A Method for Mixed Integer Programming Problems by Particle Swarm Optimization

Abstract

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 non-convex optimization problem, and few researches about optimization problems with discrete decision variables have been studied. In this paper, we present the treatment of discrete decision 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.