中文摘要：

研究一个仓库下，同质车队具有最大负载能力限制，客户同时具有送货与取货需求，产品以原有形态回收的逆向物流车辆路径问题，建立了带车辆最大行程约束的VRPSPD问题的混合整数规划模型；在蚁群系统算法的基础上，采用了基于排序的蚂蚁系统和最大最小蚂蚁系统算法的信息素更新策略，针对VRPSPD问题车辆负载量不断波动的复杂特性，设计了考虑车辆负载使用率的启发式因子；考虑车辆出仓载货量的初始化与剩余客户的送取货需求量相关，并在一定范围内随机取值．实例运算的结果表明，该算法对于求解带车辆最大行程约束的VRPSPD问题，可以有效提高车辆的负载率，避免因负载波动和最大负载能力约束而增加车辆总行程，在可接受的计算时间内收敛到满意解．

英文摘要：

This paper studies the reverse logistics vehicle routing problem of simultaneous distribution of commodities and collection of reusable ones the same size as the initial state with a single depot and a homogeneous fleet of vehicles with limited capacities and maximum distance, and constructs a mixed integer programming model. To solve this problem, an Ant Colony System （ACS） approach combining with the pheromone updating strategy of ASRank （Rankbased Version of Ant System） and MMAS （MAX-MIN Ant System） is proposed. A new heuristic factor is designed to improve the vehicle loading ability as weU as the vehicle distance, and the initial vehicle load is designed to be a random value correlated to the delivery and pick-up demand of the rest customers on the path. The experimental study indicates that the approach could improve the vehicle load rate and get rid of the additional total distance caused by the fluctuating vehicle load and the limited capacity. It could obtain the satisfied solution with high convergence speed in the acceptable time.