Abstract: To optimize vehicle routing problem with stochastic demand and time windows, a multi-objective mathematical programming model based on fuzzy satisfaction degree was established. To compute Pareto solutions, a phased optimal algorithm based on Quantum-inspired Evolutionary Algorithm(QEA)and Particle Swarm Optimization(PSO)was put forward. In the preliminary phase, QEA was applied to get Pareto candidate solutions with a certain scale, where an improved mutation operator based on optimal solution probabilistic selecting and variable rotation angle was proposed. In the following phase, the candidate solutions were mapped into continuous space, so that PSO enable to fast search. To avoid premature, neighborhood search based on nodes exchange was carried out. And to maintain the dispersion of solutions, an adaptive grid operator was designed. Compared to NSGA2, the effectiveness of the proposed method was verified by experiments on benchmarks.

Key words: stochastic demand, Pareto optimal solutions, vehicle routing problem, quantum rotate gate, adaptive grid

摘要： 为优化带时间窗的随机需求车辆路径问题，建立了基于模糊满意度的多目标数学规划模型，并提出了一种基于量子进化算法和粒子群算法分段优化的方法求解Pareto解。第一阶段使用量子进化算法获得一定规模和精度的Pareto候选解，提出了概率选择最优解和可变旋转角改进变异算子；第二阶段通过转换将候选解映射到连续空间，利用粒子群算法继续搜索Pareto最优解。引入了节点交换策略进行邻域搜索，避免算法早熟。为保持Pareto解的分散性，提出了一种自适应网格算子。通过对benchmark仿真与非支配排序的遗传算法的比较，验证显示了算法的有效性。

关键词: 随机需求, Pareto最优解, 车辆路径问题, 量子旋转门, 自适应网格