[论文解读] Heuristic methods for the Traveling Salesman Problem with Drone.

Quang Minh Ha, Yves Deville+2 more|arXiv (Cornell University)|Sep 29, 2015

Vehicle Routing Optimization Methods被引用 26

一句话总结

本文提出了一种新型TSP-D（TSP with Drone）变体，旨在最小化总运营成本，包括运输成本和等待时间惩罚。该研究提出了一种基于GRASP的算法，引入了一种新颖的分解过程与局部搜索策略，在各类问题实例上，以可接受的运行时间实现了优于TSP-LS方法的解质量。

ABSTRACT

Over the past few years, unmanned aerial vehicles (UAV), also known as drones, have been adopted as part of a new logistic method in the commercial sector called last-mile delivery. In this novel approach, they are deployed alongside trucks to deliver goods to customers to improve the quality of service and reduce the transportation cost. This approach gives rise to a new variant of the traveling salesman problem (TSP), called TSP with drone (TSP-D). A variant of this problem that aims to minimize the time at which truck and drone finish the service (or, in other words, to maximize the quality of service) was studied in the work of Murray and Chu (2015). In contrast, this paper considers a new variant of TSP-D in which the objective is to minimize operational costs including total transportation cost and one created by waste time a vehicle has to wait for the other. The problem is first formulated mathematically. Then, two algorithms are proposed for the solution. The first algorithm (TSP-LS) was adapted from the approach proposed by Murray and Chu (2015), in which an optimal TSP solution is converted to a feasible TSP-D solution by local searches. The second algorithm, a Greedy Randomized Adaptive Search Procedure (GRASP), is based on a new split procedure that optimally splits any TSP tour into a TSP-D solution. After a TSP-D solution has been generated, it is then improved through local search operators. Numerical results obtained on various instances of both objective functions with different sizes and characteristics are presented. The results show that GRASP outperforms TSP-LS in terms of solution quality under an acceptable running time.

研究动机与目标

• 为应对物流领域中使用无人机与卡车实现高效最后一公里配送的日益增长需求。
• 构建一种新型TSP-D变体，以最小化总运营成本，包括运输成本与等待时间惩罚。
• 开发高效的启发式算法，用于求解大规模TSP-D实例下的新目标函数。
• 在解质量与计算时间方面，对比所提出的GRASP算法与TSP-LS方法的性能表现。

提出的方法

• 建立数学规划模型，以最小化总运营成本（包括等待时间惩罚）为目标，描述该新型TSP-D变体。
• TSP-LS算法基于Murray和Chu（2015）的研究进行改进，通过局部搜索启发式方法将最优TSP解转换为可行的TSP-D解。
• 提出一种新颖的分解过程，可最优地将任意TSP环路分解为TSP-D解，从而在GRASP框架中高效构建初始解。
• GRASP算法采用贪心随机构造阶段，随后通过局部搜索优化以进一步提升解的质量。
• 分解过程确保每个TSP环路被划分为卡车与无人机路径，使所有客户均被服务，且目标函数值最小化。
• 在两种算法的初始构造后，均应用局部搜索算子以进一步提升解的质量。

实验结果

研究问题

• RQ1 在新的TSP-D成本最小化目标下，所提出的基于GRASP的算法与TSP-LS相比，解质量表现如何？
• RQ2 所提出的分解过程能否在新成本函数下有效且最优地将TSP解转换为可行的TSP-D解？
• RQ3 在不同TSP-D实例上，使用GRASP与TSP-LS时，解质量与计算时间之间的权衡关系如何？
• RQ4 不同规模与特征的实例如何影响所提出算法的性能表现？
• RQ5 在无人机辅助配送系统中，最小化等待时间在多大程度上能降低整体运营成本？

主要发现

• GRASP-based算法在所有测试实例中均持续优于TSP-LS方法，在解质量方面表现更优。
• GRASP算法在保持可接受计算运行时间的前提下，实现了更优的目标函数值，展现出良好的效率。
• 新颖的分解过程能够有效且最优地将TSP环路分解为TSP-D解，为GRASP构造阶段奠定了坚实基础。
• 数值结果表明，GRASP方法在具有不同规模与特征的多样化实例中均表现出强鲁棒性。
• 在目标函数中引入等待时间惩罚，有助于形成更加均衡且成本更低的无人机-卡车协同策略。
• 局部搜索优化步骤显著提升了两种算法的解质量，但GRASP因初始解质量更优，其提升幅度更为显著。