design can provide operational benefits to increase overall fleet readiness and reduce overall fleet size. This paper discusses the potential value of introducing modular design to a drone delivery system. We propose an optimization method for the operation management of a fleet of modular delivery drones. This paper presents simulation results that compare the proposed method with existing operation management methods. The results show that a simple operation management strategy can make a drone delivery system unstable with increasing demand on certain types of modules in the fleet. The results comparing modular and non-modular drone operation also prove that the proposed operation management method with modular drones can save delivery time and energy consumption during a delivery operation over non-modular drones.", "keywords": [ "Drone", "Modular design", "Payload (computing)", "Computer science", "Modularity (biology)", "Systems engineering", "Reliability engineering", "Engineering", "Computer security", "Operating system" ], "cited_by_count": 69, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1109/syscon.2017.7934790" }, { "id": "https://openalex.org/W4285252587", "doi": "10.1109/jiot.2022.3182750", "title": "JRCS: Joint Routing and Charging Strategy for Logistics Drones", "year": 2022, "publication_date": "2022-06-14", "type": "article", "language": "en", "authors": [ "Muhammad Yeasir Arafat", "Sangman Moh" ], "first_author": "Muhammad Yeasir Arafat", "venue": "IEEE Internet of Things Journal", "publisher": "Institute of Electrical and Electronics Engineers", "abstract": "Unmanned aerial vehicles (UAVs), commonly known as drones, are currently being used to combat the COVID-19 pandemic through applications, including the delivery of medical supplies, aerial spraying, and public space monitoring. In a pandemic, drone-based delivery is a promising and highly efficient method to reduce transportation time, cost, and exposure to infection. However, owing to both the limited battery lifetime and the limited functions of UAV in-flight missions, it is difficult to implement multiple deliveries over long distances in a single transportation mission. In this article, we study how to extend the drone flight time with charging stations and ensure multiple deliveries in a single mission. For multiple long-distance deliveries, optimization methods are required to design the delivery area networks of customers, charging stations, and delivery routes. We propose a joint routing and charging strategy (JRCS) comprising three phases to perform multiple deliveries in a single mission. We first split the customers of a delivery area using a clustering algorithm according to their distance from the nearest charging station and the maximum flight range. The second phase provides flight segmentation and intersegment routes between the depot, customer locations, and charging stations based on the maximum flight range and safe flight distance. The joint consideration of drone routes with charging stations minimizes the number of charging stations and ensures safe delivery. Finally, we formulate mixed-integer linear programming to solve the drone delivery route problem. According to simulation results, the proposed JRCS outperforms existing delivery approaches in terms of various performance metrics.", "keywords": [ "Drone", "Computer science", "Cluster analysis", "Routing (electronic design automation)", "Real-time computing", "Range (aeronautics)", "Computer network", "Engineering", "Aerospace engineering", "Artificial intelligence" ], "cited_by_count": 80, "is_retracted": false, "is_paratext": false, "open_access_url": "https://ieeexplore.ieee.org/ielx7/6488907/9926222/09795673.pdf" }, { "id": "https://openalex.org/W3196760408", "doi": "10.1016/j.cie.2021.107648", "title": "A comparative analysis of synchronized truck-and-drone delivery models", "year": 2021, "publication_date": "2021-08-27", "type": "article", "language": "en", "authors": [ "Mohammad Moshref‐Javadi", "Ahmad Hemmati", "Matthias Winkenbach" ], "first_author": "Mohammad Moshref‐Javadi", "venue": "Computers & Industrial Engineering", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Truck", "Routing (electronic design automation)", "Computer science", "Synchronization (alternating current)", "Reduction (mathematics)", "Operations research", "Engineering", "Automotive engineering", "Mathematics", "Computer network" ], "cited_by_count": 87, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.cie.2021.107648" }, { "id": "https://openalex.org/W4403139102", "doi": "10.3390/drones8100550", "title": "A Survey of the Routing Problem for Cooperated Trucks and Drones", "year": 2024, "publication_date": "2024-10-03", "type": "article", "language": "en", "authors": [ "Shuo Dang", "Yao Liu", "Zhihao Luo", "Zhong Liu", "Jianmai Shi" ], "first_author": "Shuo Dang", "venue": "Drones", "publisher": "Multidisciplinary Digital Publishing Institute", "abstract": "The emerging working mode of coordinated trucks and drones has demonstrated significant practical potential in various fields, including logistics and delivery, intelligence surveillance reconnaissance, area monitoring, and patrol. The seamless collaboration between trucks and drones is garnering widespread attention in academia and has emerged as a key technology for achieving efficient and secure transportation. This paper provides a comprehensive and in-depth review of the research status on the routing problem for coordinated trucks and drones, covering aspects such as application background, cooperative modes, configurations, issues that have been taken into consideration, and solution methodologies.", "keywords": [ "Drone", "Truck", "Routing (electronic design automation)", "Computer science", "Aeronautics", "Transport engineering", "Engineering", "Aerospace engineering", "Computer network", "Biology" ], "cited_by_count": 24, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.mdpi.com/2504-446X/8/10/550/pdf?version=1728980281" }, { "id": "https://openalex.org/W4386896894", "doi": "10.1002/nav.22151", "title": "A branch‐and‐price‐and‐cut algorithm for the truck‐drone routing problem with simultaneously delivery and pickup", "year": 2023, "publication_date": "2023-09-20", "type": "article", "language": "en", "authors": [ "Dongwei Li", "Joshua Ignatius", "Dujuan Wang", "Yunqiang Yin", "T.C.E. Cheng" ], "first_author": "Dongwei Li", "venue": "Naval Research Logistics (NRL)", "publisher": "Wiley", "abstract": "Abstract Increasing environmental concerns and e‐commerce has attracted a growing focus on reverse logistics that not only delivers some goods to customers but also picks up other goods from customers. To achieve cost‐efficient and fast deliveries, integrating drones into the delivery and pickup services provides a competitive advantage, which however increases the operational challenges. We consider a truck‐drone routing problem with simultaneous delivery and pickup, where each truck carries a set of heterogeneous drones. Each truck can simultaneously perform its own delivery and pickup, and serve as an intermediate movable depot from which multiple drones can be dispatched to serve customers when the truck arrives at a customer, and the truck must wait until all the drones return. The energy consumption of drones is considered during their flights. All the delivery services must be performed, whereas the pickup services are optional with certain rewards. The objective is to find the synthetic‐routes of the truck‐drone combinations so as to minimize the sum of the assignment cost and the transport cost of the trucks and drones minus the total pickup revenue. To solve the problem, we devise a tailored branch‐and‐price‐and‐cut algorithm incorporating a specialized two‐stage bidirectional labeling algorithm to solve the challenging pricing problem. To enhance the efficiency of the algorithm, we use the subset‐row inequalities to tighten the lower bound, and apply some heuristic pricing strategies to quickly solve the pricing problem. We perform extensive numerical studies to assess the performance of the developed algorithm, analyze the merit of the truck‐drone cooperative service mode over the truck‐only service mode and the superiority of the configuration with heterogeneous drones, and ascertain the impacts of the key model parameters to generate managerial insights. We also show how our model would perform should it be used for the medical supply delivery and pickup in Shenzhen, China.", "keywords": [ "Pickup", "Truck", "Drone", "Computer science", "Revenue", "Routing (electronic design automation)", "Heuristic", "Vehicle routing problem", "Operations research", "Mathematical optimization", "Business", "Engineering" ], "cited_by_count": 41, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1002/nav.22151" }, { "id": "https://openalex.org/W4391031818", "doi": "10.1080/21681015.2024.2304570", "title": "Solving the cumulative capacitated vehicle routing problem with drones", "year": 2024, "publication_date": "2024-01-18", "type": "article", "language": "en", "authors": [ "Imen Hamdi" ], "first_author": "Imen Hamdi", "venue": "Journal of Industrial and Production Engineering", "publisher": "Taylor & Francis", "abstract": "In this paper, we consider the Cumulative Capacitated Vehicle Routing Problem (CCVRP), which is used to model many real-world applications, especially in the area of supplying humanitarian aid after a natural disaster. Interestingly, in this study, Unmanned Aerial Vehicles (UAVs) so-called drones are used to assist the trucks in delivering parcels to customers. Each of them travels to different locations to perform specified tasks and meet periodically with the vehicle from which it takes off to swap its battery. In this paper, a mathematical model is formulated which is then tested with small-sized problems using CPLEX software. Due to the difficulty of solving large instances to optimality, we propose a heuristic algorithm based on a well-established type of cluster-first, route-second approach. Then, it is enhanced by some proposed properties. Hereafter, we develop a minimum spanning tree based-lower bound. Finally, extensive computational experiments are carried out by using instances from the literature. They show the good performance of the proposed heuristic algorithm to solve large instances in a very competitive running time.", "keywords": [ "Computer science", "Drone", "Swap (finance)", "Vehicle routing problem", "Heuristic", "Routing (electronic design automation)", "Truck", "Mathematical optimization", "Travelling salesman problem", "Tree (set theory)", "Artificial intelligence", "Algorithm" ], "cited_by_count": 10, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1080/21681015.2024.2304570" }, { "id": "https://openalex.org/W2894610790", "doi": "10.1287/ijoc.2017.0800", "title": "The Vehicle Routing Problem with Floating Targets: Formulation and Solution Approaches", "year": 2018, "publication_date": "2018-08-01", "type": "article", "language": "en", "authors": [ "Claudio Gambella", "Joe Naoum‐Sawaya", "Bissan Ghaddar" ], "first_author": "Claudio Gambella", "venue": "INFORMS journal on computing", "publisher": "Institute for Operations Research and the Management Sciences", "abstract": "This paper addresses a generalization of the vehicle routing problem in which the pick-up locations of the targets are nonstationary. We refer to this problem as the vehicle routing problem with floating targets and the main characteristic is that targets are allowed to move from their initial home locations while waiting for a vehicle. This problem models new applications in drone routing, ridesharing, and logistics where a vehicle agrees to meet another vehicle or a customer at a location that is away from the designated home location. We propose a Mixed Integer Second Order Cone Program (MISOCP) formulation for the problem, along with valid inequalities for strengthening the continuous relaxation. We further exploit the problem structure using a Lagrangian decomposition and propose an exact branch-and-price algorithm. Computational results on instances with varying characteristics are presented and the results are compared to the solution of the full problem using CPLEX. The proposed valid inequalities reduce the computational time of CPLEX by up to 30% on average while the proposed branch and price is capable of solving instances where CPLEX fails in finding the optimal solution within the imposed time limit.", "keywords": [ "Vehicle routing problem", "Mathematical optimization", "Lagrangian relaxation", "Routing (electronic design automation)", "Limit (mathematics)", "Exploit", "Integer programming", "Branch and cut", "Generalization", "Computer science", "Integer (computer science)", "Relaxation (psychology)" ], "cited_by_count": 37, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1287/ijoc.2017.0800" }, { "id": "https://openalex.org/W2886614777", "doi": "10.1016/j.trb.2018.08.002", "title": "Post-disaster assessment routing problem", "year": 2018, "publication_date": "2018-08-11", "type": "article", "language": "en", "authors": [ "Buse Eylul Oruc", "Bahar Y. Kara" ], "first_author": "Buse Eylul Oruc", "venue": "Transportation Research Part B Methodological", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Computer science", "Population", "Operations research", "Heuristic", "Pareto principle", "Mathematical optimization", "Routing (electronic design automation)", "Engineering", "Artificial intelligence", "Mathematics" ], "cited_by_count": 117, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.trb.2018.08.002" }, { "id": "https://openalex.org/W4401025479", "doi": "10.1016/j.eswa.2024.124880", "title": "Optimization for total energy consumption of drone inspection based on distance-constrained capacitated vehicle routing problem: A study in wind farm", "year": 2024, "publication_date": "2024-07-26", "type": "article", "language": "en", "authors": [ "Xianfei Huang", "Gaocai Wang" ], "first_author": "Xianfei Huang", "venue": "Expert Systems with Applications", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Vehicle routing