用进化算法优化无人机与卡车协同配送,显著缩短总送货时间。
An Evolutionary Algorithm For the Vehicle Routing Problem with Drones with Interceptions
- 设计进化算法求解无人机拦截卡车的配送路径优化问题。
- 在50和100节点问题上,总配送时间减少39%至60%。
- 适合研究智能物流、无人机协同配送的学者与工程师参考。
本文研究利用卡车与无人机协同解决末端配送难题的新方向。考虑无人机可在行驶途中或客户处拦截卡车的变体问题,称为带拦截的无人机车辆路径问题(VRPDi)。本文提出一种进化算法求解该问题。在此变体中,多对卡车与无人机需被调度,它们可一同或分开从枢纽出发并返回,完成对客户节点的配送。无人机可在某次配送后拦截卡车,或在下一个客户点与其会合。算法在Bouman等(2015)的带无人机旅行商问题(TSPD)数据集上执行,并将VRPDi结果与同数据集上的传统车辆路径问题(VRP)结果进行对比,结果显示总配送时间提升39%至60%。进一步分析涵盖总配送时间、行驶距离、节点调度顺序及算法执行中的多样性。同时评估了算法对VRPDi约束的处理能力。结果还与Dillon等(2023)及Ernst(2024)的算法进行基准比较,后者在VRPDi基础上增加了最大无人机飞行距离约束。分析表明,该算法在合理时间内成功求解50和100节点问题,且解的质量优于前述两篇文献的方法。
原文摘要 · Abstract (English)
The use of trucks and drones as a solution to address last-mile delivery challenges is a new and promising research direction explored in this paper. The variation of the problem where the drone can intercept the truck while in movement or at the customer location is part of an optimisation problem called the vehicle routing problem with drones with interception (VRPDi). This paper proposes an evolutionary algorithm to solve the VRPDi. In this variation of the VRPDi, multiple pairs of trucks and drones need to be scheduled. The pairs leave and return to a depot location together or separately to make deliveries to customer nodes. The drone can intercept the truck after the delivery or meet up with the truck at the following customer location. The algorithm was executed on the travelling salesman problem with drones (TSPD) datasets by Bouman et al. (2015), and the performance of the algorithm was compared by benchmarking the results of the VRPDi against the results of the VRP of the same dataset. This comparison showed improvements in total delivery time between 39% and 60%. Further detailed analysis of the algorithm results examined the total delivery time, distance, node delivery scheduling and the degree of diversity during the algorithm execution. This analysis also considered how the algorithm handled the VRPDi constraints. The results of the algorithm were then benchmarked against algorithms in Dillon et al. (2023) and Ernst (2024). The latter solved the problem with a maximum drone distance constraint added to the VRPDi. The analysis and benchmarking of the algorithm results showed that the algorithm satisfactorily solved 50 and 100-nodes problems in a reasonable amount of time, and the solutions found were better than those found by the algorithms in Dillon et al. (2023) and Ernst (2024) for the same problems.
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