Global optimization using the draining method and 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 the draining method. The draining method is an unconstrained global optimization method which utilizes a chaotic search trajectory generated by a gradient dynamics and an objective function transformation based on the theoretical analysis of the convergent characteristic of the chaotic search trajectory. In the draining method, the gradient of the objective function is used to yield driving force for a search point. Hence, its application is confined to a class of problems in which the gradient of the objective function can be computed. In this study, we introduce the simultaneous perturbation gradient approximation into the draining method in order to compute the gradient approximately so that the draining method can be applied to a class of problems whose objective function value 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.