Chaotic global optimization by direct stability control of gradient-based systems

A novel chaotic global optimization (CGO) method is proposed. A class of gradient-based systems which use the value of the objective function to manipulate the stability of all local optima plays a significant role in the method. In such a system, local optima with lower values of the objective can be made more stable. Because, with an appropriate choice of its bifurcation parameter, the globally optimal solution of an optimization problem becomes the unique stable fixed point, all trajectories can converge to the global optimum under the situation. Best of authors´ knowledge, this is the first appearance of a chaotic optimization method which only uses a single trajectory of gradient-based systems and never requires complicated operations like annealing the control parameters or finding multiple local minima. Additionally, in order to improve the applicability of the proposed CGO method, an adaptive method of directly controlling the stability at local optima is also proposed. Numerical results also show that the proposed method is promising for the tested problems.