A search method of multiple local optimal solutions based on the nonlinear dynamical system

✍ Scribed by Chikashi Nakazawa; Akihiro Oi; Shinji Kitagawa; Yoshikazu Fukuyama

• Publisher: Wiley (John Wiley & Sons)
• Year: 2008
• Tongue: English
• Weight: 1024 KB
• Volume: 91
• Category: Article
• ISSN: 1942-9533
• DOI: 10.1002/ecj.10075

✦ Synopsis

Abstract

This paper presents a systematic and efficient search method for obtaining multiple local optimal solutions based on the stability theory of nonlinear dynamical systems. The method consists of two steps. The first step is a local search step for obtaining a local optimal solution. The second step is a search step for escaping from the stability region of the obtained local optimal solution via a decomposition point. Identifying the decomposition point represents a challenge for the method. In this paper, bifurcation and a continuation method are applied for obtaining the decomposition point. For the purpose of illustrating the proposed method, well‐known test functions including high‐dimensional functions are applied and the numerical results show the effectiveness of the proposed method. © 2008 Wiley Periodicals, Inc. Electron Comm Jpn, 91(4): 1– 11, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecj.10075