Fuzzy c-means clustering and partition entropy for species-best strategy and search mode selection in nonlinear optimization by differential evolution

Differential Evolution (DE) is a newly proposed evolutionary algorithm. DE is a stochastic direct search method using a population or multiple search points. DE has been successfully applied to optimization problems including non linear, non-differentiable, non-convex and multimodal functions. However, the performance of DE degrades in problems having strong dependence among variables, where variables are related strongly to each other. In this study, we propose to utilize partition entropy given by fuzzy clustering for solving the degradation. It is thought that a directional search is desirable when search points are distributed with bias. Thus, when the entropy is low, algorithm parameters can be controlled to make the directional search. Also, we propose to use a species-best strategy for improving the efficiency and the robustness of DE. The effect of the proposed method is shown by solving some benchmark problems.