Chaotic Optimization Method without Initial Sampling Parameter Tuning - Empirical Comparisons of Two Approaches in Various Problems

Abstract

The chaotic optimization method is a global optimization method to solve unconstrained optimization problems. Its superior search capability has been confirmed through applications to optimization problems which have high dimensional and multi-peaked objective functions. However, the chaotic optimization method has a drawback in that a parameter called initial sampling parameter has to be tuned on each optimization problem. In this study, we consider two approaches to perform the chaotic optimization method without the initial sampling parameter tuning. One is the initial sampling estimation method based on the characteristics of the chaotic optimization method. In this method, the sampling parameter at which the search trajectory bifurcates from the fixed point convergence to the two periodic solution trajectory, which is called the first bifurcating parameter, is computed from the approximation matrix to Hessian obtained by the quasi-Newton method. Then, suitable initial sampling parameter is estimated using this information. The other is the descent sign vector method. In this method, a descent sign vector extracted from a gradient vector is used as a search direction of a search point. Then, its moving distance is determined so that its search process shifts from the global search to the local search. We compare two methods and their hybrid method through numerical experiments for various optimization problems.