A chaotic optimization method using a bifurcation tuning by an objective function transformation: A proposal of global optimization method "draining method"

In this paper, we propose a new global optimization method "Draining Method" which uses a tuning of the bifurcation characteristic of the discrete gradient chaos model by an objective function transformation. Specifically, firstly, we show that a local minimum, to which the chaotic orbit converges with the chaos annealing, is dominated by its bifurcation characteristic from its stability analysis. From this consideration, a tuning method of the bifurcation characteristic which takes into consideration the objective function value of each local minimum is proposed. In this method, the landscape of objective function is transformed into flat in an area whose objective function value is lower than a certain threshold value, and thereby the search point with the chaotic motion is made stable and unescapable from this area. Finally, we propose an optimization method which brings the search point close to a global minimum by gradually decreasing the threshold value (we call this decrease procedure "Draining"), confining the search point to the area where the objective function value is lower. We confirm effectiveness of our proposed model through applications to several benchmark problems whose dimension of variable is high and landscape has multi-peaks.