GLOBAL BIFURCATION STRUCTURE OF CHAOTIC NEURAL NETWORKS AND ITS APPLICATION TO TRAVELING SALESMAN PROBLEMS

This paper studies global bifurcation structure of the chaotic neural networks applied to solve the traveling salesman problem (TSP). The bi furcation analysis clarifies the dynamical basis of the chaotic neuro- dynamics which itinerates a variety of network states associated with possible solutions of TSP and efficiently 'searches' for the optimum o r near-optimum solutions. By following rite detailed merging process o f chaotic attractors via crises, we find that the crisis-induced inter mittent switches among the ruins of the previous localized chaotic att ractors underly the 'chaotic search 'for TSP solutions. OH the basis o f the present study, efficiency of the 'chaotic search' to optimizatio n problems is discussed and a guideline is provided for tuning the bif urcation parameter value which gives rise to efficient 'chaotic search '. (C) 1997 Elsevier Science Ltd. All rights reserved.