Immune co-evolutionary algorithm based partition balancing optimization for tobacco distribution system

In China, the tobacco distribution is organized by fixed districts and routes with low efficiency and high distribution cost due to its unbalanced workload. And, though the dynamic method adopting vehicle routing algorithms produces optimal routes, the unstable routes increase the delivery time and managerial cost. So it is urgent and feasible to break the fixed districts to provide periodic balanced partitions for tobacco distribution. In this paper, a multi-criteria balanced partition model is built, whose minimal objectives including total number of tours in all districts, the travel distance and time of all tours, and the balance objectives include number of tours, total demand, traveling distance and time of each district are considered. An immune co-evolutionary algorithm with two stages is designed to search the optimal balanced partitions. In the first stage, the initial balanced partitions are produced. In the second stage, the clonal selection procedure, with partition proliferation, selection and elimination, and cooperative searching among districts, is adopted to achieve balanced partition. The experiments on Lenfen city in China as a practical application reveal the efficiency of the proposed model and algorithm. First, the searching processes are analyzed by exploring the partitions and Pareto partitions. Second, the evolutionary process of the algorithm is shown by the varying of the multiple objectives. Finally, three methods including fixed districts and routes, dynamic VRP scheduling and periodic balanced partition are compared to show the value of the study.