Particle Swarm Optimization Algorithm for the Traveling Salesman Problem

Particle swarm optimization, PSO, is an evolutionary computation technique inspired in the behavior of bird flocks. PSO algorithms were first introduced by Kennedy & Eberhart (1995) for optimizing continuous nonlinear functions. The fundamentals of this metaheuristic approach rely on researches where the movements of social creatures were simulated by computers (Reeves, 1983; Reynolds, 1987; Heppner & Grenander, 1990). The research in PSO algorithms has significantly grown in the last few years and a number of successful applications concerning single and multi-objective optimization have been presented (Kennedy& Eberhart, 2001; Coello et al., 2004). This popularity is partially due to the fact that in the canonical PSO algorithm only a small number of parameters have to be tuned and also due to the easiness of implementation of the algorithms based on this technique. Motivated by the success of PSO algorithms with continuous problems, researchers that deal with discrete optimization problems have investigated ways to adapt the original proposal to the discrete case. In many of those researches, the new approaches are illustrated with the Traveling Salesman Problem, TSP, once it has been an important test ground for most algorithmic ideas. Given a graph