Solving Large-Scale TSP Using a Fast Wedging Insertion Partitioning Approach

A new partitioning method, called Wedging Insertion, is proposed for solving large-scale symmetric Traveling Salesman Problem (TSP). The idea of our proposed algorithm is to cut a TSP tour into four segments by nodes' coordinate (not by rectangle, such as Strip, FRP, and Karp). Each node is located in one of their segments, which excludes four particular nodes, and each segment does not twist with other segments. After the partitioning process, this algorithm utilizes traditional construction method, that is, the insertion method, for each segment to improve the quality of tour, and then connects the starting node and the ending node of each segment to obtain the complete tour. In order to test the performance of our proposed algorithm, we conduct the experiments on various TSPLIB instances. The experimental results show that our proposed algorithm in this paper is more efficient for solving large-scale TSPs. Specifically, our approach is able to obviously reduce the time complexity for running the algorithm; meanwhile, it will lose only about 10% of the algorithm's performance.