Solution of Multiple Travelling Salesman Problem using Particle Swarm Optimization based Algorithms
AbstractNowadays, the systems that are inspired by biological structures have gained importance and attracted the attention of researchers. The Multiple Travelling Salesman Problem (MTSP) is an extended version of the TSP. The aim in the MTSP is to find the tours for m salesmen, who all start and end at the depot, such that each intermediate node is visited exactly once and the total cost of visiting nodes is minimized. The Particle Swarm Optimization (PSO) algorithm which is a meta-heuristic algorithm based on the social behaviour of birds. In this article, 2 algorithms based on PSO, called APSO and HAPSO, were proposed to solve the MTSP. The APSO algorithm is based on the PSO and 2-opt algorithms, the path-relink and swap operators. While the HAPSO algorithm is based on the GRASP, PSO and 2-opt algorithms, the path-relink and swap operators. In the experiments, 5 TSP instances are used and the algorithms are compared with the GA and ACO algorithms. According to the results, the HAPSO algorithm has the better performance than the other algorithms on the most instances. Moreover the HAPSO algorithm produces more stable results than the APSO algorithm and the performance of the HAPSO algorithm is better in all the MTSP instances. Therefore, the HAPSO algorithm is more robust than the APSO algorithm.
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