中文摘要：

研究逆向物流车辆路径（VRPSPD）问题，建立了VRPSPD问题的混合整数规划模型。利用启发式算法的特点构造求解VRPSPD问题的一种协同PSO_SA算法，设计了该算法初始种群的编码规则、信息交换策略、2-opt邻域解生成策略和SA算法中的冷却进度表规则。实验过程以典型算例为例进行了实验，并对重要参数进行了分析。实验结果表明，该算法对于求解VRPSPD问题，可以有效提高车辆的负载使用率，避免因负载波动和最大负载能力约束而增加车辆总行程，在可以接受的迭代次数限制内可以收敛到满意解。

英文摘要：

This paper studies the vehicle routing with simultaneous delivery and pick-up problem, and constructs a mixed integer programming model. To solve this problem, a new collaborative PSO_SA （paritle swarm optimization and simulated annealing） algorithm based on characteristics of heuristic algorithm is designed, which includes the coding rules of initial solution, 2-opt information exchange strategy, neighborhood solution generation strategy and cooling schedule of SA algorithm strategy. Taking a typical instance as an example, this makes a large number of experiments, and analyzes the important parameters. The experimental study indicates that the approach could improve the vehicle load rate and get rid of theadditional total distance caused by the fluctuating vehicle load and the limited capacity, the result of the collaborative PSO_SA algorithm is better. The satisfying solutions can be obtained within acceptable time.