Finding multiple local minima using chaotic jump

Abstract

In this paper, the local minima free search algorithm using chaos is proposed for an unstructured search space. The problem is that given the quality function, find the value of a configuration that minimizes the quality function. The proposed algorithm started basically from the gradient search technique but at the prescribed points, that is, local minimum points, which are to be automatically detected the chaotic jump is introduced by the dynamics of a chaotic neuron. Chaotic motions are mainly because of the Gaussian function having a hysteresis as a refractoriness. In order to enhance the probability of finding the global minimum, a parallel search strategy is also given. The validity of the proposed method will be verified in simulation examples of the function minimization problem and the motion planning problem of a mobile robot.