A method for mixed integer programming problems by Particle Swarm Optimization

Particle Swarm Optimization (PSO) for mixed integer programming problems is proposed. PSO is mainly a method to find a global or quasi-minimum for a nonlinear and nonconvex optimization problem, and there have been few studies into optimization problems with discrete decision variables. In this paper, we present the treatment of discrete variables. To treat discrete decision variables as a penalty function, it is possible to treat all decision variables as a continuous decision variable. As a result, the penalty parameter for the penalty function is needed. In this paper, we also present how to determine the penalty parameter for the penalty function. Through mathematical and structural optimization problems, we examine the validity of PSO for the mixed decision variables. (c) 2006 Wiley Periodicals, Inc.