Global optimization using a synchronization of multiple search Points autonomously driven by a chaotic dynamic model

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.