Abstract: This paper aims at the vehicle scheduling requirements of economy, timeliness, reliability and robustness in emergency logistics. A multi-objective robust vehicle routing problem with time windows, uncertain de-mand, uncertain driving time and routing failure risk is considered. A new cost function, a satisfaction function, a risk function and a robustness function are proposed to be four optimization objectives of the model, and the uncertain model is transformed into a deterministic robust counterpart model based on the robust optimization theory. In this paper, the multi-objective model is solved based on the SPEA2 algorithm framework, but a variety of improvement strategies are proposed for the algorithm defects. The effectiveness of the improvement strategies is proved by comparison experiments.

Key words: emergency logistics, Vehicle Routing Problem（VRP）, multi-objective robust optimization, Improved Strength Pareto Evolutionary Algorithm 2（ISPEA2）

摘要： 针对应急物流车辆调度问题中对于经济性、时效性、可靠性和鲁棒性的多种要求，考虑了含有时间窗、不确定需求、不确定行驶时间，以及路段含有失效风险的多目标鲁棒车辆路径优化问题，通过定义新的成本函数、满意度函数、风险度函数和鲁棒度函数作为四个优化目标来构建模型，并基于鲁棒优化理论将不确定模型转化为确定性鲁棒对应模型求解，为解决不确定环境下优化问题提供了新的思路。算法方面，主要基于SPEA2算法框架求解该多目标模型，针对算法缺陷提出多种改进策略，并通过对比实验证明了改进策略的有效性。

关键词: 应急物流, 车辆路径优化问题, 多目标鲁棒优化, 改进SPEA2算法