problem", "Computer science", "Energy consumption", "Routing (electronic design automation)", "Mathematical optimization", "Consumption (sociology)", "Mathematics", "Embedded system", "Engineering" ], "cited_by_count": 23, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.eswa.2024.124880" }, { "id": "https://openalex.org/W4401548012", "doi": "10.1016/j.tre.2024.103709", "title": "Stochastic and robust truck-and-drone routing problems with deadlines: A Benders decomposition approach", "year": 2024, "publication_date": "2024-08-13", "type": "article", "language": "en", "authors": [ "Menghua Deng", "Yuanbo Li", "Jianpeng Ding", "Yanlin Zhou", "Lianming Zhang" ], "first_author": "Menghua Deng", "venue": "Transportation Research Part E Logistics and Transportation Review", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Truck", "Drone", "Benders' decomposition", "Decomposition", "Vehicle routing problem", "Computer science", "Routing (electronic design automation)", "Mathematical optimization", "Operations research", "Transport engineering", "Engineering", "Aerospace engineering" ], "cited_by_count": 35, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.tre.2024.103709" }, { "id": "https://openalex.org/W4403331509", "doi": "10.1016/j.cor.2024.106869", "title": "A branch-cut-and-price approach for the two-echelon vehicle routing problem with drones", "year": 2024, "publication_date": "2024-10-11", "type": "article", "language": "en", "authors": [ "Sylvain Lichau", "Ruslan Sadykov", "Julien François", "Rémy Dupas" ], "first_author": "Sylvain Lichau", "venue": "Computers & Operations Research", "publisher": "Elsevier BV", "abstract": "International audience", "keywords": [ "Vehicle routing problem", "Drone", "Branch and cut", "Branch and price", "Computer science", "Mathematical optimization", "Routing (electronic design automation)", "Integer programming", "Operations research", "Mathematics", "Computer network" ], "cited_by_count": 14, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.cor.2024.106869" }, { "id": "https://openalex.org/W4386476613", "doi": "10.1016/j.eswa.2023.121473", "title": "Computational approaches for solving two-echelon vehicle and UAV routing problems for post-disaster humanitarian operations", "year": 2023, "publication_date": "2023-09-06", "type": "article", "language": "en", "authors": [ "Tasnim Ibn Faiz", "Chrysafis Vogiatzis", "Md. Noor‐E‐Alam" ], "first_author": "Tasnim Ibn Faiz", "venue": "Expert Systems with Applications", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Vehicle routing problem", "Truck", "Computer science", "Operations research", "Humanitarian aid", "Population", "Routing (electronic design automation)", "Humanitarian Logistics", "Service (business)", "Computer security", "Business" ], "cited_by_count": 72, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.eswa.2023.121473" }, { "id": "https://openalex.org/W4408014712", "doi": "10.1016/j.cor.2025.107032", "title": "Autonomous delivery vehicle routing problem with drones based on multiple delivery modes", "year": 2025, "publication_date": "2025-02-27", "type": "article", "language": "en", "authors": [ "Jili Kong", "Hao Wang", "Minhui Xie" ], "first_author": "Jili Kong", "venue": "Computers & Operations Research", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Vehicle routing problem", "Computer science", "Routing (electronic design automation)", "Operations research", "Mathematical optimization", "Computer network", "Mathematics" ], "cited_by_count": 14, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.cor.2025.107032" }, { "id": "https://openalex.org/W3135333785", "doi": "10.3934/jimo.2021037", "title": "Optimal and heuristic algorithms for the multi-objective vehicle routing problem with drones for military surveillance operations", "year": 2021, "publication_date": "2021-03-03", "type": "article", "language": "en", "authors": [ "Namsu Ahn", "Soochan Kim" ], "first_author": "Namsu Ahn", "venue": "Journal of Industrial and Management Optimization", "publisher": "American Institute of Mathematical Sciences", "abstract": "During military operations, obtaining information on remote battlefields is essential and recent advances in unmanned aerial vehicle technology have led to the use of drones to view battlefields. However, the use of drones in military operations introduces the new problem of determining travel routes for the drones. This type of problem is similar to the well-known classical vehicle routing problem, but the main difference is its objective function. For maintenance purposes, a minimized difference in travel distances is preferred. In addition, obtaining a shorter route in terms of travel distance is important. In this research, we propose a mathematical formulation and an optimal algorithm for the problem and suggest a simple heuristic to handle the large size instance of the problem. The computational results indicate that this algorithm can solve the real-scale instances of the problem, and the heuristic exhibits good performance even when the instance size of the problem is large.", "keywords": [ "Drone", "Heuristic", "Computer science", "Routing (electronic design automation)", "Vehicle routing problem", "Mathematical optimization", "Simple (philosophy)", "Scale (ratio)", "Algorithm", "Artificial intelligence", "Mathematics" ], "cited_by_count": 17, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.3934/jimo.2021037" }, { "id": "https://openalex.org/W4408252705", "doi": "10.1016/j.apm.2025.116074", "title": "Mathematical models for truck-drone routing problem: Literature review", "year": 2025, "publication_date": "2025-03-09", "type": "article", "language": "en", "authors": [ "He Luo", "Jie Duan", "Guoqiang Wang" ], "first_author": "He Luo", "venue": "Applied Mathematical Modelling", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Truck", "Routing (electronic design automation)", "Computer science", "Vehicle routing problem", "Operations research", "Mathematical optimization", "Engineering", "Aerospace engineering", "Mathematics", "Computer network" ], "cited_by_count": 27, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.apm.2025.116074" }, { "id": "https://openalex.org/W3135653208", "doi": "10.1016/j.ejor.2021.02.039", "title": "Improved delivery policies for future drone-based delivery systems", "year": 2021, "publication_date": "2021-03-02", "type": "article", "language": "en", "authors": [ "Heng Chen", "Zhangchen Hu", "Senay Solak" ], "first_author": "Heng Chen", "venue": "European Journal of Operational Research", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Markov decision process", "Profit (economics)", "Computer science", "Order (exchange)", "Operations research", "Business", "Service (business)", "Service delivery framework", "Risk analysis (engineering)", "Operations management", "Markov process" ], "cited_by_count": 82, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.ejor.2021.02.039" }, { "id": "https://openalex.org/W2626731019", "doi": "10.5194/nhess-17-1939-2017", "title": "Brief communication: Vehicle routing problem and UAV application in the post-earthquake scenario", "year": 2017, "publication_date": "2017-11-15", "type": "article", "language": "en", "authors": [ "Marco Cannioto", "Antonino D’Alessandro", "Giosuè Lo Bosco", "Salvatore Scudero", "Giovanni Vitale" ], "first_author": "Marco Cannioto", "venue": "Natural hazards and earth system sciences", "publisher": "Copernicus Publications", "abstract": "Abstract. In this paper we simulate unmanned aerial vehicle (UAV) recognition after a possible case of diffuse damage after a seismic event in the town of Acireale (Sicily, Italy). Given a set of sites (84 relevant buildings) and the range of the UAV, we are able to find a number of vehicles to employ and the shortest survey path. The problem of finding the shortest survey path is an operational research problem called the vehicle routing problem (VRP). which has a solution that is known to be computationally time-consuming. We used the simulated annealing (SA) heuristic, which is able to provide stable solutions in a relatively short computing time. We also examined the distribution of the cost of the solutions varying the depot on a regular grid in order to find the best area for executing the survey.", "keywords": [ "Vehicle routing problem", "Shortest path problem", "Computer science", "Simulated annealing", "Heuristic", "Grid", "Routing (electronic design automation)", "Range (aeronautics)", "Set (abstract data type)", "Path (computing)", "Event (particle physics)", "Real-time computing" ], "cited_by_count": 25, "is_retracted": false, "is_paratext": false, "open_access_url": "https://nhess.copernicus.org/articles/17/1939/2017/nhess-17-1939-2017.pdf" }, { "id": "https://openalex.org/W4205292877", "doi": "10.1002/net.22087", "title": "The multivisit drone routing problem with edge launches: An iterative approach with discrete and continuous improvements", "year": 2022, "publication_date": "2022-01-04", "type": "article", "language": "en", "authors": [ "Adriano Masone", "Stefan Poikonen", "Bruce Golden" ], "first_author": "Adriano Masone", "venue": "Networks", "publisher": "Wiley", "abstract": "Abstract In recent years, the usage of drones in last‐mile logistics has stirred great interest in the operations research community. Many papers have considered schemes of hybrid truck‐and‐drone delivery. In this paper, we focus on the Multivisit Drone Routing Problem with Edge Launches (MVDRP‐EL) which assumes: a heterogenous set of packages, a drone capable of carrying multiple packages at a time and that can be launched and retrieved along an edge, a flexible launch/retrieval site set, and a user‐defined energy depletion function. We believe this paper is the first to exploit edge launch ability through a global continuous approach. In this context, we propose an original formulation based on the Covering Salesman Problem to compute a valid lower bound for the problem and an iterative solution method to determine a MVDRP‐EL solution with quality launch/retrieval sites along the road network edges. Each iteration of the solution method consists of two phases. In the first phase, the road network edges are discretized to obtain launch/retrieval sites, and a first solution is determined. In the second phase, the truck route is set and we reduce the completion time by carefully synchronizing truck and drone routes by solving an original Mixed Integer Second Order Cone Program. The lower bound formulation and the proposed method have been tested on several instances and results indicate the effectiveness of the proposed method and the potential value of launching along an edge, respectively.", "keywords": [ "Drone", "Synchronizing", "Computer science", "Context (archaeology)", "Truck", "Enhanced Data Rates for GSM Evolution", "Set (abstract data type)", "Routing (electronic design automation)", "Mathematical optimization", "Mathematics", "Computer network", "Engineering" ], "cited_by_count": 35, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1002/net.22087" }, { "id": "https://openalex.org/W3153526484", "doi": "10.1016/j.ifacol.2020.12.2004", "title": "A Novel Mathematical Model for a Cloud-Based Drone Enabled Vehicle Routing Problem considering Multi-Echelon Supply Chain", "year": 2020, "publication_date": "2020-01-01", "type": "article", "language": "en", "authors": [ "Fatemeh Farajzadeh", "Amirhossein Moadab", "Omid Fatahi Valilai", "Mahmoud Houshmand" ], "first_author": "Fatemeh Farajzadeh", "venue": "IFAC-PapersOnLine", "publisher": "Elsevier BV", "abstract": "In recent years, the product delivery system has faced a significant amount of changes with reducing cost and waiting time of last-mile delivery. Unmanned aerial vehicles, or drones, have the potential to deal with these issues effectively. This paper developed a novel mathematical formulation to investigate the optimum routing between various types of nodes in a multi-echelon supply chain, including third-party logistics companies (3PL), warehouses, and consumers. A conceptual model is represented in the paper to comprehend the readers better, and eventually, the novelty of the developed model is discussed further by explaining the concept of solving.", "keywords": [ "Drone", "Supply chain", "Computer science", "Novelty", "Vehicle routing problem", "Cloud computing", "Operations research", "Product (mathematics)", "Routing (electronic design automation)", "Stackelberg competition", "Conceptual model", "Industrial engineering" ], "cited_by_count": 21, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.ifacol.2020.12.2004" }, { "id": "https://openalex.org/W4378530167", "doi": "10.1016/j.cie.2023.109340", "title": "A GRASP/VND algorithm for the energy minimizing drone routing problem with pickups and deliveries", "year": 2023, "publication_date": "2023-05-27", "type": "article", "language": "en", "authors": [ "Nikolaos A. Kyriakakis", "Stylianos Aronis", "Magdalene Marinaki", "Yannis Marinakis" ], "first_author": "Nikolaos A. Kyriakakis", "venue": "Computers & Industrial Engineering", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Computer science", "Benchmark (surveying)", "Vehicle routing problem", "GRASP", "Energy consumption", "Supply chain", "Mathematical optimization", "Operations research", "Routing (electronic design automation)", "Business", "Engineering" ], "cited_by_count": 30, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.cie.2023.109340" }, { "id": "https://openalex.org/W4214815674", "doi": "10.1016/j.cie.2022.108057", "title": "Locating platforms and scheduling a fleet of drones for emergency delivery of perishable items", "year": 2022, "publication_date": "2022-03-04", "type": "article", "language": "en", "authors": [ "Monica Gentili", "Pitu B. Mirchandani", "Alessandro Agnetis", "Zabih Ghelichi" ], "first_author": "Monica Gentili", "venue": "Computers & Industrial Engineering", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Operations research", "Computer science", "Scheduling (production processes)", "Perishability", "Function (biology)", "Real-time computing", "Engineering", "Operations