A Novel Chaotic Neural Network And Its Application In Function Optimization

Since the Hopfield neural network is proposed by Hopfield and Tank has solved TSP (traveling salesman problem), it has been applied to complicated optimization problems extensively. Unfortunately, the HNN may easily get stuck in local minima.To overcome this difficulty, chaotic neural networks exploiting the rich behaviors of nonlinear dynamics have been developed as a new approach to extend the problem solving ability of standard HNN. There have been many CNN models and efforts in theory and applications of chaotic neural networks.In many CNN models the activation functions almost adopt sigmoid function, theoretically speaking, they are not the basic function, so the ability of solving optimization problems is less effective than whose activation functions are composed of kinds of basic functions in chaotic neural networks.The CNN depends on the self-feedback connection weight sensitively. However, most of the CNN models adopt the simulated annealing parameter which is only put a single value in the whole optimization procedure. Therefore, it has to spend much more time in converging at the optimal solution.Based on these issues, a novel chaotic neural network model is proposed in this paper. The activation function is Mexican hat wavelet function and subsection exponential annealing function is used in this model. The simulation result shows that on rapidity and accuracy of searching for the globally optimal solution, this model is obviously superior to other conventional chaotic neural network models.