[论文解读] Equity Objectives in Vehicle Routing: A Survey and Analysis

Piotr Matl, Richard F. Hartl+1 more|arXiv (Cornell University)|May 27, 2016

Vehicle Routing Optimization Methods参考文献 77被引用 4

一句话总结

本文分析了车辆路径问题（VRPs）中的公平性目标，通过公理化性质和对双目标VRP实例的数值研究，评估了六种常见的公平性度量。研究发现，成本最优解通常表现出较差的公平性，各类度量下的边际成本改进较低，且非单调公平性度量可能产生悖论性的有效解，表明在VRP建模中单调度量更为合适。

ABSTRACT

Recently, equity aspects have been considered in a growing number of models and methods for vehicle routing problems (VRPs). Equity concerns most often relate to fairly allocating workloads and to balancing the utilization of resources, and many practical applications have been reported. However, there has been only limited discussion about how equity should be modelled in the context of VRPs, and various measures for optimizing such objectives have been proposed and implemented without critical evaluation of their respective merits and consequences. This article addresses this gap by providing an analysis of classical and alternative equity measures for bi-objective VRP models. In the survey we review and categorize the literature on equitable VRP models. In the analysis, we identify a set of axiomatic properties which an ideal equity measure should satisfy, collect 6 common measures of equity, and point out important connections between their properties and the properties of the resulting Pareto-optimal solutions. To gauge the extent of some of these implications and to examine further relevant aspects for choosing an equity objective, we conduct a numerical study on bi-objective VRP instances solvable to optimality. We find that the equity of cost-optimal solutions is generally poor, while the marginal cost of improvement is low for all examined measures. We also reveal two contradictions of optimizing equity with non-monotonic measures: Pareto-optimal solutions can consist of non-TSP-optimal tours, and even if all tours are TSP-optimal, Pareto-optimal solutions can be composed of tours which are all equal to or longer than those of other Pareto-optimal solutions. Based on these analyses, we conclude that monotonic equity measures are more appropriate for some types of VRP models, and suggest several promising avenues for further research on equity in logistics applications.

研究动机与目标

• 为解决在车辆路径问题（VRPs）中对公平性建模缺乏批判性评估的问题。
• 识别理想公平性度量在VRP情境下应满足的公理化性质。
• 评估六种常见公平性度量在双目标VRP模型中的性能与影响。
• 研究公平性度量如何影响有效解的结构与质量。
• 通过识别公平物流应用中的有前景研究方向，为未来研究提供指导。

提出的方法

• 综述并分类现有关于公平VRP模型的文献，为分析奠定基础。
• 定义一组理想公平性度量在VRPs中应满足的公理化性质（例如，对称性、无关选项独立性等）。
• 收集并形式化六种广泛使用的公平性度量，包括基尼系数、泰尔指数和最大最小公平性。
• 对可求得最优解的双目标VRP实例进行数值研究，以比较公平性结果与解结构。
• 分析每种公平性度量下的有效解，以检测结构悖论与低效性。
• 评估公平性改进的边际成本，以评估成本与公平性之间的权衡。

实验结果

研究问题

• RQ1 在车辆路径问题的背景下，理想公平性度量应满足哪些公理化性质？
• RQ2 不同公平性度量如何影响VRP有效解的结构与公平性？
• RQ3 在VRP模型中使用非单调公平性度量会产生何种影响？
• RQ4 成本最优性在多大程度上与VRP解中的公平工作量分配相冲突？
• RQ5 不同公平性度量下，公平性改进的边际成本如何变化？

主要发现

• 成本最优的VRP解通常表现出较差的公平性，表明成本效率与公平性之间存在显著权衡。
• 在所有评估的公平性度量中，公平性改进的边际成本均较低，表明通过较小的成本增加即可实现更公平的解。
• 非单调公平性度量可能产生包含非TSP最优路径的有效解，即使所有路径本身均为最优。
• 即使所有路径均为TSP最优，非单调度量下的有效解仍可能由比其他有效解更长的路径组成。
• 研究揭示了非单调度量中的结构悖论，例如存在总路径长度更高但更公平的解。
• 单调公平性度量因其在解生成过程中的一致且直观的行为，被证明更适合用于VRP模型。