Proceedings of the 6th WSEAS Int. Conf. on Artificial Intelligence, Knowledge Engineering and Data Bases, Corfu Island, Greece, February 16-19, 2007 201 Particle Swarm Optimization with Simulated Annealing for TSP LUPING FANG, PAN CHEN, SHIHUA LIU Software Institute of Zhejiang University of Technology Zhejiang University of Technology, Zhaohui No.6 Area, Hangzhou, 310014 CHINA Abstract: - Aiming at the shortcoming of basic PSO algorithm, that is, easily trapping into local minimum, we propose an advanced PSO algorithm with SA and apply this new algorithm for solving TSP problem. The core of algorithm is based on the PSO algorithm. SA method is used to slow down the degeneration of the PSO swarm and increase the swarm's diversity. The comparative experiments were made between PSO-SA, basic GA, basic SA and basic ACA on solving TSP problem. Results show PSO-SA is more superior to other methods. Key-Words: - particle swarm optimization; simulating annealing algorithm; TSP; GA 1 Introduction The travel salesman problem (TSP) has been studied extensively over the past several decades. In this paper , this problem is solved by a new method called PSO with SA. The Particle Swarm Optimization(PSO) algorithm was first introduced by Kennedy and Eberhart in 1995[1-2] and is widely used to solve continuous quantities problems. Recently, some researches apply this algorithm to problems of discrete quantities. It has been reported that PSO has better performance in solving some optimization problems. However, basic PSO algorithm suffers a serious problem that all particles are prone to be trapped into the local minimum in the later phase of convergence. The optimal value found is often a local minimum instead of a global minimum. The optimal value found is often a local minimum instead of a global minimum. Aiming at solving the shortcoming of the basic PSO algorithm, many variations, such as Fuzzy PSO [3], Hybrid PSO [4], Intelligent PSO [5], Niching PSO [6] and Guarantee Locally Convergent PSO[7]. have been proposed to increase the diversity of particles and improve the convergence performance In the paper, we proposed a new solution which combines PSO algorithm with the simulated annealing algorithm (SA) and apply it to solve TSP problem. SA is a kind of stochastic method and is well known for its feature of effective escaping from local minimum trap. By integrating SA to the PSO, the new algorithm, which we call it PSO-SA can not only escape from local minimum trap in the later phase of convergence, but also simplify the implementation of the algorithm. In the experiments, four algorithms have been used and the results have been compared, among which PSO-SA algorithm has the best performance in solving TSP problem. 2 Basic PSO Algorithm The concept of PSO roots from the social behaviour of organisms such as bird flocking and fishing schooling. Through cooperation between individuals, the group often can achieve their goal efficiently and effectively. PSO simulates this social behaviour as an optimization tool to solve some optimization problems. In a PSO system, each particle having two properties of position