Global optimization using a multipoint type quasi-chaotic optimization method

This paper proposes a new global optimization method called the multipoint type quasi-chaotic optimization method. In the proposed method, the simultaneous perturbation gradient approximation is introduced into a multipoint type chaotic optimization method in order to carry out optimization without gradient information. The multipoint type chaotic optimization method, which has been proposed recently, is a global optimization method for solving unconstrained optimization problems in which multiple search points which implement global searches driven by a chaotic gradient dynamic model are advected to their elite search points (best search points among the current search histories). The chaotic optimization method uses a gradient to drive search points. Hence, its application is restricted to a class of problems in which the gradient of the objective function can be computed. In this paper, the simultaneous perturbation gradient approximation is introduced into the multipoint type chaotic optimization method in order to approximate gradients so that the chaotic optimization method can be applied to a class of problems for which only the objective function values can be computed. Then, the effectiveness of the proposed method is confirmed through application to several unconstrained multi-peaked, noisy, or discontinuous optimization problems with 100 or more variables, comparing to other major meta-heuristics.

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► A global optimization method based on chaotic optimization method is proposed.
► A stochastic gradient approximation technique is introduced.
► Quasi-chaotic search trajectory from the approximated gradient dynamics is utilized.
► The proposed method is applied to high dimensional and multi-peaked problems.
► The proposed method performs well, comparing to other major meta-heuristics.