management", "Business" ], "cited_by_count": 83, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.cie.2022.108057" }, { "id": "https://openalex.org/W4226256297", "doi": "10.1016/j.procs.2022.01.339", "title": "A novel mathematical approach for the Truck-and-Drone Location-Routing Problem", "year": 2022, "publication_date": "2022-01-01", "type": "conference-paper", "language": "en", "authors": [ "Laura Castro Montaña", "Laura Malagón-Alvarado", "Paola Andrea Miranda", "Mateo Montealegre Arboleda", "Elyn Lizeth Solano Charris", "Carlos Alberto Vega-Mejía" ], "first_author": "Laura Castro Montaña", "venue": "Procedia Computer Science", "publisher": "Elsevier BV", "abstract": "During the last decade, e-commerce has increased last-mile deliveries, impacting the (CO2) emissions footprint. Considering this environmental impact, sustainable technologies have emerged for transport operations, e.g., drones and electric vehicles. This paper deals with the Location-Routing Problem for delivering orders to a set of customers. The problem aims to minimize the total CO2 emissions due to freight transportation in last-mile deliveries with Trucks-and-Drones. A mathematical model is proposed for solving the problem. We test the model in different scenarios varying the number of clients (between 10 and 25), the number of trucks and drones (between 4 and 12 and between 5 and 13, respectively), and the available depots (i.e., between 5 and 15 parking lots). Our results provide insights on how shifting to cleaner transportation technologies can aid in the reduction of the carbon footprint of distribution activities and present a preamble of the significant impact that UAVs have in parcel delivery routing problems.", "keywords": [ "Drone", "Truck", "Computer science", "Carbon footprint", "Routing (electronic design automation)", "Vehicle routing problem", "Last mile (transportation)", "Operations research", "Transport engineering", "Footprint", "Mile", "Greenhouse gas" ], "cited_by_count": 23, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.sciencedirect.com/science/article/pii/S1877050922003489/pdf" }, { "id": "https://openalex.org/W2980631912", "doi": "10.1016/j.procs.2019.09.158", "title": "On a cooperative truck-and-drone delivery system", "year": 2019, "publication_date": "2019-01-01", "type": "conference-paper", "language": "en", "authors": [ "Gloria Cerasela Crişan", "Elena Nechita" ], "first_author": "Gloria Cerasela Crişan", "venue": "Procedia Computer Science", "publisher": "Elsevier BV", "abstract": "During the last decade drones, or unmanned aerial vehicles, have been intensively studied from various perspectives. Important advances in drone technology and numerous experiments concerning drone infusion in various services and businesses have generated intensive research on modeling delivery systems that include drones. Combinatorial Optimization Problems such as Traveling Salesman Problem and Vehicle Routing Problem have been extended by considering drones and optimize various cost functions. This paper introduces a new greedy heuristic for minimizing the total transportation time of a truck-and-drone delivery system, proposes a new cost function to include the flying time of the drone and performs a comparison with previous similar approaches. Experiments with different parameter settings on two large area Traveling Salesman Problem instances show significant total time savings for the proposed approach and supports future research when considering real-world scenarios.", "keywords": [ "Drone", "Travelling salesman problem", "Computer science", "Truck", "Heuristic", "Vehicle routing problem", "Greedy algorithm", "Routing (electronic design automation)", "2-opt", "Operations research", "Function (biology)", "Traveling purchaser problem" ], "cited_by_count": 48, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.sciencedirect.com/science/article/pii/S1877050919313365/pdf" }, { "id": "https://openalex.org/W4388773809", "doi": "10.1016/j.eswa.2023.122485", "title": "Data-driven robust optimization for a multi-trip truck-drone routing problem", "year": 2023, "publication_date": "2023-11-16", "type": "article", "language": "en", "authors": [ "Mohsen Roytvand Ghiasvand", "Donya Rahmani", "Mohammad Moshref‐Javadi" ], "first_author": "Mohsen Roytvand Ghiasvand", "venue": "Expert Systems with Applications", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Computer science", "Vehicle routing problem", "Cluster analysis", "Drone", "Truck", "Robust optimization", "Column generation", "Mathematical optimization", "Routing (electronic design automation)", "Newsvendor model", "Machine learning", "Supply chain" ], "cited_by_count": 30, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.eswa.2023.122485" }, { "id": "https://openalex.org/W2970684949", "doi": "10.11606/d.55.2019.tde-29082019-091040", "title": "The Vehicle Routing Problem with Drones", "year": 2019, "publication_date": "2019-08-29", "type": "dissertation", "language": "en", "authors": [ "Joao Guilherme Cavalcanti Costa" ], "first_author": "Joao Guilherme Cavalcanti Costa", "venue": null, "publisher": null, "abstract": "In this Dissertation, the Vehicle Routing Problem with Drones (VRPD), motivated by the growing interest on Unmanned Aerial Vehicles (UAVs, or Drones) by the industry and their applications in logistics is studied.A pioneer work by (MURRAY; CHU, 2015) shows a combination between UAV and a truck to deliver products, presenting an adaptation to the Traveling Salesman Problem (TSP).After a literature review, an extension of the model from Murray and Chu (2015) we present a model for the problem with multiple vehicles.This model is developed as a Mixed Integer Linear Programming (MILP) problem and solved with the solver CPLEX.A heuristic based on a Hybrid Genetic Algorithm (HGA) is also developed and presented.Our results show that the use of drones reduces the total mileage of the trucks by a significant percentage.", "keywords": [ "Travelling salesman problem", "Drone", "Vehicle routing problem", "Solver", "Truck", "Integer programming", "Routing (electronic design automation)", "Heuristic", "Computer science", "Mathematical optimization", "Genetic algorithm", "2-opt" ], "cited_by_count": 5, "is_retracted": false, "is_paratext": false, "open_access_url": "http://www.teses.usp.br/teses/disponiveis/55/55134/tde-29082019-091040/publico/JoaoGuilhermeCavalcantiCosta_revisada.pdf" }, { "id": "https://openalex.org/W4360619128", "doi": "10.1007/s40305-023-00471-7", "title": "The Multi-visits Drone-Vehicle Routing Problem with Simultaneous Pickup and Delivery Service", "year": 2023, "publication_date": "2023-03-23", "type": "book-chapter", "language": "en", "authors": [ "Si Zhang", "Lu Li" ], "first_author": "Si Zhang", "venue": "Journal of the Operations Research Society of China", "publisher": "Springer Science+Business Media", "abstract": null, "keywords": [ "Drone", "Travelling salesman problem", "Vehicle routing problem", "Pickup", "Computer science", "Heuristics", "Schedule", "Service (business)", "Scalability", "Routing (electronic design automation)", "Mathematical optimization", "Operations research" ], "cited_by_count": 12, "is_retracted": false, "is_paratext": false, "open_access_url": "https://link.springer.com/content/pdf/10.1007/s40305-023-00471-7.pdf" }, { "id": "https://openalex.org/W4387747530", "doi": "10.1016/j.ejor.2023.10.021", "title": "The multi-visit drone-assisted pickup and delivery problem with time windows", "year": 2023, "publication_date": "2023-10-18", "type": "article", "language": "en", "authors": [ "Shanshan Meng", "Yanru Chen", "Dong Li" ], "first_author": "Shanshan Meng", "venue": "European Journal of Operational Research", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Computer science", "Truck", "Vehicle routing problem", "Context (archaeology)", "Operations research", "Pickup", "Mathematical optimization", "Routing (electronic design automation)", "Engineering", "Mathematics", "Automotive engineering" ], "cited_by_count": 80, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.ejor.2023.10.021" }, { "id": "https://openalex.org/W4315489741", "doi": "10.1016/j.swevo.2023.101246", "title": "A GV-drone arc routing approach for urban traffic patrol by coordinating a ground vehicle and multiple drones", "year": 2023, "publication_date": "2023-01-10", "type": "article", "language": "en", "authors": [ "Binjie Xu", "Kexin Zhao", "Qizhang Luo", "Guohua Wu", "Witold Pedrycz" ], "first_author": "Binjie Xu", "venue": "Swarm and Evolutionary Computation", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Computer science", "Simulated annealing", "Patrolling", "Real-time computing", "Algorithm" ], "cited_by_count": 47, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.swevo.2023.101246" }, { "id": "https://openalex.org/W3117135908", "doi": "10.1002/net.22015", "title": "Trucks and drones cooperation in the last‐mile delivery process", "year": 2020, "publication_date": "2020-12-24", "type": "article", "language": "en", "authors": [ "Luigi Di Puglia Pugliese", "Giusy Macrina", "Francesca Guerriero" ], "first_author": "Luigi Di Puglia Pugliese", "venue": "Networks", "publisher": "Wiley", "abstract": "Abstract We address the problem of routing a fleet of trucks equipped with unmanned aerial vehicles, commonly known as drones, to perform deliveries in last‐mile delivery process. The customers can be served by either a truck or a drone within the respective time window of each. Each capacitated truck carries drones that can be launched to perform deliveries. The drone takes off from a truck located either at a customer or at the depot and it must land on the same truck after visiting a customer to be served. The aim is to serve all customers at minimum cost, under time window, capacity, and flying endurance constraints. We formulate the problem as a mixed integer linear program (MILP) and develop a heuristic procedure where a two‐phase strategy is embedded in a multi‐start framework. The computational results are carried out on instances generated by starting from vehicle routing problem with time windows benchmarks. We analyze the behavior of the considered transportation system by mean of the solutions provided by the MILP. The proposed formulation is able to solve instances with up to 15 customers. The solutions of the MILP are used as benchmark to assess the effectiveness of the proposed heuristic procedure.", "keywords": [ "Truck", "Drone", "Vehicle routing problem", "Computer science", "Benchmark (surveying)", "Heuristic", "Last mile (transportation)", "Integer programming", "Process (computing)", "Routing (electronic design automation)", "Integer (computer science)", "Linear programming" ], "cited_by_count": 56, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1002/net.22015" }, { "id": "https://openalex.org/W3198959149", "doi": "10.1177/03611981211032219", "title": "A Solution to Drone Routing Problems using Docking Stations for Pickup and Delivery Services", "year": 2021, "publication_date": "2021-09-14", "type": "article", "language": "en", "authors": [ "Murugaiyan Pachayappan", "Vijayakumar Sudhakar" ], "first_author": "Murugaiyan Pachayappan", "venue": "Transportation Research Record Journal of the Transportation Research Board", "publisher": "SAGE Publishing", "abstract": "The paper proposes a mathematical model and a heuristic solution for planning optimal pickup and delivery routes in drone operations. In the proposed system, the drone is synchronized with the docking station for a charge during pickup and delivery services within a definite set distance radius. The optimization model presented here minimizes the distance traveled by the drone to complete the scheduled services. It also ensures the optimal use of the drone’s battery capacity, ensuring the safe return of the drone without running out of battery during operations. The solution quality and the computational performance of the Mixed-Integer Linear Programming (MILP) model proved satisfactory in addressing a variety of problems. A real-world case study is conducted to enumerate the practical implications which will be of benefit to drone service providers in the field of logistics.", "keywords": [ "Drone", "Pickup", "Integer programming", "Computer science", "Heuristic", "Linear programming", "Routing (electronic design automation)", "Vehicle routing problem", "Mathematical optimization", "Operations research", "Simulation", "Engineering" ], "cited_by_count": 28, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1177/03611981211032219" }, { "id": "https://openalex.org/W4400768492", "doi": "10.3390/su16146145", "title": "The Multi-Visit Vehicle Routing Problem with Drones under Carbon Trading Mechanism", "year": 2024, "publication_date": "2024-07-18", "type": "article", "language": "en", "authors": [ "Qinxin Xiao", "Jiaojiao Gao" ], "first_author": "Qinxin Xiao", "venue": "Sustainability", "publisher": "Multidisciplinary Digital Publishing Institute", "abstract": "In the context of the carbon trading mechanism, this study investigated a multi-visit vehicle routing problem with a truck-drone collaborative delivery model. This issue involves the route of a truck fleet and drones, each truck equipped with a drone, allowing drones to provide services to multiple customers. Considering the carbon emissions during both the truck’s travel and the drone’s flight, this study established a mixed integer programming model to minimize the sum of fixed costs, transportation costs, and carbon trading costs. A two-stage heuristic algorithm was proposed to solve the problem. The first stage employed a “Scanning and Heuristic Insertion” algorithm to generate an initial feasible solution. In the second stage, an enhanced variable neighborhood search algorithm was designed with problem-specific neighborhood structures and customized search strategies. The effectiveness of the proposed algorithm was validated with numerical experiments. Additionally, this study analyzed the impact of various factors on carbon trading costs, revealing that there exists an optimal combination of drones and trucks. It was also observed