An Adaptive Layered Clustering Framework with Improved Genetic Algorithm for Solving Large-Scale Traveling Salesman Problems

Abstract

Traveling salesman problems (TSPs) are well-known combinatorial optimization problems, and most existing algorithms are challenging for solving TSPs when their scale is large. To improve the efficiency of solving large-scale TSPs, this work presents a novel adaptive layered clustering framework with improved genetic algorithm (ALC_IGA). The primary idea behind ALC_IGA is to break down a large-scale problem into a series of small-scale problems. First, the k-means and improved genetic algorithm are used to segment the large-scale TSPs layer by layer and generate the initial solution. Then, the developed two phases simplified 2-opt algorithm is applied to further improve the quality of the initial solution. The analysis reveals that the computational complexity of the ALC_IGA is between O(nlogn) and O(n2). The results of numerical experiments on various TSP instances indicate that, in most situations, the ALC_IGA surpasses the compared two-layered and three-layered algorithms in convergence speed, stability, and solution quality. Specifically, with parallelization, the ALC_IGA can solve instances with 2×105 nodes within 0.15 h, 1.4×106 nodes within 1 h, and 2×106 nodes in three dimensions within 1.5 h.