带回程取货的逆向物流车辆路径建模及其蚁群算法

对逆向物流车辆路径问题进行了概述和分类，构建了以VRPPDTW为基础的带回程取货的逆向物流车辆路径数学模型，设计了求解该模型的最大-最小蚁群算法，对设计要素进行了详细介绍，包括初始蚁群分布，状态转移策略，以及信息素更新策略等，并给出了具体的算法步骤. 最后，以Solomon中的R101、R102、R103、R104和R105等5项示例为背景，分别取前25节点和50节点，以取货点的取货量比例分别占全部客户节点需求量的10％、30％、50％取货，得到30个算例的计算结果，并将其与Tangian和模拟退火等计算结果进行了比较，结果表明最大-最小蚁群算法在某种程度上优于其他算法

Modeling of Vehicle Routing Problems with Backhauls of Reverse Logistics and Ant Colony Algorithm

This paper summarized the vehicle routing problem with reverse logistics and its classification. A mathematical model of the vehicle problem with reverse logistics was constructed based on VRPPDTW and a max-min ant colony algorithm was designed to solve this model. Then, the elements such as initial ant distribution, strategy of state-transition, and pheromone update strategy were introduced and specific calculate steps of the algorithm were provided. In the example, the anterior 25 nodes and 50 nodes are selected under the background of five examples of R101, R102, R103, R104, and R105 in Solomon. The proportions of the waste from every nodes were 10％, 20％, and 30％, respectively, and the results of 30 examples were obtained. They were also compared with the results from Tangian and simulated annealing algorithm. It was found that the max-min ant colony algorithm was superior to other algorithms to some extent.