that changes in carbon quotas do not affect carbon emissions but do alter the total delivery costs. These results provide insights for logistics enterprise operations management and government policy-making.", "keywords": [ "Drone", "Mechanism (biology)", "Vehicle routing problem", "Routing (electronic design automation)", "Computer science", "Business", "Computer network", "Biology" ], "cited_by_count": 11, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.mdpi.com/2071-1050/16/14/6145/pdf?version=1721381044" }, { "id": "https://openalex.org/W4281660045", "doi": "10.1016/j.ejor.2022.05.046", "title": "Robust drone selective routing in humanitarian transportation network assessment", "year": 2022, "publication_date": "2022-06-02", "type": "article", "language": "en", "authors": [ "Guowei Zhang", "Ning Jia", "Ning Yan Zhu", "Yossiri Adulyasak", "Shoufeng Ma" ], "first_author": "Guowei Zhang", "venue": "European Journal of Operational Research", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Vehicle routing problem", "Computer science", "Routing (electronic design automation)", "Operations research", "Business", "Computer network", "Computer security", "Aeronautics", "Engineering" ], "cited_by_count": 65, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.ejor.2022.05.046" }, { "id": "https://openalex.org/W4224044750", "doi": "10.3390/su14084651", "title": "Optimal Model and Algorithm of Medical Materials Delivery Drone Routing Problem under Major Public Health Emergencies", "year": 2022, "publication_date": "2022-04-13", "type": "article", "language": "en", "authors": [ "Lijing Du", "Xiaohuan Li", "Yuan Gan", "Kaijun Leng" ], "first_author": "Lijing Du", "venue": "Sustainability", "publisher": "Multidisciplinary Digital Publishing Institute", "abstract": "To reduce distribution risk and improve the efficiency of medical materials delivery under major public health emergencies, this paper introduces a drone routing problem with time windows. A mixed-integer programming model is formulated considering contactless delivery, total travel time, and customer service time windows. Utilizing Dantzig–Wolfe decomposition, the proposed optimization model is converted into a path-based master problem and a pricing subproblem based on an elementary shortest path problem with resource constraints. We embed the pulse algorithm into a column generation framework to solve the proposed model. The effectiveness of the model and algorithm is verified by addressing different scales of Solomon datasets. A case study on COVID-19 illustrates the application of the proposed model and algorithm in practice. We also perform a sensitivity analysis on the drone capacity that may affect the total distribution time. The experimental results enrich the research related to vehicle routing problem models and algorithms under major public health emergencies and provide optimized relief distribution solutions for decision-makers of emergency logistics.", "keywords": [ "Vehicle routing problem", "Column generation", "Computer science", "Drone", "Path (computing)", "Shortest path problem", "Routing (electronic design automation)", "Integer programming", "Sensitivity (control systems)", "Resource (disambiguation)", "Operations research", "Mathematical optimization" ], "cited_by_count": 35, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.mdpi.com/2071-1050/14/8/4651/pdf?version=1649848456" }, { "id": "https://openalex.org/W4387643390", "doi": "10.1016/j.ejor.2023.10.015", "title": "Drone routing problem with swarm synchronization", "year": 2023, "publication_date": "2023-10-14", "type": "article", "language": "en", "authors": [ "Hongqi Li", "Feilong Wang", "Zhuopeng Zhan" ], "first_author": "Hongqi Li", "venue": "European Journal of Operational Research", "publisher": "Elsevier BV", "abstract": "The advantages of rotary-wing drone (RWD) delivery modes have already been delineated. However, single-unit RWDs do not completely solve real problems in last-mile parcel deliveries because of limited payload capacity and flight endurance. Currently, drone swarm technology is being rapidly developed. An RWD swarm can deliver heavy or multiple packages to customers; therefore, the RWD swarm strategy can address the payload capacity limitation of RWDs. Herein, an RWD delivery mode that involves dynamic swarms of RWDs in addition to single-unit RWDs is explored. The “dynamic” characteristic permits the RWD members in swarms to vary by coupling/decoupling operations at nodes. From the routing plan perspective, using RWD swarms for last-mile parcel deliveries is challenging; accordingly, we introduce a swarm synchronization mode that involves interactions among RWD routes. We formally define the drone routing problem with swarm synchronization (DRP-SS) and develop a mixed-integer linear programming model, which considers the decision on RWD swarms and multi trips. An adaptive large neighborhood search heuristic with specific operators is proposed. In the computational experiments, both small- and large-scale instances are used to validate the effectiveness of the mathematical formulation and the heuristic. Several managerial insights are obtained regarding the influence of detours, the utilization of RWD swarms, and the benefits of multi trips. The DRP-SS model and solution method can be used to estimate the performance of the selection of RWD swarms in practical situations.", "keywords": [ "Swarm behaviour", "Computer science", "Payload (computing)", "Mathematical optimization", "Drone", "Heuristic", "Scheduling (production processes)", "Synchronization (alternating current)", "Reservation", "Distributed computing", "Artificial intelligence", "Mathematics" ], "cited_by_count": 14, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.ejor.2023.10.015" }, { "id": "https://openalex.org/W3108381699", "doi": "10.1109/access.2020.3040790", "title": "Commanding Cooperative UGV-UAV With Nested Vehicle Routing for Emergency Resource Delivery", "year": 2020, "publication_date": "2020-01-01", "type": "article", "language": "en", "authors": [ "Gao Wei", "Junren Luo", "Wanpeng Zhang", "Yuan Weilin", "Zhiyong Liao" ], "first_author": "Gao Wei", "venue": "IEEE Access", "publisher": "Institute of Electrical and Electronics Engineers", "abstract": "Unmanned ground vehicles (UGVs) and unmanned aerial vehicles (UAVs) have been widely used in delivery. In the context of the COVID-2019, in order to control the development of the epidemic, many places have adopted measures to isolate and close the area once a confirmed case is found. While reducing the contact between people, it also blocks the normal driving of vehicles. Only by changing the traditional logistics and distribution methods can customers who have been in a closed and isolated area for a long time be served. Therefore, we use the Cooperative UGV-UAV to achieve it. In this article, when commanding cooperative UGV and UAV for emergency resource delivery, we mainly focus on two questions: how to accept the operation order (OPORD) from the commander, how to generate a nested vehicle routing planning. We first employ one intelligent task understanding module to drive the intelligent unmanned vehicles to accept and process the C-BML (Coalition Battle Management Language) formatted OPORD with 5W (what, who, where, why, when) elements. Then, we slove the nested vehicle routing planning problem as a mixed integer linear program (MILP) with the outputs of what is the UGV route, what is the UGV sortie, and how to control the customers' distribution between the UGV and the UAV. Experimental results of random instances and case study show that using the iterative improvement algorithm increase the speed rate of solving more than 10%.", "keywords": [ "Unmanned ground vehicle", "Computer science", "Context (archaeology)", "Routing (electronic design automation)", "Task (project management)", "Resource allocation", "Vehicle routing problem", "Resource (disambiguation)", "Real-time computing", "Operations research", "Artificial intelligence", "Computer network" ], "cited_by_count": 56, "is_retracted": false, "is_paratext": false, "open_access_url": "https://ieeexplore.ieee.org/ielx7/6287639/6514899/09272274.pdf" }, { "id": "https://openalex.org/W4281718519", "doi": "10.1007/s10846-022-01632-1", "title": "Scheduling Diagnostic Testing Kit Deliveries with the Mothership and Drone Routing Problem", "year": 2022, "publication_date": "2022-06-01", "type": "article", "language": "en", "authors": [ "Hyung Jin Park", "Reza Mirjalili", "Murray J. Côté", "Gino J. Lim" ], "first_author": "Hyung Jin Park", "venue": "Journal of Intelligent & Robotic Systems", "publisher": "Springer Science+Business Media", "abstract": null, "keywords": [ "Drone", "Scheduling (production processes)", "Computer science", "Schedule", "Job shop scheduling", "Pandemic", "Column generation", "Real-time computing", "Coronavirus disease 2019 (COVID-19)", "Simulation", "Engineering", "Medicine" ], "cited_by_count": 23, "is_retracted": false, "is_paratext": false, "open_access_url": "https://link.springer.com/content/pdf/10.1007/s10846-022-01632-1.pdf" }, { "id": "https://openalex.org/W4221016150", "doi": "10.1016/j.ress.2022.108457", "title": "Optimal routes and aborting strategies of trucks and drones under random attacks", "year": 2022, "publication_date": "2022-03-12", "type": "article", "language": "en", "authors": [ "Rui Qi Yan", "Xiaoping Zhu", "Xiaoning Zhu", "Rui Peng" ], "first_author": "Rui Qi Yan", "venue": "Reliability Engineering & System Safety", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Truck", "Drone", "Computer science", "Computer security", "Aeronautics", "Engineering", "Operations research", "Aerospace engineering" ], "cited_by_count": 62, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.ress.2022.108457" }, { "id": "https://openalex.org/W2615484421", "doi": "10.3390/s17051144", "title": "A Two-Echelon Cooperated Routing Problem for a Ground Vehicle and Its Carried Unmanned Aerial Vehicle", "year": 2017, "publication_date": "2017-05-17", "type": "article", "language": "en", "authors": [ "Zhihao Luo", "Zhong Liu", "Jianmai Shi" ], "first_author": "Zhihao Luo", "venue": "Sensors", "publisher": "Multidisciplinary Digital Publishing Institute", "abstract": "In this paper, a two-echelon cooperated routing problem for the ground vehicle (GV) and its carried unmanned aerial vehicle (UAV) is investigated, where the GV travels on the road network and its UAV travels in areas beyond the road to visit a number of targets unreached by the GV. In contrast to the classical two-echelon routing problem, the UAV has to launch and land on the GV frequently to change or charge its battery while the GV is moving on the road network. A new 0-1 integer programming model is developed to formulate the problem, where the constraints on the spatial and temporal cooperation of GV and UAV routes are included. Two heuristics are proposed to solve the model: the first heuristic (H1) constructs a complete tour for all targets and splits it by GV routes, while the second heuristic (H2) constructs the GV tour and assigns UAV flights to it. Random instances with six different sizes (25-200 targets, 12-80 rendezvous nodes) are used to test the algorithms. Computational results show that H1 performs slightly better than H2, while H2 uses less time and is more stable.", "keywords": [ "Heuristics", "Heuristic", "Routing (electronic design automation)", "Computer science", "Integer programming", "Vehicle routing problem", "Rendezvous", "Mathematical optimization", "Real-time computing", "Algorithm", "Computer network", "Artificial intelligence" ], "cited_by_count": 178, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.mdpi.com/1424-8220/17/5/1144/pdf?version=1495015202" }, { "id": "https://openalex.org/W2949957913", "doi": "10.1007/978-3-030-21803-4_101", "title": "A Genetic Algorithm for Solving the Truck-Drone-ATV Routing Problem", "year": 2019, "publication_date": "2019-06-14", "type": "conference-paper", "language": "en", "authors": [ "Mahdi Moeini", "Hagen Salewski" ], "first_author": "Mahdi Moeini", "venue": "Advances in intelligent systems and computing", "publisher": "Springer Nature", "abstract": null, "keywords": [ "Drone", "Truck", "Grid", "Computer science", "Vehicle routing problem", "Merge (version control)", "Routing (electronic design automation)", "Engineering", "Operations research", "Computer network", "Geography", "Aerospace engineering" ], "cited_by_count": 20, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1007/978-3-030-21803-4_101" }, { "id": "https://openalex.org/W4213437443", "doi": "10.1016/j.ijdrr.2022.102859", "title": "Coordinated routing system for fire detection by patrolling trucks with drones", "year": 2022, "publication_date": "2022-02-24", "type": "article", "language": "en", "authors": [ "Maryam Momeni", "Hamed Soleimani", "Shahrooz Shahparvari", "Behrouz Afshar-Nadjafi" ], "first_author": "Maryam Momeni", "venue": "International Journal of Disaster Risk Reduction", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Patrolling", "Truck", "Routing (electronic design automation)", "Vehicle routing problem", "Computer science", "Integer programming", "Transport engineering", "Operations research", "Constraint (computer-aided design)", "Process (computing)", "Engineering" ], "cited_by_count": 53, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.ijdrr.2022.102859" }, { "id": "https://openalex.org/W3043824816", "doi": "10.1504/ejie.2020.108581", "title": "Maximising reward from a team of surveillance drones: a simheuristic approach to the stochastic team orienteering problem", "year": 2020, "publication_date": "2020-01-01", "type": "article", "language": "en", "authors": [ "Javier Panadero", "Angel Alejandro Juan", "Christopher Bayliss", "Christine S. M. Currie" ], "first_author": "Javier Panadero", "venue": "European J of Industrial Engineering", "publisher": "Inderscience Publishers", "abstract": "We consider the problem of routing a team of unmanned aerial vehicles (drones) being used to take surveillance observations of target locations, where the value of information at each location is different and not all locations need be visited. As a result, this problem can be described as a stochastic team orienteering problem (STOP), in which travel times are modelled as random variables following generic probability distributions. The orienteering problem is a vehicle-routing problem in which each of a set of customers can be visited either just once or not at all within a limited time period. In order to solve this STOP, a simheuristic algorithm based on an original and fast heuristic is developed. This heuristic is then extended into a variable neighbourhood search (VNS) metaheuristic. Finally, simulation is incorporated into the VNS framework to transform it into a simheuristic algorithm, which is then employed to solve the STOP. [Received 5 January 2019; Revised 15 June 2019; Accepted 13 October 2019]", "keywords": [ "Orienteering", "Metaheuristic", "Heuristic", "Vehicle routing problem", "Computer science", "Operations research", "Variable neighborhood search", "Drone", "Mathematical optimization", "Set (abstract data type)", "Routing (electronic design automation)", "Engineering" ], "cited_by_count": 78, "is_retracted": false, "is_paratext": false, "open_access_url": "https://eprints.soton.ac.uk/444063/1/Currie_A_VNS_SimHeu_for_TOPST_EJIE_blind_.pdf" }, { "id": "https://openalex.org/W4401644320", "doi": "10.1016/j.eswa.2024.124996", "title": "A modelling and solution approach for wind-affected drone-truck routing problem under uncertainty", "year": 2024, "publication_date": "2024-08-16", "type": "article", "language": "en", "authors": [ "Mercedeh Dodge", "S.