Abstract: Considering the vehicle routing problem with fuzzy demand and fuzzy time window, this paper designed a multi-objective fuzzy chance constrained model, with the objectives of minimizing the total travel distance and the number of vehicles, and maximizing the satisfaction of average customers. In order to improve the diversity of the population, the crossover operator was improved. Based on the introduction of the local search algorithm and Arena’s principle, a hybrid genetic algorithm was designed to solve the multi-objective vehicle routing problem. Experiments of VRPTW standard examples not only show that the algorithm can effectively solve the vehicle routing problem with time windows, but also show the influence of the dispatcher preference index on the decision objective. The research results can provide a way for solving the vehicle routing problem with fuzzy demand and time window, and guidance for actual distribution path planning.

Key words: vehicle routing problem, fuzzy demand, fuzzy time window, hybrid genetic algorithm, Arena's principle

摘要： 针对带模糊需求与模糊时间窗的车辆路径问题，以总行驶距离、车辆使用数最小化，以及平均客户满意度最大化为目标，构建基于可信性测度理论的多目标模糊机会约束模型。为提高种群的多样性，改进了交叉算子，在引入局部优化算法及擂台法则的基础上，设计了适合求解多目标车辆路径问题的混合遗传算法。通过VRPTW标准算例实验，表明算法能够有效地求解带时间窗的车辆路径问题，以及模型的合理性，同时显示了决策者偏好值对决策目标的影响。研究成果可为求解带模糊需求与时间窗的车辆路径问题提供一种思路，也可为实际配送路径规划提供指导。

关键词: 车辆路径问题, 模糊需求, 模糊时间窗, 混合遗传算法, 擂台法则