A novel method for solving min-max problems by using a modified particle swarm optimization

Abstract

In this paper, a method for solving min-max problems, especially for finding a solution which satisfies “min-max = max-min” condition, by using a modified particle swarm optimization (PSO) algorithm, is proposed. According to recent development in computer science, multi-point global search methods, most of which are classified into evolutionary computation and/or meta-heuristic methods, have been proposed and applied to various types of optimization problems. However, applications of them to min-max problems have been scarce despite their theoretical and practical importance. Since direct application of evolutionary computation methods to min-max problems wouldn't work effectively, a modified PSO algorithm for solving them is proposed. The proposed method is designed: (1) to approximate the minimized and maximized functions of min-max problems by using a finite number of search points; and, (2) to obtain one of “min-max = max-min” solutions by finding the minimum of the maximized function and the maximum of the minimized function. Numerical examples demonstrate the usefulness of the proposed method.