​A. MirHassani", "Farnaz Hooshmand" ], "first_author": "Mercedeh Dodge", "venue": "Expert Systems with Applications", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Truck", "Computer science", "Routing (electronic design automation)", "Vehicle routing problem", "Wind speed", "Operations research", "Mathematical optimization", "Aeronautics", "Automotive engineering", "Meteorology", "Computer network" ], "cited_by_count": 27, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.eswa.2024.124996" }, { "id": "https://openalex.org/W4291940579", "doi": "10.3390/su14169978", "title": "A Variable Neighborhood Descent Matheuristic for the Drone Routing Problem with Beehives Sharing", "year": 2022, "publication_date": "2022-08-12", "type": "article", "language": "en", "authors": [ "Maria Elena Bruni", "Sara Khodaparasti" ], "first_author": "Maria Elena Bruni", "venue": "Sustainability", "publisher": "Multidisciplinary Digital Publishing Institute", "abstract": "In contemporary urban logistics, drones will become a preferred transportation mode for last-mile deliveries, as they have shown commercial potential and triple-bottom-line performance. Drones, in fact, address many challenges related to congestion and emissions and can streamline the last leg of the supply chain, while maintaining economic performance. Despite the common conviction that drones will reshape the future of deliveries, numerous hurdles prevent practical implementation of this futuristic vision. The sharing economy, referred to as a collaborative business model that foster sharing, exchanging and renting resources, could lead to operational improvements and enhance the cost control ability and the flexibility of companies using drones. For instance, the Amazon patent for drone beehives, which are fulfilment centers where drones can be restocked before flying out again for another delivery, could be established as a shared delivery systems where different freight carriers jointly deliver goods to customers. Only a few studies have addressed the problem of operating such facilities providing services to retail companies. In this paper, we formulate the problem as a deterministic location-routing model and derive its robust counterpart under the travel time uncertainty. To tackle the computational complexity of the model caused by the non-linear energy consumption rates in drone battery, we propose a tailored matheuristic combining variable neighborhood descent with a cut generation approach. The computational experiments show the efficiency of the solution approach especially compared to the Gurobi solver.", "keywords": [ "Drone", "Computer science", "Variable (mathematics)", "Operations research", "Flexibility (engineering)", "Sharing economy", "Economics", "Engineering" ], "cited_by_count": 21, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.mdpi.com/2071-1050/14/16/9978/pdf?version=1669295644" }, { "id": "https://openalex.org/W4311111778", "doi": "10.1002/nav.22087", "title": "Branch‐price‐and‐cut for the truck–drone routing problem with time windows", "year": 2022, "publication_date": "2022-12-01", "type": "article", "language": "en", "authors": [ "Hongqi Li", "Feilong Wang" ], "first_author": "Hongqi Li", "venue": "Naval Research Logistics (NRL)", "publisher": "Wiley", "abstract": "Abstract Considering the important realistic benefits of drones combined with trucks for last‐mile parcel deliveries, we define the truck–drone routing problem with time windows (TDRP‐TW). The TDRP‐TW has the characteristics of time windows, synchronization en route, direct delivery, multiple trucks, and multiple drones carried by each truck. Customers covered by truck routes can be used as drone launch/retrieval locations, which are called satellites in this study. The synchronization en route enables drones to launch from trucks to return to paired trucks at nodes other than departure sites if necessary. We present an effective branch‐price‐and‐cut algorithm, in which a concept named candidate forward‐satellite (CFS) is introduced to manage the labeling challenge caused by the synchronization en route. In addition, the branch‐price‐and‐cut algorithm is combined with an adaptive large neighborhood search to obtain approximation solutions for large‐scale instances. In the computational experiments, instances with up to 50 customers are solved to optimality, and approximation solutions of large‐scale instances with 100 customers are presented.", "keywords": [ "Truck", "Drone", "Computer science", "Routing (electronic design automation)", "Synchronization (alternating current)", "Vehicle routing problem", "Scale (ratio)", "Real-time computing", "Operations research", "Computer network", "Engineering", "Automotive engineering" ], "cited_by_count": 21, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1002/nav.22087" }, { "id": "https://openalex.org/W3196621926", "doi": "10.1016/j.cor.2021.105524", "title": "A learning based algorithm for drone routing", "year": 2021, "publication_date": "2021-09-06", "type": "article", "language": "en", "authors": [ "Umut Ermağan", "Barış Yıldız", "F. Sibel Salman" ], "first_author": "Umut Ermağan", "venue": "Computers & Operations Research", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Computer science", "Column generation", "Routing (electronic design automation)", "Heuristic", "Routing algorithm", "Algorithm", "Integer programming", "Mathematical optimization", "Artificial intelligence", "Mathematics", "Routing protocol" ], "cited_by_count": 41, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.cor.2021.105524" }, { "id": "https://openalex.org/W4396853091", "doi": "10.1109/tits.2024.3395930", "title": "A Parallel Genetic Algorithm With Variable Neighborhood Search for the Vehicle Routing Problem in Forest Fire-Fighting", "year": 2024, "publication_date": "2024-05-13", "type": "article", "language": "en", "authors": [ "Xiang Li", "Nan Chen", "Hongguang Ma", "Fapeng Nie", "Xianzhe Wang" ], "first_author": "Xiang Li", "venue": "IEEE Transactions on Intelligent Transportation Systems", "publisher": "Institute of Electrical and Electronics Engineers", "abstract": "With the challenge of making online decisions in the face of escalating losses, the vehicle routing problem in forest fire-fighting places great emphasis on the computing efficiency of algorithms. This paper investigates the route optimization for fire-fighting vehicles and formulates a mixed integer linear programming model to minimize the total losses of overall fire spots. A parallel genetic algorithm with variable neighborhood search (PGA-VNS) is developed, which includes a parallelized evolution process of multiple sub-populations for ensuring the fast convergency to a high-quality solution, and a multi-operator variable searching process to promote the convergency to a nearly optimal solution. By comparing the computational results for various-scale instances, the PGA-VNS is demonstrated to be more effective than the baseline algorithms (i.e., Gurobi, GA, PSO, ALNS, VNS, GA-ALNS, and GA-VNS). Furthermore, the proposed model is extended to the scenario of unmanned aerial vehicles (UAVs), taking into account limited flight range and load impact constraints. The results could support the scheduling and routing for fire engines or UAVs in minimizing the losses caused by forest fires.", "keywords": [ "Variable (mathematics)", "Vehicle routing problem", "Genetic algorithm", "Computer science", "Routing (electronic design automation)", "Algorithm", "Mathematical optimization", "Mathematics", "Computer network", "Machine learning" ], "cited_by_count": 37, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1109/tits.2024.3395930" }, { "id": "https://openalex.org/W4319302559", "doi": "10.1109/tro.2023.3236945", "title": "RACER: Rapid Collaborative Exploration With a Decentralized Multi-UAV System", "year": 2023, "publication_date": "2023-02-06", "type": "article", "language": "en", "authors": [ "Boyu Zhou", "Hao Xu", "Shaojie Shen" ], "first_author": "Boyu Zhou", "venue": "IEEE Transactions on Robotics", "publisher": "Institute of Electrical and Electronics Engineers", "abstract": "Although the use of multiple unmanned aerial vehicles (UAVs) has great potential for fast autonomous exploration, it has received far too little attention. In this article, we present a RApid Collaborative ExploRation (RACER) approach using a fleet of decentralized UAVs. To effectively dispatch the UAVs, a pairwise interaction based on an online hgrid space decomposition is used. It ensures that all UAVs simultaneously explore distinct regions, using only asynchronous and limited communication. Furthermore, we optimize the coverage paths of unknown space and balance the workloads partitioned to each UAV with a capacitated vehicle routing problem formulation. Given the task allocation, each UAV constantly updates the coverage path and incrementally extracts crucial information to support the exploration planning. A hierarchical planner finds exploration paths, refines local viewpoints, and generates minimum-time trajectories in sequence to explore the unknown space agilely and safely. The proposed approach is evaluated extensively, showing high exploration efficiency, scalability, and robustness to limited communication. Furthermore, for the first time, we achieve fully decentralized collaborative exploration with multiple UAVs in the real world. We will release our implementation as an open-source package.", "keywords": [ "Scalability", "Computer science", "Robustness (evolution)", "Asynchronous communication", "Distributed computing", "Planner", "Motion planning", "Space exploration", "Viewpoints", "Real-time computing", "Robot", "Artificial intelligence" ], "cited_by_count": 245, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1109/tro.2023.3236945" }, { "id": "https://openalex.org/W2956047314", "doi": "10.1109/access.2019.2925531", "title": "Low-Altitude Navigation for Multi-Rotor Drones in Urban Areas", "year": 2019, "publication_date": "2019-01-01", "type": "article", "language": "en", "authors": [ "Ahmed Bahabry", "Xiangpeng Wan", "Hakim Ghazzai", "Hamid Menouar", "Gregg Vesonder", "Yehia Massoud" ], "first_author": "Ahmed Bahabry", "venue": "IEEE Access", "publisher": "Institute of Electrical and Electronics Engineers", "abstract": "Multi-rotor drones have witnessed a drastic usage increase in several smart city applications due to their 3D mobility, flexibility, and low cost. Collectively, they can be used to accomplish different short- and long-term missions that require low-altitude motion in urban areas. Therefore, it is important to efficiently manage the operation of the fleet to leverage its use and maximize its application performances. In this paper, we propose to investigate the path routing problem for the multiple drones in urban areas, where obstacles with different heights exist. The objective is to find the best trajectories in this 3D environment while ensuring collision-free navigation. The collision is prevented by three possible alternatives: forcing the drone to statically hover, so its peer can pass first, making it fly at a different altitude, or completely changing its path. Multiple charging stations are made available to allow the drones to recharge their batteries when needed. A mixed integer linear program is first developed to model the problem and achieve optimal navigation of the fleet. Afterward, two heuristic algorithms with different conceptual constructions are designed to solve the trajectory planning problem with faster convergence speed. The selected simulation results illustrate the performance of our framework in realistic 3D maps and show that the designed heuristic approaches provide close performances to the optimal ones.", "keywords": [ "Drone", "Altitude (triangle)", "Computer science", "Aeronautics", "Aerospace engineering", "Environmental science", "Remote sensing", "Geography", "Engineering", "Mathematics" ], "cited_by_count": 58, "is_retracted": false, "is_paratext": false, "open_access_url": "https://ieeexplore.ieee.org/ielx7/6287639/8600701/08747351.pdf" }, { "id": "https://openalex.org/W1936177838", "doi": "10.3390/s151127783", "title": "Multi-UAV Routing for Area Coverage and Remote Sensing with Minimum Time", "year": 2015, "publication_date": "2015-11-02", "type": "article", "language": "en", "authors": [ "Gustavo Silva Castilho de Avellar", "Guilherme A. S. Pereira", "Luciano C. A. Pimenta", "Paulo Iscold" ], "first_author": "Gustavo Silva Castilho de Avellar", "venue": "Sensors", "publisher": "Multidisciplinary