Particle swarm for the traveling salesman problem

This paper presents a competitive Particle Swarm Optimization algorithm for the Traveling Salesman Problem, where the velocity operator is based upon local search and path-relinking procedures. The paper proposes two versions of the algorithm, each of them utilizing a distinct local search method. The proposed heuristics are compared with other Particle Swarm Optimization algorithms presented previously for the same problem. The results are also compared with three effective algorithms for the TSP. A computational experiment with benchmark instances is reported. The results show that the method proposed in this paper finds high quality solutions and is comparable with the effective approaches presented for the TSP.