Realizing ideal spatiotemporal chaotic searching dynamics for optimization algorithms using neural networks

Abstract

This paper proposes an optimization algorithm, which utilizes ideal spatiotemporal chaotic dynamics for solution search in a high dimensional solution space. Such chaotic dynamics is generated by the Lebesgue spectrum filter, which has been applied to the chaotic CDMA in previous researches to minimize the cross-correlation among the sequences. In the proposed method, such a filter is applied to the output functions of optimization neural networks to realize an ideal chaotic search, which generates ideally complicated searching dynamics. The proposed scheme is applied to two combinatorial optimization approaches, the Hopfield-Tank neural network with additive noise and a heuristic algorithm driven by neural networks, which solve the Traveling Salesman Problems and the Quadratic Assignment Problems. The simulation results show that the proposed approach using the ideal chaotic dynamics simply improves the performance of the chaotic algorithms without searching appropriate parameter values even for large-scale problems. © 2010 Springer-Verlag.