Digital Publishing Institute", "abstract": "This paper presents a solution for the problem of minimum time coverage of ground areas using a group of unmanned air vehicles (UAVs) equipped with image sensors. The solution is divided into two parts: (i) the task modeling as a graph whose vertices are geographic coordinates determined in such a way that a single UAV would cover the area in minimum time; and (ii) the solution of a mixed integer linear programming problem, formulated according to the graph variables defined in the first part, to route the team of UAVs over the area. The main contribution of the proposed methodology, when compared with the traditional vehicle routing problem's (VRP) solutions, is the fact that our method solves some practical problems only encountered during the execution of the task with actual UAVs. In this line, one of the main contributions of the paper is that the number of UAVs used to cover the area is automatically selected by solving the optimization problem. The number of UAVs is influenced by the vehicles' maximum flight time and by the setup time, which is the time needed to prepare and launch a UAV. To illustrate the methodology, the paper presents experimental results obtained with two hand-launched, fixed-wing UAVs.", "keywords": [ "Integer programming", "Task (project management)", "Computer science", "Cover (algebra)", "Routing (electronic design automation)", "Linear programming", "Graph", "Vehicle routing problem", "Real-time computing", "Integer (computer science)", "Mathematical optimization", "Algorithm" ], "cited_by_count": 310, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.3390/s151127783" }, { "id": "https://openalex.org/W2968747584", "doi": "10.1109/uemcon.2018.8796684", "title": "Perpetual Flight for UAV Drone Swarms Using Continuous Energy Replenishment", "year": 2018, "publication_date": "2018-11-01", "type": "conference-paper", "language": "en", "authors": [ "Andrew Boggio-Dandry", "Tolga Soyata" ], "first_author": "Andrew Boggio-Dandry", "venue": null, "publisher": null, "abstract": "Today's off-the-shelf, inexpensive Unmanned Aerial Vehicles (UAVs) are an emerging breed of devices that promise to reshape tomorrow's search and rescue landscape. Multiple identical drones can be utilized to achieve more complex tasks when arranged in a swarm formation. In either the single-drone or swarm configuration, these Lithium Polymer (LiPo) battery-powered machines can only stay in the air for a brief period of time (usually between 10 and 30 minutes) due to the high power consumption of their motors. For example, drones weighing only 200 to 600 grams can consume between 100-600 Watts. Most search-and-rescue operations last for days, even weeks, rendering these inexpensive drones impractical.A novel charge replenishment mechanism is proposed in this paper that allows a swarm of drones to stay in the air perpetually. This is achieved by employing a fleet of drones much larger than the flying swarm in order to continuously replace and charge energy-depleted drones. The required fleet size for various drone models is calculated analytically and through a simulation. A rule-of-thumb formula is derived based on Queuing Theory and Energy Conversation to confirm the feasibility of this proposal with simulation results.", "keywords": [ "Drone", "Swarm behaviour", "Computer science", "Quadcopter", "Energy consumption", "Battery (electricity)", "Real-time computing", "Simulation", "Power (physics)", "Automotive engineering", "Engineering", "Aerospace engineering" ], "cited_by_count": 26, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1109/uemcon.2018.8796684" }, { "id": "https://openalex.org/W4408708598", "doi": "10.1109/tits.2025.3548426", "title": "Multi-Objective Multi-Drone Collaborative Routing Problem With Heterogeneous Delivery and Pickup Service", "year": 2025, "publication_date": "2025-03-22", "type": "article", "language": "en", "authors": [ "Fangyu Hong", "Guohua Wu", "Yalin Wang", "Qizhang Luo", "Ling Wang", "Jianmai Shi" ], "first_author": "Fangyu Hong", "venue": "IEEE Transactions on Intelligent Transportation Systems", "publisher": "Institute of Electrical and Electronics Engineers", "abstract": "With the development of e-commerce, the types of logistics services have become diverse. In response to the logistics requirements in urban environments, this paper introduces a logistics system that multiple drones and smart parcel lockers (SPLs) collaborate to provide package pickup, delivery and intra-city on-demand delivery services for customers. Different from pickup and delivery services, the intra-city on-demand delivery services need drones to pick up a package from a customer and deliver it to another customer. The multi-drone collaborative routing problem is crucial to find a reasonable tour over customers with flexible time-window. A multi-objective mixed-integer programming model is formulated to describe the proposed problem with simultaneously minimizing transportation costs and maximizing customer satisfaction. The model integrates dynamic energy consumption, soft time-windows, and task precedence constraints arising from the single unit capacity of drones. To tackle this problem, an adaptive-large-neighborhood-search based multi-objective algorithm (ALNSMO) is devised. CPLEX is used to verify the accuracy of the model and the quality of the proposed algorithm. Meanwhile, numerous experiments and analyses are conducted to demonstrate the superiority and practicability of the proposed mode and ALNSMO.", "keywords": [ "Pickup", "Drone", "Routing (electronic design automation)", "Vehicle routing problem", "Computer science", "Service (business)", "Computer network", "Distributed computing", "Business", "Artificial intelligence" ], "cited_by_count": 24, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1109/tits.2025.3548426" }, { "id": "https://openalex.org/W3045008494", "doi": "10.1109/tte.2020.3011682", "title": "Round Trip Routing for Energy-Efficient Drone Delivery Based on a Public Transportation Network", "year": 2020, "publication_date": "2020-07-24", "type": "article", "language": "en", "authors": [ "Hailong Huang", "Andrey V. Savkin", "Chao Huang" ], "first_author": "Hailong Huang", "venue": "IEEE Transactions on Transportation Electrification", "publisher": "Institute of Electrical and Electronics Engineers", "abstract": "Focusing on using drones to deliver packages, this article considers a new delivery mode exploiting public transportation vehicles. Due to the battery capacity constraint, which limits the delivery area of drones, the public transportation vehicles are used to transport a drone to someplace unreachable by flying only. The problem under investigation is the round trip routing problem that finds the shortest path in terms of time in a time-dependent network, subject to the delivery deadline constraint and the energy budget constraint. The time-dependent network composes of the transit network and some extra drone flights. An exact solution algorithm is developed to find the optimal round trip path, and then, it is extended to accommodate the randomness of the considered network. The effectiveness is demonstrated via computer simulations.", "keywords": [ "Drone", "Randomness", "Public transport", "Computer science", "Constraint (computer-aided design)", "Routing (electronic design automation)", "Path (computing)", "Shortest path problem", "Budget constraint", "Flow network", "Mathematical optimization", "Operations research" ], "cited_by_count": 70, "is_retracted": false, "is_paratext": false, "open_access_url": "https://unsworks.unsw.edu.au/bitstreams/32d3f12f-2bc0-4220-a252-c60d61a0c137/download" }, { "id": "https://openalex.org/W4386609857", "doi": "10.1016/j.asoc.2023.110831", "title": "Adaptive large neighborhood search algorithm for the Unmanned aerial vehicle routing problem with recharging", "year": 2023, "publication_date": "2023-09-11", "type": "article", "language": "en", "authors": [ "Jianmai Shi", "Huiting Mao", "Zhongbao Zhou", "Long Zheng" ], "first_author": "Jianmai Shi", "venue": "Applied Soft Computing", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Computer science", "Benchmark (surveying)", "Simulated annealing", "Variable neighborhood search", "Vehicle routing problem", "Ant colony optimization algorithms", "Routing (electronic design automation)", "Mathematical optimization", "Algorithm", "Set (abstract data type)", "Heuristic", "Local search (optimization)" ], "cited_by_count": 30, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.asoc.2023.110831" }, { "id": "https://openalex.org/W2979415718", "doi": "10.1201/9780367824037-20", "title": "Vehicle routing in drone-based package delivery services", "year": 2019, "publication_date": "2019-09-19", "type": "book-chapter", "language": "en", "authors": [ "Anita Agárdi", "László Kovács", "Tamás Bányai" ], "first_author": "Anita Agárdi", "venue": null, "publisher": null, "abstract": "The Industry 4.0 enables the operation of new logistics equipment and new logistic solutions based on cyber-physical systems. The usage of new transport devices is discussed in this article in case of the Vehicle Routing Problem. In basic Vehicle Routing Problems, the demands of customers must be served. This article discusses a new Vehicle Routing Problem where drones are also used to improve the flexibility, reliability and cost efficiency of the whole last-mile solution. During the problem, a drone is assigned to the truck performing package delivery services, and some customers are visited by the truck while the drone is sent to certain customers located in the near environment of the truck. The drone has a capacity limit, so it is able to visit only a limited number of customers. After visiting the customers, the drone recovers the goods from the truck and serves the demands of new customers. In this article, the above mentioned problem is solved with construction and improvement algorithms. The construction algorithms are the Nearest Neighbour Algorithm and Arbitrary Insertion Algorithm, the improvement algorithms are the Genetic Algorithm and the Hill Climbing Algorithm.", "keywords": [ "Drone", "Routing (electronic design automation)", "Computer science", "Computer network", "Biology" ], "cited_by_count": 12, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1201/9780367824037-20" }, { "id": "https://openalex.org/W4406748871", "doi": "10.1016/j.tre.2025.103974", "title": "Multi-agent deep reinforcement learning-based truck-drone collaborative routing with dynamic emergency response", "year": 2025, "publication_date": "2025-01-23", "type": "article", "language": "en", "authors": [ "Wenhao Peng", "Dujuan Wang", "Yunqiang Yin", "T.C.E. Cheng" ], "first_author": "Wenhao Peng", "venue": "Transportation Research Part E Logistics and Transportation Review", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Reinforcement learning", "Truck", "Drone", "Emergency response", "Reinforcement", "Routing (electronic design automation)", "Computer science", "Transport engineering", "Engineering", "Artificial intelligence", "Automotive engineering", "Medical emergency" ], "cited_by_count": 75, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.tre.2025.103974" }, { "id": "https://openalex.org/W4366378404", "doi": "10.1109/tits.2023.3267103", "title": "Multi-Objective Optimization Algorithm With Adaptive Resource Allocation for Truck-Drone Collaborative Delivery and Pick-Up Services", "year": 2023, "publication_date": "2023-04-19", "type": "article", "language": "en", "authors": [ "Qizhang Luo", "Guohua Wu", "Anupam Trivedi", "Fangyu Hong", "Ling Wang", "Dipti Srinivasan" ], "first_author": "Qizhang Luo", "venue": "IEEE Transactions on Intelligent Transportation Systems", "publisher": "Institute of Electrical and Electronics Engineers", "abstract": "To efficiently implement the truck-drone collaborative logistics system, we introduce a multi-objective truck-drone collaborative routing problem with delivery and pick-up services (MCRP-DP). A truck collaborating with a fleet of drones serves three types of customers that require delivery, pick-up, and simultaneous delivery & pick-up services, respectively. Different from most of the existing studies where the drone visits only one customer in a flight, we allow the drone to serve another customer requiring pick-up service when it completes a delivery service. Meanwhile, we simultaneously optimize three objectives: transportation costs, waiting time of vehicles (i.e., truck and drone), and service reliability. To solve MCRP-DP, we propose an objective space decomposition-based multi-objective evolutionary algorithm with adaptive resource allocation (ODEA-ARA) In ODEA-ARA, an objective space decomposition strategy is used to maintain the diversity while an adaptive resource allocation strategy is designed to improve convergence. We design an ensemble of relative improvement and relative contribution to assist the resource allocation and a variable neighborhood Pareto local search integrating 7 problem-specific neighborhood structures to improve the solution. Extensive computational experiments are carried out to evaluate the performance of ODEA-ARA. The experimental results show that ODEA-ARA outperforms its competitors. Meanwhile, several useful managerial insights are presented.", "keywords": [ "Drone", "Truck", "Resource allocation", "Computer science", "Pareto principle", "Service (business)", "Vehicle routing problem", "Resource (disambiguation)", "Decomposition", "Convergence (economics)", "Routing (electronic design automation)", "Operations research" ], "cited_by_count": 89, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1109/tits.2023.3267103" }, { "id": "https://openalex.org/W4399126460", "doi": "10.1109/mits.2024.3396430", "title": "Low-Noise Flight Path Planning of Drones Based on a Virtual Flight Noise Simulator: A Vehicle Routing Problem", "year": 2024, "publication_date": "2024-05-29", "type": "article", "language": "en", "authors": [ "Qichen Tan", "Siyang Zhong", "Renhao Qu", "Yuhong Li", "Peng Zhan Zhou", "Hong Kam Lo", "Xin