1 A Hybrid Method for Optimization (Discrete PSO + CLA) B. Jafarpour M. R. Meybodi S. Shiry Computer Engineering and Information Technology Department Amirkabir University of Technology Tehran Iran Email: (jafarpour@cic.aut.ac.ir, mmeybodi@aut.ac.ir, shiry@aut.ac.ir) Abstract Particle Swarm Optimization (PSO) is an evolutionary algorithm that is inspired from collective behavior of animals such as fish schooling or bird flocking. A location and a velocity are assigned to every particle in swarm. Velocities of particles are adjusted according to best solution that itself and other members of swarm have found so far. One of the drawbacks of this model is premature convergence and trapping in local optima. In this paper we propose a solution to this problem in discrete PSO using Learning Automata and introduce a Cellular Learning Automata (CLA) based discrete PSO. Experimental results on five optimization problems show the superiority of the proposed algorithm. Keywords: Particle Swarm Optimization, Learning Automata, Cellular Learning Automata, Optimization 1. Introduction Particle Swarm Optimization (PSO) method was first proposed by Kennedy and Eberhart [1] in 1995. According to PSO, the behavior of each particle is affected by the best solution that is found by that particle and the best global particle to help it fly through a search space. Moreover, a particle can learn from its past experience to adjust its flying speed and direction. Therefore, by observing the behavior of the flock and memorizing their flying histories all particles in swarm can quickly converge to near optimal geographical with a well preserved population density distribution [20]. PSO is considered as an evolutionary computation approach in that it possesses many characteristics that are used by evolutionary algorithms such as, initializing with a population of random solutions, searching for optima by updating generations, the adjustment of individuals and evaluating them by a fitness function. However unlike evolutionary algorithms, the updates of particles are not accomplished by crossover or mutation[8]. The particle swarm algorithms reported in the literatures are classified into two groups: discrete PSO and continuous PSO [1][2][3]. In continuous PSO the particles operate in continuous search space, where the trajectories are defined as changes in position on some number of dimensions. But in discrete PSO the particles operates on discrete search space, and the trajectories are defined as changes in the probability that a coordinate will take on a value from feasible discrete values. One of the drawbacks of standard PSO model is premature convergence and trapping in local optima. Recently three solutions based on learning automata for solving this problem have been proposed [3][11][12]. In [3] a discrete version of PSO based on learning automata is proposed. In the proposed algorithm, learning automata are used by the particles to model the dynamics of the group to which the particles belong. The set of leaning automata associated to a particle, by observing the behavior of the group help the particle in searching for optimal geographical with a well preserved population density distribution. In the proposed algorithm the set of learning automata assigned to a particle may be viewed as the brain of the particle determining its position from its own and other particles past experience. To show the effectiveness of the proposed algorithm the authors have tested the algorithm on several function optimization problems. The numerical results have shown that the performance of the proposed algorithm is better than Kennedy’s discrete approach for most of the test problems. In [11] a continuous version of PSO based on learning automata has been proposed. In this model a learning automaton is used to balance exploration and exploitation made by the PSO algorithm. In this paper a new PSO model called PSO-LA is proposed in which a learning automaton takes the role of configuring the behavior of particles and creating a balance between the process of global and local search. The results of experiments conducted by the authors on some standard problems show that the proposed algorithm produces better results than the standard PSO.