Chaotic neural networks with Gauss wavelet self-feedback and their applications to optimization

This paper proposes chaotic neural networks with nonlinear Gauss wavelet self-feedback. Chaotic neural networks with wavelet self-feedback not only have the ability of globally searching optimum due to chaos but also have the ability of local approximation due to wavelet. The analyses of asymptotical stability demonstrate the proposed networks can converge stably. The experimental results show that the performance of chaotic neural networks with Gauss wavelet self-feedback is superior to those only with linear self-feedback.

[1]  Zhou Chang-song,et al.  Chaotic neural network with nonlinear self-feedback and its application in optimization , 1997, Neurocomputing.

[2]  J. J. Hopfield,et al.  “Neural” computation of decisions in optimization problems , 1985, Biological Cybernetics.

[3]  Kate Smith-Miles,et al.  On chaotic simulated annealing , 1998, IEEE Trans. Neural Networks.

[4]  Yuyao He,et al.  Chaotic simulated annealing with decaying chaotic noise , 2002, IEEE Trans. Neural Networks.

[5]  Lipo Wang,et al.  Noisy Chaotic Neural Networks for Combinatorial Optimization , 2007, Challenges for Computational Intelligence.

[6]  Wang Ling A Kind of Chaotic Neural Network Optimization Algorithm Based on Annealing Strategy , 2000 .

[7]  Kate Smith-Miles,et al.  Experimental analysis of chaotic neural network models for combinatorial optimization under a unifying framework , 2000, Neural Networks.

[8]  D. Fogel Applying evolutionary programming to selected traveling salesman problems , 1993 .

[9]  Hayakawa,et al.  Effects of the chaotic noise on the performance of a neural network model for optimization problems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  Kate Smith-Miles,et al.  A unified framework for chaotic neural-network approaches to combinatorial optimization , 1999, IEEE Trans. Neural Networks.

[11]  K. Aihara,et al.  Chaos and asymptotical stability in discrete-time neural networks , 1997, chao-dyn/9701020.

[12]  Lipo Wang,et al.  A noisy chaotic neural network for solving combinatorial optimization problems: stochastic chaotic simulated annealing , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[13]  Henry Leung,et al.  Critical temperature of the transiently chaotic neural network , 2003 .

[14]  Lipo Wang Discrete-time convergence theory and updating rules for neural networks with energy functions , 1997, IEEE Trans. Neural Networks.

[15]  Liying Zheng,et al.  An Approach to Improve Wang-Smith Chaotic Simulated Annealing , 2002, Int. J. Neural Syst..

[16]  Kazuyuki Aihara,et al.  Chaotic simulated annealing by a neural network model with transient chaos , 1995, Neural Networks.