TY - GEN
T1 - A novel method for solving min-max problems by using a modified particle swarm optimization
AU - Masuda, Kazuaki
AU - Kurihara, Kenzo
AU - Aiyoshi, Eitaro
PY - 2011/12/23
Y1 - 2011/12/23
N2 - 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.
AB - 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.
KW - Lagrange multiplier method
KW - game theory
KW - min-max problem
KW - particle swarm optimization (PSO)
UR - http://www.scopus.com/inward/record.url?scp=83755221167&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=83755221167&partnerID=8YFLogxK
U2 - 10.1109/ICSMC.2011.6083984
DO - 10.1109/ICSMC.2011.6083984
M3 - Conference contribution
AN - SCOPUS:83755221167
SN - 9781457706523
T3 - Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics
SP - 2113
EP - 2120
BT - 2011 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2011 - Conference Digest
T2 - 2011 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2011
Y2 - 9 October 2011 through 12 October 2011
ER -