Zhang" ], "first_author": "Qichen Tan", "venue": "IEEE Intelligent Transportation Systems Magazine", "publisher": "Institute of Electrical and Electronics Engineers", "abstract": "The vehicle routing problem is common for drone delivery in urban areas, and the routing strategies can impact both transport efficiency and community noise. In this article, we propose an optimization method for drone routing to reduce the en route noise impact during the delivery process. A hybrid cost function is adopted to evaluate the quality of the routing strategies, considering both the noise impact and path length. The en route noise is evaluated based on an efficient flight simulation and noise assessment platform, which enables accurate sound source modeling for a practical delivery drone and sound propagation computation in a realistic urban environment. A three-phase heuristic algorithm is employed to optimize the routing strategy. Large-scale simulations conducted in a representative metropolitan area demonstrate significant reductions in both instantaneous and accumulated noise levels. This article highlights the importance of incorporating noise optimization strategies in urban drone delivery systems to improve public acceptance and sustainable air transport.", "keywords": [ "Drone", "Simulation", "Noise (video)", "Computer science", "Flight simulator", "Routing (electronic design automation)", "Motion planning", "Aeronautics", "Aerospace engineering", "Engineering", "Embedded system", "Artificial intelligence" ], "cited_by_count": 12, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1109/mits.2024.3396430" }, { "id": "https://openalex.org/W4389921894", "doi": "10.3390/wevj14120354", "title": "A GRASP Approach for the Energy-Minimizing Electric Vehicle Routing Problem with Drones", "year": 2023, "publication_date": "2023-12-18", "type": "article", "language": "en", "authors": [ "Nikolaos A. Kyriakakis", "Themistoklis Stamadianos", "Magdalene Marinaki", "Yannis Marinakis" ], "first_author": "Nikolaos A. Kyriakakis", "venue": "World Electric Vehicle Journal", "publisher": "Multidisciplinary Digital Publishing Institute", "abstract": "This study addresses the Electric Vehicle Routing Problem with Drones (EVRPD) by implementing and comparing two variants of the Greedy Randomized Adaptive Search Procedure (GRASP). The primary objective of the EVRPD is to optimize the routing of a combined fleet of ground and aerial vehicles, with the aim of improving delivery efficiency and minimizing energy consumption, which is directly influenced by the weight of the packages. The study assumes a standardized packing system consisting of three weight classes, where deliveries are exclusively performed by drones, while ground vehicles function as mobile depots. The two employed GRASP variants vary in their methods of generating the Restricted Candidate List (RCL), with one utilizing a cardinality-based RCL and the other adopting a value-based RCL. To evaluate their performance, benchmark instances from the existing EVRPD literature are utilized, extensive computational experiments are conducted, and the obtained computational results are compared and discussed. The findings of the research highlight the considerable impact of RCL generation strategies on solution quality. Lastly, the study reports four new best-known values.", "keywords": [ "GRASP", "Benchmark (surveying)", "Vehicle routing problem", "Computer science", "Greedy randomized adaptive search procedure", "Drone", "Mathematical optimization", "Routing (electronic design automation)", "Cardinality (data modeling)", "Energy consumption", "Energy (signal processing)", "Operations research" ], "cited_by_count": 7, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.mdpi.com/2032-6653/14/12/354/pdf?version=1702893267" }, { "id": "https://openalex.org/W4403670380", "doi": "10.1016/j.trb.2024.103101", "title": "The multi-visit drone-assisted routing problem with soft time windows and stochastic truck travel times", "year": 2024, "publication_date": "2024-10-23", "type": "article", "language": "en", "authors": [ "Shanshan Meng", "Dong Li", "Jiyin Liu", "Yanru Chen" ], "first_author": "Shanshan Meng", "venue": "Transportation Research Part B Methodological", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Truck", "Drone", "Vehicle routing problem", "Computer science", "Routing (electronic design automation)", "Transport engineering", "Operations research", "Simulation", "Engineering", "Automotive engineering", "Computer network" ], "cited_by_count": 27, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.trb.2024.103101" }, { "id": "https://openalex.org/W2915502992", "doi": "10.20944/preprints201902.0183.v1", "title": "Two-Echelon Routing Problem for Parcel Delivery by Cooperated Truck and Drone", "year": 2019, "publication_date": "2019-02-19", "type": "preprint", "language": "en", "authors": [ "Yao Liu", "Jianmai Shi", "Guohua Wu", "Zhong Liu", "Witold Pedrycz" ], "first_author": "Yao Liu", "venue": "Preprints.org", "publisher": null, "abstract": "A new variant of two-echelon routing problem is investigated, where the truck and the drone are used to cooperatively complete the deliveries of all parcels. The truck not only acts as a tool for parcel delivery, but also serves as a moving depot for the drone. The drone can carry several parcels and take off from the truck, while returning to the truck after completing the delivery. The energy consumption model for the routing process of the drone is analyzed, when it is utilized to deliver multiple parcels. A two-stage route-based modelling approach is proposed to optimize both the truck’s main route and the drone’s adjoint flying routes. A hybrid heuristic integrating nearest neighbor and cost saving strategies is developed to quickly construct a feasible solution. The simulated annealing algorithm is applied to improve the quality of the solution, where a Tabu list is employed to improve the search efficiency. Random instances at different scales are used to test the performance of the proposed algorithm. A case study based on the practical road network in Changsha, China, is presented, through which the sensitivity analysis is conducted with respect to some critical factors.", "keywords": [ "Drone", "Truck", "Simulated annealing", "Routing (electronic design automation)", "Tabu search", "Computer science", "Vehicle routing problem", "Heuristic", "Process (computing)", "Operations research", "Transport engineering", "Engineering" ], "cited_by_count": 18, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.preprints.org/manuscript/201902.0183/v1/download" }, { "id": "https://openalex.org/W4385142943", "doi": "10.1002/net.22176", "title": "The multi‐purpose K‐drones general routing problem", "year": 2023, "publication_date": "2023-07-22", "type": "article", "language": "en", "authors": [ "James F. Campbell", "Ángel Corberán", "Isaac Plana", "José María Sanchis", "Paula Segura" ], "first_author": "James F. Campbell", "venue": "Networks", "publisher": "Wiley", "abstract": "Abstract In this article, we present and solve the multi‐purpose ‐drones general routing problem (MP ‐DGRP). In this optimization problem, a fleet of multi‐purpose drones, aerial vehicles that can both make deliveries and conduct sensing activities (e.g., imaging), have to jointly visit a set of nodes to make deliveries and map one or more continuous areas. This problem is motivated by global healthcare applications that deploy multipurpose drones that combine delivery trips with collection of aerial imaging data for use in emergency preparedness and resilience planning. The continuous areas that have to be mapped may correspond to terrain surfaces (e.g., flooded areas or regions with a disease outbreak) or to infrastructure networks to be inspected. The continuous areas can be modeled as a set of lines so that each area is completely serviced if all the lines covering it are traversed. Thus, given a set of nodes and a set of lines, the problem is to design drone routes of shortest total duration traversing the lines and visiting the nodes, while not exceeding the range limit (flight time) and capacity (loading) of the drones. Unlike ground vehicles in classical routing problems, drones can enter a line through any of its points, service only a part of that line and then exit through another of its points. The possibility of flying directly between any two points of the network offered by drones can lead to reduced costs, but it increases the difficulty of the problem. To deal with this problem, the lines are discretized, allowing drones to enter and exit each line only at a finite set of points, thus obtaining an instance of the ‐vehicles general routing problem (‐GRP). We present in this article an integer programming formulation for the ‐GRP and propose a matheuristic algorithm and a branch‐and‐cut procedure for its solution. Results are provided for problems with up to 20 deliveries and up to 28 continuous areas.", "keywords": [ "Drone", "Routing (electronic design automation)", "Computer science", "Resilience (materials science)", "Terrain", "Operations research", "Set (abstract data type)", "Line (geometry)", "Real-time computing", "Computer network", "Geography", "Mathematics" ], "cited_by_count": 14, "is_retracted": false, "is_paratext": false, "open_access_url": "https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/net.22176" }, { "id": "https://openalex.org/W2774532011", "doi": "10.1109/soli.2017.8120986", "title": "Post-production analysis approach for drone delivery fleet", "year": 2017, "publication_date": "2017-09-01", "type": "conference-paper", "language": "en", "authors": [ "Asma Troudi", "Sid-Ali Addouche", "Sofiène Dellagi", "Abderrahman El Mhamedi" ], "first_author": "Asma Troudi", "venue": null, "publisher": null, "abstract": "This paper treats a drone delivery parcel's problematic in an urban area. The civil application of drone has been developed during these last decades especially drone delivery applications. In this paper, we focus on drone delivery application in the urban area for last-mile parcel delivery. The new issue is not only the drone design but also the logistics support of a massive fleet of drones with a mission to deliver parcels in a dense urban area. We hereby treat problematic by focusing on Logistics Support System. In this context, the commercialized drone is a considered as a system on the shelf. we propose a Post-Production Logistics Support Analysis to cover the exploitation phase of a drone delivery operator.", "keywords": [ "Drone", "Context (archaeology)", "Last mile (transportation)", "Computer science", "City logistics", "Aeronautics", "Transport engineering", "Engineering", "Mile", "Geography" ], "cited_by_count": 10, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1109/soli.2017.8120986" }, { "id": "https://openalex.org/W4390024498", "doi": "10.1016/j.cie.2023.109849", "title": "Cooperative trucks and drones for rural last-mile delivery with steep roads", "year": 2023, "publication_date": "2023-12-20", "type": "article", "language": "en", "authors": [ "Jiuhong Xiao", "Ying Li", "Zhiguang Cao", "Jianhua Xiao" ], "first_author": "Jiuhong Xiao", "venue": "Computers & Industrial Engineering", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Mile", "Truck", "Drone", "Last mile (transportation)", "Transport engineering", "Aeronautics", "Engineering", "Forensic engineering", "Business", "Geography", "Automotive engineering" ], "cited_by_count": 47, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.cie.2023.109849" }, { "id": "https://openalex.org/W2322344890", "doi": "10.2514/6.2008-6838", "title": "Vehicle Routing with Linear Temporal Logic Specifications: Applications to Multi-UAV Mission Planning", "year": 2008, "publication_date": "2008-06-15", "type": "conference-paper", "language": "en", "authors": [ "Sertaç Karaman", "Emilio Frazzoli" ], "first_author": "Sertaç Karaman", "venue": "AIAA Guidance, Navigation, and Control Conference and Exhibit", "publisher": null, "abstract": "The Vehicle Routing Problem (VRP) and several of its variants have been used as an algorithmic basis for mission planning and trajectory generation for Uninhabited Aerial Vehicles (UAVs). This paper proposes a new class of problems that generalizes the standard VRP to incorporate more complex mission specifications, for example relative timing constraints on the completion of tasks. These timing constraints are specified using the Linear Temporal Logic language LTL−X. A systematic procedure is presented that converts a given set of LTL−X specifications into a set of constraints suitable to a Mixed-Integer Linear Programming (MILP) formulation of optimal mission planning problems. The application of this new variant of VRP to complex mission planning and UAV-routing problems are also considered by employing two different MILP formulations of VRP commonly used in related literature. Examples of UAV mission planning problems are discussed in detail.", "keywords": [ "Computer science", "Routing (electronic design automation)", "Temporal logic", "Linear temporal logic", "Real-time computing", "Computer network", "Theoretical computer science" ], "cited_by_count": 41, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.2514/6.2008-6838" }, { "id": "https://openalex.org/W4407748640", "doi": "10.3390/app15042207", "title": "Time-Dependent Vehicle Routing Problem with Drones Under Vehicle Restricted Zones and No-Fly Zones", "year": 2025, "publication_date": "2025-02-19", "type": "article", "language": "en", "authors": [ "Shuo Wei", "Houming Fan", "Xiaoxue Ren", "Xiaolong Diao" ], "first_author": "Shuo Wei", "venue": "Applied Sciences", "publisher": "Multidisciplinary Digital Publishing Institute", "abstract": "This paper addresses the time-dependent vehicle routing problem with drones in vehicle-restricted zones and no-fly zones (TDVRPD-VRZ-NFZ). The optimization model considers the impacts of vehicle-restricted zones, no-fly zones, and time-dependent road networks on delivery paths. The objective is to minimize the total cost, including vehicle dispatch costs, energy consumption