Chaotic Neural Networks and Their Applications

Many difficult combinatorial optimization problems arising from science and technology are often difficult to solve exactly. Hence a great number of approximate algorithms for solving combinatorial opthintion problems have been developed [lo], [IS]. Hopfield and Tank applied the continuowtime, continuous-output Hopfield neural network (CTCGH?W) to TSP, thereby initialing a new approach to optimbtion problem. But Hopfield neural network is often trapped in local minima because of its gradient descent property. A n u " of modifications have been done on Hopfield neural network for escaping h m local minima. As so k, incorporating chaos into the Hopfield neural network his been proved to be successful approach to improve the Convergent prope~ty of the HNNs. In this paper, we fim review three chaotic neural network models, and then propose a novel approach to chaotic simulated annealing. Second, we apply all of them to 10 city TSP, nspcctively. 'Ibe time evolutions of e n q functions and outputs of ncurang for each model arc given. "be features and effcaiveness of four mahods ate discussed and evaluated according to the simulation results. We conclude that proposed neural network with simulated annealing bas more powerful ability to obtain global minima than any other chaotic "I network model when applied to difficult combinatorial opthimion problems.