Chaos generator exploiting a gradient model with sinusoidal perturbations for global optimization

Recently, global optimization methods using chaotic dynamics have been investigated. In those methods, it is significant what kind of chaotic dynamical system is selected. However, the system used in most existing methods for generating a chaotic sequence is sometimes not suitable for solving the problem because the system often has some windows and a generated sequence tends to overconcentrate around the boundary of the feasible region. In this paper, in order to improve them, we propose a new dynamical system which generates a chaotic sequence by the steepest descent method for minimizing an objective function with additional sinusoidal perturbation terms. In addition, we theoretically show the sufficient condition under which an approximated dynamical system of the proposed model at any local minimum or the global minimum is chaotic. Through numerical experiments we analyze properties of the proposed model for optimization to overcome these drawbacks. Furthermore, we compare the proposed method with the existing method through computational experiments by applying them to some global optimization problems.