Chaos driven differential evolution in the task of chaos control optimization

Abstract

This paper focuses on the application of chaos driven Differential Evolution to the chaos control optimization problem. The focus of this paper is the embedding of chaotic systems in the form of the chaos number generator for Differential Evolution. The aim of this paper is also to show extreme sensitivity of quality of results on the selection of evolutionary algorithm, setting-up of evolutionary algorithm, construction of cost function and any small change in its design. As a model of deterministic chaotic system, the two dimensional Henon map was used. Two complex targeting cost functions were tested in this work. The optimization was realized in several ways, each one for another desired behavior of system. Repeated simulations demonstrated the robustness of the used method and constructed cost function. Finally, the obtained results are compared with evolutionary algorithms, Self-Organizing Migrating Algorithm (SOMA) and canonical Differential Evolution.