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

Kazuaki Masuda, Kenzo Kurihara, Eitaro Aiyoshi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

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.

Original languageEnglish
Title of host publication2011 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2011 - Conference Digest
Pages2113-2120
Number of pages8
DOIs
Publication statusPublished - 2011 Dec 23
Event2011 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2011 - Anchorage, AK, United States
Duration: 2011 Oct 92011 Oct 12

Publication series

NameConference Proceedings - IEEE International Conference on Systems, Man and Cybernetics
ISSN (Print)1062-922X

Other

Other2011 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2011
CountryUnited States
CityAnchorage, AK
Period11/10/911/10/12

Keywords

  • Lagrange multiplier method
  • game theory
  • min-max problem
  • particle swarm optimization (PSO)

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Human-Computer Interaction

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    Masuda, K., Kurihara, K., & Aiyoshi, E. (2011). A novel method for solving min-max problems by using a modified particle swarm optimization. In 2011 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2011 - Conference Digest (pp. 2113-2120). [6083984] (Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics). https://doi.org/10.1109/ICSMC.2011.6083984