Combinatorial optimization by chaotic dynamics

It is shown that chaotic simulated annealing (CSA) with transient chaotic neural networks (TCNN) not only is efficient but also has global searching ability for combinatorial optimization. Sufficient conditions for asymptotical convergence of the dynamics are derived. Then the local bifurcations are investigated to show the bifurcation process for chaotic simulated annealing. Furthermore, sufficient conditions are given for existence of global attracting set which ensures that CSA at high temperature carry out the global search. An example for TSP was used to demonstrate CSA. Since the models used in this paper are simple and general, the obtained theoretical results hold for a wide class of discrete-time neural networks