Fuzzy Particle Swarm Optimization with Simulated Annealing and Neighborhood Information Communication for Solving TSP

Abstract

In this paper, an effective hybrid algorithm based on Particle Swarm Optimization (PSO) is proposed for solving the Traveling Salesman Problem (TSP), which is a well-known NP-complete problem. The hybrid algorithm combines the high global search efficiency of fuzzy PSO with the powerful ability to avoid being trapped in local minimum. In the fuzzy PSO system, fuzzy matrices were used to represent the position and velocity of the particles in PSO and the operators in the original PSO position and velocity formulas were redefined. Two strategies were employed in the hybrid algorithm to strengthen the diversity of the particles and to speed up the convergence process. The first strategy is based on Neighborhood Information Communication (NIC) among the particles where a particle absorbs better historical experience of the neighboring particles. This strategy does not depend on the individual experience of the particles only, but also the neighbor sharing information of the current state. The second strategy is the use of Simulated Annealing (SA) which randomizes the search algorithm in a way that allows occasional alterations that worsen the solution in an attempt to increase the probability of escaping local optima. SA is used to slow down the degeneration of the PSO swarm and increase the swarm’s diversity. In SA, a new solution in the neighborhood of the original one is generated by using a designed ? search method. A new solution with fitness worse than the original solution is accepted with a probability that gradually decreases at the late stages of the search process. The hybrid algorithm is examined using a set of benchmark problems from the TSPLIB with various sizes and levels of hardness. Comparative experiments were made between the proposed algorithm and regular fuzzy PSO, SA, and basic ACO. The computational results demonstrate the effectiveness of the proposed algorithm for TSP in terms of the obtained solution quality and convergence speed.