Abstract
Chaotic neural networks have been proved to be strong tools to solve the optimization problems. In order to escape the local minima, a new chaotic neural network model called Fourier series chaotic neural network was presented. The activation function of the new model is non-monotonous, which is composed of sigmoid and trigonometric function. First, the figures of the reversed bifurcation and the maximal Lyapunov exponents of single neural unit were given. Second, the new model is applied to solve several function optimizations. Finally, 10-city traveling salesman problem is given and the effects of the non-monotonous degree in the model on solving 10-city traveling salesman problem are discussed. Seen from the simulation results, the new model we proposed is more effective.
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References
Hopfield, J., Tank, D.W.: Neural Computation of Decision in Optimization Problems. Biol. Cybern. 52, 141–152 (1985)
Hopfield, J.: Neural Networks and Physical Systems with Emergent Collective Computational Abilities. In: Proc. Natl. Acad. Sci., vol. 79, pp. 2554–2558 (1982)
Xu, Y., Sun, M., Duan, G.: 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)
Kali, M.: A Potapove Robust chaos in neural networks. Phys. Lett. A 277(6), 310–322 (2000)
Shuai, J.W., Chen, Z.X., Liu, R.T.: Self-evolution Neural Model. Phys. Lett. A 221(5), 311–316 (1996)
Chen, L., Aihara, K.: Chaotic Simulated Annealing by a Neural Network Model with Transient Chaos. Neural Networks 8(6), 915–930 (1995)
Wang, L.: Intelligence optimization algorithm and its application. Press of TUP (2001)
Xu, Y., Sun, M.: Gauss Morlet Sigmoid Chaotic Neural Networks. In: Huang, D.-S., Li, K., Irwin, G.W. (eds.) ICIC 2006. LNCS, vol. 4113, pp. 115–125. Springer, Heidelberg (2006)
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Xu, Yq., He, Sp. (2008). Fourier Series Chaotic Neural Networks. In: Huang, DS., Wunsch, D.C., Levine, D.S., Jo, KH. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Contemporary Intelligent Computing Techniques. ICIC 2008. Communications in Computer and Information Science, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85930-7_12
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DOI: https://doi.org/10.1007/978-3-540-85930-7_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85929-1
Online ISBN: 978-3-540-85930-7
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