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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2019年 122卷 350-364页

作者： Wang, Zheng Sheu, Jiuh-Biing Dalian Maritime Univ Sch Maritime Econ & Management 1 Linghai Rd Dalian 116026 Peoples R China Natl Taiwan Univ Dept Business Adm 1Sect 4Roosevelt Rd Taipei 10617 Taiwan

The vehicle routing problem with drones (VRPD) is an extension of the classic capacitated vehicle routing problem, where not only trucks but drones are used to deliver parcels to customers. One distinctive feature of the VRPD is that a drone may travel with a truck, take off from its stop to serve customers, and land at a service hub to travel with another truck as long as the flying range and loading capacity limitations are satisfied. routing trucks and drones in an integrated manner makes the problem much more challenging and different from classical vehicle routing literature. We propose a mixed integer programming model, and develop a branch-and-price algorithm. Extensive experiments are conducted on the instances randomly generated in a practical setting, and the results demonstrate the good computational performance of the proposed algorithm. We also conduct sensitivity analysis on a key factor that may affect the total cost of a solution. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： vehicle routing problem with drones Branch and price Column generation

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A branch-cut-and-price approach for the two-echelon vehicle routing problem with drones

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COMPUTERS & OPERATIONS RESEARCH 2025年 173卷

作者： Lichau, Sylvain Sadykov, Ruslan Francois, Julien Dupas, Remy Univ Bordeaux CNRS IMS UMR 5218Bordeaux INP F-33400 Talence France Atopima 16 Pl Sainte Eulalie F-33000 Bordeaux France

We present anew set-partitioning model for the two-echelon vehicle routing problem with drones (2E-VRPD). In this model, partial routes corresponding to drone movements are enumerated by an efficient dynamic program. A state-of-the-art exact branch-cut-and-price algorithm solves the model using a labeling algorithm for the pricing problems. We further propose an adaptation of the well-known rounded capacity cuts, specifically tailored to address this problem, as well as pre-processing methods designed to enhance the algorithm's efficiency. In addition, we propose an effective heuristic branch-cut-and-price based on the exact algorithm. Computational experiments demonstrate that the exact algorithm solves all instances from the 2E-VRP-D literature and significantly increases the size of optimally solved clustered instances. Finally, a sensitivity analysis is conducted to assess the impact of the proposed enhancements.

关键词： vehicle routing problem with drones Branch-cut-and-price

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vehicle routing problem with drones considering time windows

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EXPERT SYSTEMS WITH APPLICATIONS 2022年第0期191卷 116264-116264页

作者： Kuo, R. J. Lu, Shih-Hao Lai, Pei-Yu Mara, Setyo Tri Windras Natl Taiwan Univ Sci & Technol Dept Ind Management 43Sect 4Keelung Rd Taipei 106 Taiwan Natl Taiwan Univ Sci & Technol Dept Business Adm 43Sect 4Keelung Rd Taipei 106 Taiwan Univ Gadjah Mada Fac Engn Dept Mech & Ind Engn Yogyakarta 55284 Special Region Indonesia

The cooperation of trucks and unmanned aerial vehicles (UAV) has become a new delivery method in the area of logistics and transportation. In this form of cooperation, the trucks are not only able to provide services to the customers, but also serve as a 'launch pad' for the drones, in which the drones can be launched to service a customer and then recovered at the rendezvous node. This study intends to explore this cooperation by developing a model for the vehicle routing problem with drones that considers the presence of customer time windows (VRPTWD). A mixed-integer programming (MIP) model is presented to minimize the total travelling costs. Then, a simple yet effective variable neighborhood search (VNS) procedure with a novel solution representation is proposed as a solver. The numerical results indicate the ability of the proposed VNS to solve the VRPTWD, as well as the improvement of delivery performance using drones.

关键词： vehicle routing problem with drones Time windows Unmanned aerial vehicles Logistics Variable neighborhood search

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OPTIMAL AND HEURISTIC ALGORITHMS FOR THE MULTI-OBJECTIVE vehicle routing problem with drones FOR MILITARY SURVEILLANCE OPERATIONS

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2022年第3期18卷 1651-1663页

作者： Ahn, Namsu Kim, Soochan Korea Mil Acad Dept Mech & Syst Engn Seoul 01805 South Korea

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.

