Abstract
Chaotic neural networks have been proved to be powerful tools to solve the optimization problems. And the chaotic neural networks whose activation function is non-monotonous will be more effective than Chen’s chaotic neural network in solving optimization problems, especially in searching global minima of continuous function and traveling salesman problems. In this paper, a novel chaotic neural network for function optimization is introduced. In contrast to the Chen’s chaotic neural network, the activation function of the novel chaotic neural network is wavelet function and the different-parameters annealing function are adopted in different period, so it performs extremely better when compared to the convergence speed and the accuracy of the results. And two elaborate examples of function optimization are given to show its superiority. This chaotic neural network can be a new powerful approach to solving a class of function optimization problems.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Hopfield, J.J., Tank, D.W.: Neural computation of decisions in optimization problems. Biological Cybernetics 52, 141–152 (1985)
Hopfield, J.: Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. 79, 2554–2558 (1982)
Wilson, G.V., Pawley, G.S.: On the stability of the tap algorithm of hopfield and tank. Biol. Cybern. 58, 63–70 (1988)
Smith, K., Palaniswami, M., Krishnamoorthy, M.: Neural techniques for combinatorial optimization with applications. IEEE Trans. Neural Network 9(6), 1301–1318 (1998)
Yao, Y., Freeman, W.J.: Model of biological pattern recognition with spatially chaotic dynamics. Neural Networks 3, 156–170
Aihara, K., Takabe, T., Toyoda, M.: Chaotic neural networks. Phys. Lett. A 144(6,7), 333–340 (1999)
Chen, L.N., Aihara, K.: Chaotic simulated annealing by a neural network model with transient chaos. Neural Networks 8(6), 915–930 (1995)
Wang, L.: Oscillatory and chaotic dynamics in neural networks under varying operating conditions. IEEE Trans. Neural Networks 7, 1382–1388 (1996)
Tokuda, I., Aihara, K., Nagashima, T.: Adapitive annealing for chaotic optimization. Phys. Rev. E 58, 5157–5160 (1998)
Hirasawa, K., Murata, J., Hu, J., Jin, C.Z.: Chaos control on universal learning networks. IEEE Trans. Syst. Man, Cybern. C 30, 95–104 (2000)
Chuanquan, X., Chen, H.: Simulated annealing mechanics in chaotic neural networks. Jounal of Shanghai Jiaotong University 37(3), 36–39 (2003)
Zhou, C., Chen, T.: Chaotic annealing for optimization. Physical Review E 55(3), 2580–2587 (1997)
Bo, K., Xinyu, L., Bingchao, L.: Improved simulated annealing mechanics in transiently chaotic neural network. In: International conference on communications, Circuits and systems, vol. 2, pp. 1057–1060 (2004)
Potapove, A., Kali, M.: Robust chaos in neural networks. Physics Letters A 277(6), 310–322 (2000)
Shuai, J.W., Chen, Z.X., Liu, R.T.: Self-evolution neural model. Physics Letters A 221(5), 311–316 (1996)
Xu, Y.-q., Sun, M., Shen, J.-h.: Gauss wavelet chaotic neural networks. In: King, I., Wang, J., Chan, L.-W., Wang, D. (eds.) ICONIP 2006. LNCS, vol. 4232, pp. 467–476. Springer, Heidelberg (2006)
Xu, Y.-q., Sun, M., Shen, J.-h.: Shannon wavelet chaotic neural networks. In: Wang, T.-D., Li, X.-D., Chen, S.-H., Wang, X., Abbass, H.A., Iba, H., Chen, G.-L., Yao, X. (eds.) SEAL 2006. LNCS, vol. 4247, pp. 244–251. Springer, Heidelberg (2006)
Xu, Y.-q., Sun, M., Duan, G.-R.: Wavelet chaotic neural networks and their application to optimization problems. In: Adi, A., Stoutenburg, S., Tabet, S. (eds.) RuleML 2005. LNCS, vol. 3791, pp. 379–384. Springer, Heidelberg (2005)
Haykin, S.: Neural Networks: A Comprehensive Foundation, 2nd edn., pp. 680–696. Prentice Hall International, Englewood Cliffs (1999)
Yunyu, T., Xiangdong, L., Chunbo, X.: A novel neural network with transient chaos and its application in function optimization. Computer engineer and science 28(3), 116–118 (2006)
Yanchun, L., Chungang, C., Shoufan, L.: Optimization of Rosenbrock’s function based on genetic algorithms. Journal of Sohare 8(9), 701–708 (1997)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhou, T., Jia, Z., Liu, X. (2008). A Novel Chaotic Neural Network for Function Optimization. In: Ishikawa, M., Doya, K., Miyamoto, H., Yamakawa, T. (eds) Neural Information Processing. ICONIP 2007. Lecture Notes in Computer Science, vol 4985. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69162-4_44
Download citation
DOI: https://doi.org/10.1007/978-3-540-69162-4_44
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69159-4
Online ISBN: 978-3-540-69162-4
eBook Packages: Computer ScienceComputer Science (R0)