Wavelet chaotic neural networks and their application to continuous function optimization

Jia-Hai Zhang,Yao-Qun Xu

doi:10.4236/ns.2009.13027

Abstract

Neural networks have been shown to be pow-erful tools for solving optimization problems. In this paper, we first retrospect Chen’s chaotic neural network and then propose several novel chaotic neural networks. Second, we plot the figures of the state bifurcation and the time evolution of most positive Lyapunov exponent. Third, we apply all of them to search global minima of continuous functions, and respec-tively plot their time evolution figures of most positive Lyapunov exponent and energy func-tion. At last, we make an analysis of the per-formance of these chaotic neural networks.

Highlights

Hopfield and Tank first applied the continuous-time, continuous-output Hopfield neural network (HNN) to solve TSP [1], thereby initiating a new approach to optimization problems [2,3]
The Hopfield neural network, one of the well-known models of this type, converges to a stable equilibrium point due to its gradient decent dynamics; it causes sever local-minimum problems whenever it is applied to optimization problems
We plot the figures of the state bifurcation and the time evolution of most positive Lyapunov exponent

Summary

INTRODUCTION

Hopfield and Tank first applied the continuous-time, continuous-output Hopfield neural network (HNN) to solve TSP [1], thereby initiating a new approach to optimization problems [2,3]. M-SCNN has been proved to be more power than Chen’s chaotic neural network in solving optimization problems, especially in searching global minima of continuous function and traveling salesman problems [4]. We first review the Chen’s chaotic neural network. We plot the figures of the state bifurcation and the time evolution of most positive Lyapunov exponent. We apply all of them to search global minima of continuous functions, and respectively plot their time evolution figures of most positive Lyapunov exponent and energy function. Simulation results are summarized in a Table in order to make an analysis of their performance

Chen’s Chaotic Neural Network

RESEARCH ON CONTINUOUS FUNCTION PROBLEMS

ANALYSIS OF THE SIMULATION RESULTS