Global optimization using a synchronization of multiple search Points autonomously driven by a chaotic dynamic model |
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Authors: | Takashi Okamoto Eitaro Aiyoshi |
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Institution: | (1) Graduate School of Engineering, Chiba University, 1-33, Yayoi-cho, Inage-ku, Chiba-shi Chiba, 263-8522, Japan;(2) Faculty of Science and Technology, Keio University, 3-14-1, Hiyoshi, Kouhoku-ku, Yokohama-shi Kanagawa, 223-8522, Japan |
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Abstract: | In the present paper, we propose a new multipoint type global optimization model using a chaotic dynamic model and a synchronization
phenomenon in nonlinear dynamic systems for a continuously differentiable optimization problem. We first improve the Discrete
Gradient Chaos Model (DGCM), which drives each search point’s autonomous movement, based on theoretical analysis. We then
derive a new coupling structure called PD type coupling in order to obtain stable synchronization of all search points with
the chaotic dynamic model in a discrete time system. Finally, we propose a new multipoint type global optimization model,
in which each search point moves autonomously by improved DGCM and their trajectories are synchronized to elite search points
by the PD type coupling model. The proposed model properly achieves diversification and intensification, which are reported
to be important strategies for global optimization in the Meta-heuristics research field. Through application to proper benchmark
problems Liang et al. Novel composition test functions for numerical global optimization. In: Proceedings of Swarm Intelligence
Symposium, 2005 (SIS 2005), pp. 68–75 (2005); Liang et al. Nat. Comput. 5(1), 83–96, 2006] (in which the drawbacks of typical benchmark problems are improved) with 100 or 1000 variables, we confirm
that the proposed model is more effective than other gradient-based methods. |
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Keywords: | Global Optimization Chaos Multiple Points Synchronization phenomenon Discrete gradient model |
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