costs for vehicles and drones, and time-window penalty costs. The model is verified for correctness using Gurobi. In response to the problem’s characteristics, a hybrid genetic algorithm and variable neighborhood search with a learning mechanism (HGAVNS-LM) is proposed to solve the problem. The algorithm starts by generating the initial population using a combination of logistic mapping and reverse learning. It then improves the genetic operators and variable neighborhood search operators to optimize the initial population. To improve the algorithm’s performance, an individual elite archive is used for knowledge learning, and a self-learning mechanism is established to dynamically adjust the algorithm’s key parameters. The solution obtained by HGAVNS-LM shows a deviation of −0.2% to −0.3% compared to Gurobi, but it saves 99.68% in solving time. Compared to the genetic neighborhood search algorithm and the hybrid genetic algorithm, the improvement rates are 5.1% and 13.0%, respectively. Through the analysis of multiple sets of test cases, it is concluded that time-varying road networks, vehicle-restricted zones and no-fly zones, and different detour rules all affect delivery costs and delivery plans. The research results provide a more scientific theoretical basis for logistics companies to customize delivery solutions.", "keywords": [ "Drone", "Computer science", "Biology", "Genetics" ], "cited_by_count": 9, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.mdpi.com/2076-3417/15/4/2207/pdf?version=1739959335" }, { "id": "https://openalex.org/W7104022509", "doi": "10.1016/j.aei.2025.104008", "title": "Multi-depot electric vehicle routing problem with drones considering time-dependent traffic", "year": 2025, "publication_date": "2025-11-05", "type": "article", "language": "en", "authors": [ "Hao Fan", "Kai Liu", "Jiangbo Wang", "Jian Zhao" ], "first_author": "Hao Fan", "venue": "Advanced Engineering Informatics", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Initialization", "Vehicle routing problem", "Population", "Particle swarm optimization", "Genetic algorithm", "Crossover", "Electric vehicle" ], "cited_by_count": 8, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.aei.2025.104008" }, { "id": "https://openalex.org/W2912632897", "doi": "10.3390/en12071385", "title": "Two-Layer Routing for High-Voltage Powerline Inspection by Cooperated Ground Vehicle and Drone", "year": 2019, "publication_date": "2019-04-10", "type": "article", "language": "en", "authors": [ "Yao Liu", "Jianmai Shi", "Zhong Liu", "Jincai Huang", "Tianren Zhou" ], "first_author": "Yao Liu", "venue": "Energies", "publisher": "Multidisciplinary Digital Publishing Institute", "abstract": "A novel high-voltage powerline inspection system was investigated, which consists of the cooperated ground vehicle and drone. The ground vehicle acts as a mobile platform that can launch and recycle the drone, while the drone can fly over the powerline for inspection within limited endurance. This inspection system enables the drone to inspect powerline networks in a very large area. Both vehicle’ route in the road network and drone’s routes along the powerline network have to be optimized for improving the inspection efficiency, which generates a new Two-Layer Point-Arc Routing Problem (2L-PA-RP). Two constructive heuristics were designed based on “Cluster First, Route Second” and “Route First, Split Second”. Then, local search strategies were developed to further improve the quality of the solution. To test the performance of the proposed algorithms, different-scale practical cases were designed based on the road network and powerline network of Ji’an, China. Sensitivity analysis on the parameters related to the drone’s inspection speed and battery capacity was conducted. Computational results indicate that technical improvement on the inspection sensor is more important for the cooperated ground vehicle and drone system.", "keywords": [ "Drone", "Routing (electronic design automation)", "Heuristics", "Real-time computing", "Computer science", "Engineering", "Embedded system" ], "cited_by_count": 56, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.mdpi.com/1996-1073/12/7/1385/pdf?version=1554896042" }, { "id": "https://openalex.org/W3155393628", "doi": "10.1016/j.ejor.2021.03.064", "title": "The Piggyback Transportation Problem: Transporting drones launched from a flying warehouse", "year": 2021, "publication_date": "2021-04-13", "type": "article", "language": "en", "authors": [ "Kai Wang", "Erwin Pesch", "Dominik Kreß", "Ilia Fridman", "Nils Boysen" ], "first_author": "Kai Wang", "venue": "European Journal of Operational Research", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Launched", "Drone", "Warehouse", "Transport engineering", "Operations research", "Business", "Computer science", "Aeronautics", "Operations management", "Engineering", "Marketing" ], "cited_by_count": 50, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.ejor.2021.03.064" }, { "id": "https://openalex.org/W4401246692", "doi": "10.1109/access.2024.3438079", "title": "Guided Genetic Algorithm for Solving Capacitated Vehicle Routing Problem With Unmanned-Aerial-Vehicles", "year": 2024, "publication_date": "2024-01-01", "type": "article", "language": "en", "authors": [ "Ali Najm Jasim", "Lamia Chaari Fourati" ], "first_author": "Ali Najm Jasim", "venue": "IEEE Access", "publisher": "Institute of Electrical and Electronics Engineers", "abstract": "This study proposes a capacitated vehicle routing problem (CVRP) approach to optimise Vehicle Routing Problem (VRP) and pesticides spraying. The VRP consists of finding the route which covers every point of a certain area of interest. This paper considers a search and pesticides spraying mission, using group of Unmanned Aerial Vehicles (UAVs). In this scenario, the objective is to minimise the total battery consumption level and tank consumption level to not exceed their maximum battery and tank capacities. A hybrid metaheuristic optimisation algorithm is formulated by integrating Genetic Algorithm (GA) with a guided local search algorithm called guided genetic algorithm (GGA). The performance of the proposed GGA algorithm is compared to four single-solution based metaheuristic algorithms (Guided Local Search [GLS], Tabu Search [TS], Simulated Annealing [SA], and Iterated Local Search [ILS]) and two population-based metaheuristics algorithms (GA and Particle Swarm Optimisation [PSO] algorithm). The results revealed that the proposed GGA outperformed the other algorithms in most instances. GGA showed competitive results, closely following the TS’s performance across different scenarios. The evaluation of GGA is conducted by analysing its mean, standard deviation, best solution, and worst solution of ten iterations. In addition, Wilcoxon signed-rank test is conducted across a total of 36 instances. The optimisation results and discussion provide confirmation that the proposed GGA method beat the compared algorithms.", "keywords": [ "Vehicle routing problem", "Tabu search", "Metaheuristic", "Simulated annealing", "Particle swarm optimization", "Algorithm", "Computer science", "Iterated local search", "Mathematical optimization", "Genetic algorithm", "Population", "Local search (optimization)" ], "cited_by_count": 28, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1109/access.2024.3438079" }, { "id": "https://openalex.org/W4296767464", "doi": "10.1016/j.engappai.2022.105439", "title": "Machine learning approach for truck-drones based last-mile delivery in the era of industry 4.0", "year": 2022, "publication_date": "2022-09-20", "type": "article", "language": "en", "authors": [ "Ali Arishi", "Krishna Krishnan", "Majed Arishi" ], "first_author": "Ali Arishi", "venue": "Engineering Applications of Artificial Intelligence", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Truck", "Computer science", "Travelling salesman problem", "Cluster analysis", "Last mile (transportation)", "Vehicle routing problem", "Routing (electronic design automation)", "Mile", "Operations research", "Artificial intelligence", "Computer network" ], "cited_by_count": 66, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.engappai.2022.105439" }, { "id": "https://openalex.org/W4212838089", "doi": "10.3390/drones6020050", "title": "Load and Wind Aware Routing of Delivery Drones", "year": 2022, "publication_date": "2022-02-17", "type": "article", "language": "en", "authors": [ "Satoshi Ito", "Keishi Akaiwa", "Yusuke Funabashi", "Hiroki Nishikawa", "Xiangbo Kong", "Ittetsu Taniguchi", "Hiroyuki Tomiyama" ], "first_author": "Satoshi Ito", "venue": "Drones", "publisher": "Multidisciplinary Digital Publishing Institute", "abstract": "Delivery drones have been attracting attention as one of the promising technologies to deliver packages. Several research studies on routing problems specifically for drone delivery scenarios have extended Vehicle Routing Problems (VRPs). Most existing VRPs are based on Traveling Salesman Problems (TSPs) for minimizing the overall distance. On the other hand, VRPs for drone delivery have been aware of energy consumption due to the consideration of battery capacity. Despite hovering motions with loading packages accounting for a large portion of energy consumption since delivery drones need to hover with several packages, little research has been conducted on drone routing problems that aim at the minimization of overall flight times. In addition, flight time is strongly influenced by windy conditions such as headwinds and tailwinds. In this paper, we propose a VRP for drone delivery in which flight time is dependent on the weight of packages in a windy environment, called Flight Speed-aware Vehicle Routing Problem with Load and Wind (FSVRPLW). In this paper, flight speed changes depending on the load and wind. Specifically, a heavier package slows down flight speeds and a lighter package speeds up flight speeds. In addition, a headwind slows down flight speeds and a tailwind speed up flight speeds. We mathematically derived the problem and developed a dynamic programming algorithm to solve the problem. In the experiments, we investigate how much impact both the weight of packages and the wind have on the flight time. The experimental results indicate that taking loads and wind into account is very effective in reducing flight times. Moreover, the results of comparing the effects of load and wind indicate that flight time largely depends on the weight of packages.", "keywords": [ "Drone", "Wind speed", "Routing (electronic design automation)", "Computer science", "Vehicle routing problem", "Travelling salesman problem", "Energy consumption", "Simulation", "Real-time computing", "Engineering", "Meteorology", "Embedded system" ], "cited_by_count": 31, "is_retracted": false, "is_paratext": false, "open_access_url": "https://www.mdpi.com/2504-446X/6/2/50/pdf?version=1646644665" }, { "id": "https://openalex.org/W4408055499", "doi": "10.1287/ijoc.2023.0484", "title": "A Branch-and-Price Algorithm for Robust Drone-Vehicle Routing Problem with Time Windows", "year": 2025, "publication_date": "2025-02-28", "type": "article", "language": "en", "authors": [ "Jaegwan Joo", "Chungmok Lee" ], "first_author": "Jaegwan Joo", "venue": "INFORMS journal on computing", "publisher": "Institute for Operations Research and the Management Sciences", "abstract": "This paper considers a cooperative routing problem in which trucks and multiple drones serve a set of customers collaboratively. A truck can operate as a drone station, dispatching and collecting multiple drones for nearby customers to overcome the drone’s short operation range. Each customer has a time window, so either a truck or a drone must serve the customer within the time window. The travel time uncertainties of the truck and drone are addressed by adopting the robust optimization approach. We first present a compact mathematical formulation for the problem. Then, we develop a decomposition approach based on the branch-and-price framework. After defining extended variables for trucks and drones separately, we decompose the column generation subproblem into two optimization problems, resulting in a two-phase column generation algorithm. We also develop a heuristic algorithm based on the proposed column generation scheme for larger instances. The results of numerical experiments, including real-life benchmark instances, show that the proposed algorithm outperforms the state-of-the-art mixed-integer programming solver. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: Financial support from the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Science, ICT & Future Planning [Grant NRF-2021R1F1A1 048540] is gratefully acknowledged. C. Lee was supported by the Hankuk University of Foreign Studies Research Fund. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0484 ), as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0484 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .", "keywords": [ "Vehicle routing problem", "Drone", "Computer science", "Branch and price", "Routing (electronic design automation)", "Mathematical optimization", "Algorithm", "Integer programming", "Mathematics", "Embedded system" ], "cited_by_count": 7, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1287/ijoc.2023.0484" }, { "id": "https://openalex.org/W4298148253", "doi": "10.1016/j.cor.2022.106039", "title": "Collaborative vehicle-drone distribution network optimization for perishable products in the epidemic situation", "year": 2022, "publication_date": "2022-09-29", "type": "article", "language": "en", "authors": [ "Jie Zhang", "Yanfeng Li" ], "first_author": "Jie Zhang", "venue": "Computers & Operations Research", "publisher": "Elsevier BV", "abstract": null, "keywords": [ "Drone", "Computer science", "Vehicle routing problem", "Cluster analysis", "Mathematical optimization", "Genetic algorithm", "Sorting", "Tabu search", "Optimization problem", "Metaheuristic", "Perishability", "Local search (optimization)" ], "cited_by_count": 51, "is_retracted": false, "is_paratext": false, "open_access_url": "https://doi.org/10.1016/j.cor.2022.106039" } ]