Global optimization using a multi-point type quasi-chaotic optimization method with the simultaneous perturbation gradient approximation

In this study, we propose a new global optimization method in which the simultaneous perturbation gradient approximation is introduced into a multi-point type chaotic optimization method. The multi-point type chaotic optimization method, which has been proposed recently, is a global optimization method to solve unconstrained optimization problems in which multiple search points which implement global search driven by a chaotic gradient dynamic model are synchronized to their elite search points. The chaotic optimization method uses gradient as a driving force for search points. Hence, its application is confined to a class of problems in which gradient of the objective function can be computed. In this study, we introduce the simultaneous perturbation gradient approximation into the multi-point type chaotic optimization method in order to compute gradient approximately so that the chaotic optimization method can be applied to a class of problems whose objective function values only can be computed. Then, we confirm effectiveness of the proposed method through applications to several unconstrained multi-peaked optimization problems with 100 variables comparing to other major meta-heuristics.