A Chaotic Optimization Method without Initial Sampling Parameter Tuning

Abstract

The chaotic optimization method is a global optimization method to solve unconstrained optimization problems. Its superior effectiveness 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 paper, we consider a chaotic optimization method without the initial sampling parameter tuning. In this method, first, a direction vector is extracted from a gradient vector. Then, the search point is moved to the direction. Its moving distance is decreased automatically so that search range is shifted from global search to local search. We also propose an initial sampling parameter estimation method. In this method, the initial sampling parameter is estimated from the search history, and the estimated parameter is exploited in the local search phase. We confirm effectiveness of the proposed method through numerical experiments.