A Hierarchical Algorithm Based on Density Peaks Clustering and Ant Colony Optimization for Traveling Salesman Problem

Abstract

This paper proposed a hierarchical hybrid algorithm for traveling salesman problem (TSP) according to the idea of divide-and-conquer. The TSP problem is decomposed into a few subproblems with small-scale nodes by density peaks clustering algorithm. Every subproblem is resolved by ant colony optimization algorithm, this is the lower layer. The center nodes of all subproblems constitute a new TSP problem, which forms the upper layer. All local tours of these subproblems are joined to generate the initial global tour in the same order that the center nodes are traversed in the upper layer TSP problem. Finally, the global tour is optimized by k-Opt algorithms. Thirty benchmark instances taken from TSPLIB are divided into three groups on the basis of problem size: small-scale, large-scale, and very large-scale. The experimental result shows that the proposed algorithm can obtain the solutions with higher accuracy and stronger robustness, and significantly reduce runtime, especially for the very large-scale TSP problem.