A chaotic optimization method using a bifurcation tuning by an objective function transformation: A proposal of global optimization method "draining method"

Yuki Watanabe, Takashi Okamoto, Eitaro Aiyoshi

Research output: Contribution to journalArticle

Abstract

In this paper, we propose a new global optimization method "Draining Method" which uses a tuning of the bifurcation characteristic of the discrete gradient chaos model by an objective function transformation. Specifically, firstly, we show that a local minimum, to which the chaotic orbit converges with the chaos annealing, is dominated by its bifurcation characteristic from its stability analysis. From this consideration, a tuning method of the bifurcation characteristic which takes into consideration the objective function value of each local minimum is proposed. In this method, the landscape of objective function is transformed into flat in an area whose objective function value is lower than a certain threshold value, and thereby the search point with the chaotic motion is made stable and unescapable from this area. Finally, we propose an optimization method which brings the search point close to a global minimum by gradually decreasing the threshold value (we call this decrease procedure "Draining"), confining the search point to the area where the objective function value is lower. We confirm effectiveness of our proposed model through applications to several benchmark problems whose dimension of variable is high and landscape has multi-peaks.

Original languageEnglish
JournalIEEJ Transactions on Electronics, Information and Systems
Volume126
Issue number12
Publication statusPublished - 2006

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Bifurcation (mathematics)
Global optimization
Tuning
Chaos theory
Orbits
Annealing

Keywords

  • Chaos
  • Global optimization
  • Gradient system
  • Objective function transformation

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

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title = "A chaotic optimization method using a bifurcation tuning by an objective function transformation: A proposal of global optimization method {"}draining method{"}",
abstract = "In this paper, we propose a new global optimization method {"}Draining Method{"} which uses a tuning of the bifurcation characteristic of the discrete gradient chaos model by an objective function transformation. Specifically, firstly, we show that a local minimum, to which the chaotic orbit converges with the chaos annealing, is dominated by its bifurcation characteristic from its stability analysis. From this consideration, a tuning method of the bifurcation characteristic which takes into consideration the objective function value of each local minimum is proposed. In this method, the landscape of objective function is transformed into flat in an area whose objective function value is lower than a certain threshold value, and thereby the search point with the chaotic motion is made stable and unescapable from this area. Finally, we propose an optimization method which brings the search point close to a global minimum by gradually decreasing the threshold value (we call this decrease procedure {"}Draining{"}), confining the search point to the area where the objective function value is lower. We confirm effectiveness of our proposed model through applications to several benchmark problems whose dimension of variable is high and landscape has multi-peaks.",
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T1 - A chaotic optimization method using a bifurcation tuning by an objective function transformation

T2 - A proposal of global optimization method "draining method"

AU - Watanabe, Yuki

AU - Okamoto, Takashi

AU - Aiyoshi, Eitaro

PY - 2006

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N2 - In this paper, we propose a new global optimization method "Draining Method" which uses a tuning of the bifurcation characteristic of the discrete gradient chaos model by an objective function transformation. Specifically, firstly, we show that a local minimum, to which the chaotic orbit converges with the chaos annealing, is dominated by its bifurcation characteristic from its stability analysis. From this consideration, a tuning method of the bifurcation characteristic which takes into consideration the objective function value of each local minimum is proposed. In this method, the landscape of objective function is transformed into flat in an area whose objective function value is lower than a certain threshold value, and thereby the search point with the chaotic motion is made stable and unescapable from this area. Finally, we propose an optimization method which brings the search point close to a global minimum by gradually decreasing the threshold value (we call this decrease procedure "Draining"), confining the search point to the area where the objective function value is lower. We confirm effectiveness of our proposed model through applications to several benchmark problems whose dimension of variable is high and landscape has multi-peaks.

AB - In this paper, we propose a new global optimization method "Draining Method" which uses a tuning of the bifurcation characteristic of the discrete gradient chaos model by an objective function transformation. Specifically, firstly, we show that a local minimum, to which the chaotic orbit converges with the chaos annealing, is dominated by its bifurcation characteristic from its stability analysis. From this consideration, a tuning method of the bifurcation characteristic which takes into consideration the objective function value of each local minimum is proposed. In this method, the landscape of objective function is transformed into flat in an area whose objective function value is lower than a certain threshold value, and thereby the search point with the chaotic motion is made stable and unescapable from this area. Finally, we propose an optimization method which brings the search point close to a global minimum by gradually decreasing the threshold value (we call this decrease procedure "Draining"), confining the search point to the area where the objective function value is lower. We confirm effectiveness of our proposed model through applications to several benchmark problems whose dimension of variable is high and landscape has multi-peaks.

KW - Chaos

KW - Global optimization

KW - Gradient system

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