Two-level genetic algorithm for clustered traveling salesman problem with application in large-scale TSPs

Abstract

Let G = (V, E) be a complete undirected graph with vertex set V, edge set E, and edge weights /(e) satisfying the triangle inequality. The vertex set V is partitioned into clusters V <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> , V <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> , …, V <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</inf> . The clustered traveling salesman problem (CTSP) seeks to compute the shortest Hamiltonian tour that visits all the vertices, in which the vertices of each cluster are visited consecutively. A two-level genetic algorithm (TLGA) was developed for the problem, which favors neither intra-cluster paths nor inter-cluster paths, thus realized integrated evolutionary optimization for both levels of the CTSP. Results show that the algorithm is more effective than known algorithms. A large-scale traveling salesman problem (TSP) can be converted into a CTSP by clustering so that it can then be solved by the algorithm. Test results demonstrate that the clustering TLGA for large TSPs is more effective and efficient than the classical genetic algorithm.