Wavelet chaotic neural networks and their application to continuous function optimization ()
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.
Share and Cite:
Zhang, J. and Xu, Y. (2009) Wavelet chaotic neural networks and their application to continuous function optimization.
Natural Science,
1, 204-209. doi:
10.4236/ns.2009.13027.
Conflicts of Interest
The authors declare no conflicts of interest.
References
[1]
|
J. J. Hopfield and D. W. Tank, (1985) Neural com- putation of decision in optimization problems. Biol. Cybern., 52, 141-152.
|
[2]
|
J. Hopfield, (1982) Neural networks and physical systems with emergent collective computa-tional abilities. In: Proc Natl Acad Sci, 79, 2554-2558.
|
[3]
|
J. Hopfield, (1984) Neural networks and physical systems with emergent collective computational abilities. 81, Proc. Natl. Acad. Sci., 3088-3092.
|
[4]
|
Y. Q. Xu, M. Sun, and G. R. Duan, (2006) Wavelet chaotic neural networks and their application to optimi- zation problems. Lecture Notes in Computer Science.
|
[5]
|
L. P. Wang and F. Y. Tian, (2000) Noisy chaotic neural networks for solving combinatorial optimization pro- blems. International Joint Conference on Neural Net- works. Italy, IEEE, 37-40.
|
[6]
|
L. Chen and K. Aihara, (1995) Chaotic simulated annealing by a neural network model with transient chaos. Neural Networks., 8, 915-930.
|
[7]
|
L. Wang, (2001) Intelligence optimization algorithm and its application. Press of TUP.
|
[8]
|
C. Q. Xie, C. He, and H. W. Zhu, (2002) Improved noisy chaotic neural networks for solving combinational opti-mization problems. Journal of Shanghai Jiaotong univer-sity, 36, 351-354.
|
[9]
|
Y. Q. Xu and M. Sun, (2006) Gauss-morlet-sigmoid cha-otic neural networks. ICIC, LNCS.
|