随机时变车辆路径问题的多目标鲁棒优化方法

车辆路径问题 （vehicle routing problem，VRP） 是物流配送的核心问题之一，为了提高物流配送的时效性，在传统VRP模型的基础上，同时考虑了路网交通状态的时变性和随机性，基于最小最大准则，提出了一种带硬时间窗的随机时变车辆路径问题 （stochastic time-dependent vehicle routing problem，STDVRP） 的多目标鲁棒优化模型. 设计了一种非支配排序蚁群算法 （non-dominated sorting ant colony optimisation，NSACO），求解STDVRP多目标优化模型；通过测试算例，对比分析了NSACO算法与改进型非支配排序遗传算法 （non-dominated sorting genetic algorithm II，NSGA-II）. 研究结果表明:对于车辆数最小的Pareto边界解，NSACO算法的平均车辆数比NSGA-II算法小3.33%；对于最坏行程时间最小的Pareto边界解，NSACO算法的平均最坏行程时间比NSGA-II算法小17.49%. 

Multi-Objective Robust Optimisation Method for Stochastic Time-Dependent Vehicle Routing Problem

The vehicle routing problem (VRP) is a core issue of distribution logistics. In order to improve the timeliness of deliveries, a multi-objective robust optimisation model based on the minimax criterion was proposed for the stochastic time-dependent vehicle routing problem (STDVRP) with hard time windows, considering both the stochastic and time-varying nature of link travel times. A non-dominated sorting ant colony optimisation (NSACO) algorithm was designed to solve this multi-objective optimisation model for the STDVRP. The NSACO algorithm was compared with the non-dominated sorting genetic algorithm II (NSGA-II) through computational instances. The results show that for the Pareto boundary of the minimised number of vehicles, the average number of vehicles for NSACO is 3.33% less than that of NSGA-II, and for the Pareto boundary of the minimised worst travel time, the average worst travel time for NSACO is 17.49% less than that of NSGA-II.