Basic examination on particle Swarm optimization and its application to the mixed design variable problems

Abstract

In this paper we examine the basic characters of Particle Swarm Optimization (PSO), and apply it the mixed design variable problems. Some models of PSO have been proposed, but the basic characters of PSO are not well described. PSO is mainly a method to find a global or quasi-minimum for a nonlinear and non-convex optimization problem of the continuous design variables, and few researches of PSO about optimization problems with the discrete design variables have been reported. In this paper we also show the penalty function approach to treat the discrete design variables. To treat the discrete design variables as penalty function, it is possible to treat all design variables as the continuous design variables. As a result, the penalty parameter for the penalty function is needed. Additionally, we also present how to determine the penalty parameter for the penalty function. Through typical mathematical and structural optimization problems, the validity of proposed approach is examined.