关键词： vehicle routing problem with drones traveling salesman problem with drones multi-objective military surveillance operation

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A multi-visit flexible-docking vehicle routing problem with drones for simultaneous pickup and delivery services

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2024年第1期312卷 125-137页

作者： Jiang, Jie Dai, Ying Yang, Fei Ma, Zujun Southwest Jiaotong Univ Sch Econ & Management Chengdu 610031 Peoples R China Zhejiang Univ Finance & Econ Sch Business Adm Hangzhou 310018 Peoples R China

This study investigates a multi-visit flexible-docking vehicle routing problem that uses a truck and drone fleet to fulfill pickup and delivery requests in rural areas. In this collaborative truck-drone system, each drone may serve multiple customers per trip (multi-visit services), dock to the same or different truck from where it launched (flexible docking), and perform simultaneous pickup and delivery. These characteristics complicate the temporal, spatial, and loading synchronization for trucks and drones, making the decisions of order allocation and vehicle routing highly interdependent and intractable. This problem is formulated as a mixed-integer linear programming model and solved by a tailored adaptive large neighborhood search metaheuristic. Numerical experiments are conducted on sparse rural networks to demonstrate the efficiency of the proposed method. We observe that the proposed truck-drone system shows an average cost saving of 34% compared to the truck-only case. Moreover, deep insights into the impacts of multi-visit services, flexible docking, and simultaneous pickup and delivery on the performance of the truck-drone system are discussed.

关键词： Logistics vehicle routing problem with drones Pickup and delivery services Mixed-integer linear programming Adaptive large neighborhood search

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Aerial-ground collaborative routing with time constraints

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Chinese Journal of Aeronautics 2023年第2期36卷 270-283页

作者： Jiahao XING Lichen SU Wenjing HONG Lu TONG Renli LYU Wenbo DU School of Electronics and Information Engineering Beihang UniversityBeijing 100091China School of Future Aerospace Technology/Shen Yuan Honors College Beihang UniversityBejing 100091China School of Automation Science and Electrical Engineering Beihang UniversityBejing 100091China Guangdong Provincial Key Laboratory of Brain-Inspired Intelligent Computation Shenzhen 518055China Department of Computer Science and Engineering Southern University of Science and TechnologyShenzhen 518055China Research Institute of Frontier Science Beihang UniversityBeijing 100083China CAAC Key Laboratory of General Aviation Operation Civil Aviation Management Institute of ChinaBeijing 100102China

The advancement of autonomous technology makes electric-powered drones an excellent choice for flexible logistics services at the last mile delivery *** reach a balance between green transportation and competitive edge,the collaborative routing of drones in the air and trucks on the ground is increasingly invested in the next generation of delivery,where it is particularly reasonable to consider customer time windows and time-dependent travel times as two typical time-related factors in daily *** this paper,we propose the vehicle routing problem with drones under Time constraints(VRPD-T)and focus on the time constraints involved in realistic scenarios during the delivery.A mixed-integer linear programming model has been developed to minimize the total delivery completion ***,to overcome the limitations of standard solvers in handling large-scale complex issues,a space-time hybrid heuristic-based algorithm has been developed to effectively identify a high-quality *** numerical results produced from randomly generated instances demonstrate the effectiveness of the proposed algorithm.

关键词： Aerial-ground collaborative delivery Mixed-integer programming Space-time hybrid heuristic algorithm vehicle routing problem with drones Time-dependent travel times

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A-VRPD: Automating Drone-Based Last-Mile Delivery Using Self-Driving Cars

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2023年第9期24卷 9599-9612页

作者： Imran, Navid Mohammad Mishra, Sabyasachee Won, Myounggyu Univ Memphis Dept Comp Sci Memphis TN 38152 USA Univ Memphis Dept Civil Engn Memphis TN 38152 USA

Drone-based last-mile delivery is an emerging technology that uses drones loaded onto a truck to deliver parcels to customers. In this paper, we introduce a fully automated system for drone-based last-mile delivery through incorporation of autonomous vehicles (AVs). A novel problem called the autonomous vehicle routing problem with drones (A-VRPD) is defined. A-VRPD is to select AVs from a pool of available AVs based on crowd sourcing, assign selected AVs to customer groups, and schedule routes for selected AVs to optimize the total operational cost. We formulate A-VRPD as a Mixed Integer Linear Program (MILP) and propose an optimization framework to solve the problem. A greedy algorithm is also developed to significantly improve the running time for large-scale delivery scenarios. Extensive simulations were conducted taking into account real-world operational costs for different types of AVs, traveled distances calculated considering the real-time traffic conditions using Google Map API, and varying load capacities of AVs. We evaluated the performance in comparison with two different state-of-the-art solutions: an algorithm designed to address the traditional vehicle routing problem with drones (VRP-D), which involves human-operated trucks working in tandem with drones to deliver parcels, and an algorithm for the two echelon vehicle routing problem (2E-VRP), wherein parcels are first transported to satellite locations and subsequently delivered from those satellites to the customers. The results indicate a substantial increase in profits for both the delivery company and vehicle owners compared with the state-of-the-art algorithms.

