Fuzzy discrete particle swarm optimization for solving traveling salesman problem

Abstract

Particle swarm optimization, as an evolutionary computing technique, has succeeded in many continuous problems, but research on discrete problems especially combinatorial optimization problem has been done little according to Kennedy and Eberhart (1997) and Mohan and Al-kazemi (2001). In this paper, a modified particle swarm optimization (PSO) algorithm was proposed to solve a typical combinatorial optimization problem: traveling salesman problem (TSP), which is a well-known NP-hard problem. Fuzzy matrices were used to represent the position and velocity of the particles in PSO and the operators in the original PSO formulas were redefined. Then the algorithm was tested with concrete examples in TSPLIB, experiment shows that the algorithm can achieve good results.