A method for searching multiple local optimal solutions of nonlinear optimization problems

Author

Nakazawa, Chikashi ; Kitagawa, Shinji ; Fukuyama, Yoshikazu ; Chiang, Hsiao-Dong

Author_Institution

Optimization Syst. Group, Fuji Electr. Adv. Technol. Co., Ltd, Tokyo, Japan

fYear

2005

fDate

23-26 May 2005

Firstpage

4907

Abstract

This paper presents a systematic method for searching multiple local optimal solutions of continuous nonlinear optimization problems. The presented method consists of two major algorithms for searching the solutions. The first part of the algorithms is for a global search, and the second one is for a local search. The effective global search algorithm based on bifurcation theory has been developed to escape from a stability region (basin of attraction) of a stable equilibrium point, and move to another stable equilibrium point via a type I unstable equilibrium point on the stability boundary (basin boundary) using the continuation method. The proposed method is verified by two well-known numerical examples.

Keywords

bifurcation; nonlinear dynamical systems; optimisation; search problems; stability; basin boundary; basin of attraction; bifurcation theory; continuation method; continuous nonlinear optimization problems; global search; local search; multiple local optimal solutions; stability boundary; stability region; stable equilibrium point; type I unstable equilibrium point; Bifurcation; Large-scale systems; Nonlinear dynamical systems; Nonlinear equations; Optimization methods; Stability;

fLanguage

English

Publisher

ieee

Conference_Titel

Circuits and Systems, 2005. ISCAS 2005. IEEE International Symposium on

Print_ISBN

0-7803-8834-8

Type

conf

DOI

10.1109/ISCAS.2005.1465733

Filename

1465733