关键词： drones Costs vehicle routing Traveling salesman problems Scalability routing Logistics Drone-based last-mile delivery vehicle routing problem with drones traveling salesman problem with drones

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Optimal decision-making of post-disaster emergency material scheduling based on helicopter-truck-drone collaboration

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2024年 127卷

作者： Shi, Yong Yang, Junhao Han, Qian Song, Hao Guo, Haixiang China Univ Geosci Sch Econ & Management Lumo Rd Wuhan 430074 Peoples R China China Univ Geosci Lab Nat Disaster Risk Prevent & Emergency Manageme Lumo Rd Wuhan 430074 Peoples R China China Univ Geosci Lumo Rd 388 Wuhan Peoples R China

In the last decades, natural disasters, such as earthquakes and landslides, have occurred frequently, seriously threatening the safety of people's lives and property. How emergency material is scheduled and delivered efficiently to the affected sites after a disaster has become a critical issue in emergency management. Current studies on emergency material scheduling mainly focus on truck or helicopter transport. Inspired by the success of employing drones in commercial logistics, this work investigates the emergency material scheduling issue based on the cooperative transport of drones, helicopters, and trucks. Specifically, this paper considers the limited transport capacity, road conditions in the early stage of the disaster rescue, and affected sites restricted by road conditions that can only be served by helicopters or drones. The studied problem is formulated as a mixed integer programming model, and a two-stage heuristic algorithm is developed to solve the model. For the proposed model, instances of different sizes are generated, and extensive experiments are performed to test the efficiency of the proposed algorithm. The comparison between the solutions obtained by the twostage algorithm and Gurobi Solver for the small instances validates the effectiveness of the proposed heuristic algorithm. Experimental results for the larger instances show that the proposed two-stage algorithm can effectively solve the problem of emergency material scheduling. Sensitivity analysis of ten typical instances is performed to provide managerial insights. Finally, a case study of the Sichuan earthquake and the visualization of transport routes are presented. The model and solving approach proposed in this work can provide essential decision references for emergency management decision-making.

关键词： Emergency materials dispatching Tabu search vehicle routing problem with drones Two-stage algorithm

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vehicle-drone collaborative distribution path planning based on neural architecture search under the influence of carbon emissions

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DISCOVER COMPUTING 2024年第1期27卷 42页

作者： Ma, Jia Ma, Xinru Li, Chulian Li, Tongyan Shenyang Aerosp Univ Sch Econ & Management Shenyang 110136 Peoples R China

Intelligent operation and green distribution have become a mainstream task to enable fast development of urban distribution applications. However, how to improve the distribution efficiency with low operating costs, and mitigate environmental pollution with high service quality is still a significant challenge in the practical industry applications. To address the above challenge, in this paper, we take into account both the economic cost and environmental cost, and propose a joint distribution path planning model based on neural architecture search (NAS) for electric vehicles with double-decked drones. More specifically, in our design, the factors such as energy consumption and carbon emissions of vehicles and drones during different distribution stages are considered. Then, a mixed integer linear programming model is established under the constraints of customer time window, vehicle capacity and vehicle battery capacity. Based on this model, a hybrid genetic algorithm is proposed to solve the optimization problem, where the carbon emission cost is estimated by the convolution neural network model, which is optimized by the neural architecture search technique. We conduct extensive experiments to validate the effectiveness of the proposed method. The experimental results show that, compared with CPLEX, the proposed method excelled in both solution quality and speed, which verify the effectives of our hybrid algorithm in dealing with the 2E-VRPD problem, where delivery routes can be well optimized, the efficiency of vehicle-machine collaborative delivery can be improved, and delivery costs are reduced.

关键词： vehicle routing problem with drones Convolution neural network model Hybrid genetic algorithm Large-scale neighborhood search

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A novel mathematical model and a hybrid grouping evolution strategy algorithm for an automated last mile delivery system considering wind effect

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2024年第PartB期127卷

作者： Ahmadi, Mohammad Zegordi, Seyed Hessameddin Tarbiat Modares Univ Fac Ind & Syst Engn POB 14115143 Tehran Iran

Efficient and timely delivery of goods in last-mile logistics is a key challenge for e-commerce companies. With the rise of drone technology, drone-based delivery has emerged as a promising solution to address the challenges of traditional last-mile logistics. In light of the environmental and social challenges faced by last-mile delivery, integrating sustainability into logistics planning has become a vital requirement rather than a mere option. drones have been identified as a potential solution to reduce greenhouse gas emissions and improve the sustainability of last-mile logistics. In this study, we present a mathematical model for the multi-depot multi-period drone delivery problem, which considers wind patterns and multi-periodicity to optimize the routing of multiple drones from multiple depots over a planning horizon of one day or shift. We included the wind profiles in our modeling to achieve a more realistic drone route planning. To address the complexity of the problem, we employ the Dantzig-Wolfe decomposition method to obtain a lower bound for the problem. Since we have a grouping problem, a novel metaheuristic algorithm, based on a grouping evolution strategy algorithm is developed for efficient drone routing. The algorithm uses the structural information along with the problem with the aid of a proposed constructive heuristic based on the well-known best fit strategy. Results show that proposed approach, achieved a solution with a gap of 2.99% to the lower bound on average, demonstrating its effectiveness in addressing the complexity of the multi-depot multi-period drone delivery problem while considering the impact of wind patterns.

关键词： Grouping evolutionary strategy algorithm Column generation Multi depot vehicle routing problem with drones Wind effect Best fit algorithm

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