[论文解读] Dynamic Vehicle Routing Problem: A Monte Carlo approach

Michał Okulewicz, Jacek Mańdziuk|arXiv (Cornell University)|Jun 15, 2020

Vehicle Routing Optimization Methods参考文献 21被引用 9

一句话总结

本文提出一种结合蒙特卡洛树（MCTree）与粒子群优化（PSO）的方法，以解决动态车辆路径问题（DVRP），其中客户请求在一天内动态到达。通过基于已知请求统计和空间边界的生成人工请求，MCTree提升了解的质量与质量达成时间的权衡，在时间限制严格的情况下，优于普通启发式方法和2MPSO，尤其在优化预算较小时表现更优。

ABSTRACT

In this work we solve the Dynamic Vehicle Routing Problem (DVRP). DVRP is a modification of the Vehicle Routing Problem, in which the clients' requests (cities) number and location might not be known at the beginning of the working day Additionally, all requests must be served during one working day by a fleet of vehicles with limited capacity. In this work we propose a Monte Carlo method (MCTree), which directly approaches the dynamic nature of arriving requests in the DVRP. The method is also hybridized (MCTree+PSO) with our previous Two-Phase Multi-swarm Particle Swarm Optimization (2MPSO) algorithm. Our method is based on two assumptions. First, that we know a bounding rectangle of the area in which the requests might appear. Second, that the initial requests' sizes and frequency of appearance are representative for the yet unknown clients' requests. In order to solve the DVRP we divide the working day into several time slices in which we solve a static problem. In our Monte Carlo approach we randomly generate the unknown clients' requests with uniform spatial distribution over the bounding rectangle and requests' sizes uniformly sampled from the already known requests' sizes. The solution proposal is constructed with the application of a clustering algorithm and a route construction algorithm. The MCTree method is tested on a well established set of benchmarks proposed by Kilby et al. and is compared with the results achieved by applying our previous 2MPSO algorithm and other literature results. The proposed MCTree approach achieves a better time to quality trade-off then plain heuristic algorithms. Moreover, a hybrid MCTree+PSO approach achieves better time to quality trade-off then 2MPSO for small optimization time limits, making the hybrid a good candidate for handling real world scale goods delivery problems.

研究动机与目标

• 为解决动态车辆路径问题（DVRP），其中客户请求在当天开始时尚未知，且必须在一天工作日内完成服务。
• 在时间预算有限的动态路径规划场景中，提升解的质量与计算效率。
• 评估人工请求生成与混合元启发式算法在增强基于启发式的DVRP解方面的有效性。
• 在标准DVRP基准上，将所提方法与现有算法（2MPSO、GA2007、GA2014、ACOLNS）进行对比评估。

提出的方法

• 该方法将工作日划分为时间片，并在每个时间片内使用蒙特卡洛方法模拟未知的未来请求，求解静态VRP。
• 人工客户请求在边界矩形内均匀分布生成，请求规模从已知请求规模中均匀采样。
• 基于克鲁斯卡尔算法的聚类算法将请求分配给车辆，随后使用2-OPT局部搜索启发式算法构建路径。
• MCTree+PSO混合方法将蒙特卡洛树与两阶段多粒子群优化（2MPSO）结合，以优化解。
• PSO组件采用可变的群组规模（1–4）和迭代次数（1–28），以平衡解的质量与计算时间。
• 采用Kilby等人提供的基准进行评估，性能通过质量达成时间权衡与路径长度比值进行衡量。

实验结果

研究问题

• RQ1 人工请求生成能否提升基于启发式的动态车辆路径算法的性能？
• RQ2 在时间约束下，MCTree方法与普通启发式方法及2MPSO相比，在解的质量与计算效率方面表现如何？
• RQ3 在小规模优化时间限制下，MCTree+PSO混合方法是否能实现优于2MPSO的质量达成时间权衡？
• RQ4 所提方法在最大达10,000个请求的大规模问题上，其可扩展性如何？

主要发现

• 在平均优化时间限制低于10秒的情况下，MCTree+PSO混合方法在质量达成时间权衡上优于2MPSO。
• MCTree+PSO在22个基准中的10个上优于2MPSO，在21个基准中的6个上优于GA2007，其平均路径长度为GA2007的1.0144倍。
• MCTree的平均路径长度比GA2014短1.0126倍，比ACOLNS短1.0178倍，同时在大规模基准上满足了严格的时间限制。
• 回归分析证实所有方法的理论时间复杂度为O(m²log m)，且所有拟合的R²值均大于95%。
• 采用单次PSO评估的MCTree+PSO在平均处理时间上表现最佳，可在单台PC上处理最多约10,000个请求，耗时8小时。
• 该方法展现出良好的可扩展性，最大MCTree+PSO配置在8小时内可处理约5,400个请求，而2MPSO采用2个粒子和14次迭代的配置可处理约4,700个请求。