A Search Method of Multiple Local Optimal Solutions Based on the Nonlinear Dynamical Systems

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 must be a challenge task for the method. In this paper, bifurcations 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.