Chaotic Local Search Algorithm

Abstract

The steepest descent search algorithm is modified in conjunction withchaos to solve the optimization problem of an unstructured search space. The problem is that given only the gradient information of the quality function at the present configuration,X(t), we must find the value of a configuration vector that minimizes the quality function. The proposed algorithm starts basically from the steepest descent search technique but at the prescribed points, i.e., local minimum points, the chaotic jump is performed by the dynamics of a chaotic neuron. Chaotic motions are mainly caused because the Gaussian function has a hysteresis as a refractoriness. An adaptation mechanism to adjust the size of the chaotic jump is also given. In order to enhance the probability of finding the global minimum, a parallel search strategy is developed. The validity of the proposed method is verified in simulation examples of the function minimization problem and the motion planning problem of a mobile robot.