Abstract
This paper applies a new version of the transiently chaotic neural network (TCNN), the speedy convergent chaotic neural network (SCCNN), to solve the k-coloring problem, a classic NP-complete graph optimization problem, which has many real-world applications. From analyzing the chaotic states of its computational energy, we reach the conclusion that, like the TCNN, the SCCNN can avoid getting stuck in local minima and thus yield excellent solutions, which overcome the disadvantage of the Hopfield neural network (HNN). In addition, the experimental results verify that the SCCNN converges more quickly than the TCNN does in solving the k-coloring problem, which leads it to be a practical algorithm like the HNN. Therefore, the SCCNN not only adopts the advantages of the HNN as well as the TCNN but also avoids their drawbacks, thus provides an effective and efficient approach to solve the k-coloring problem.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of Np-Completeness. W. H. Freeman, New York (1979)
Hopfield, J., Tank, D.: Neural Computation of Decisions in Optimization Problems. Biological Cybernetics 52, 141–152 (1985)
Takefuji, Y., Lee, K.C.: Artificial Neural Networks for Four-Coloring Map Problem and for K-Colorability Problems. IEEE Transactions on Circuits and Systems 38, 326–333 (1991)
Berger, M.O.: k-Coloring Vertices Using a Neural Network with Convergence to Valid Solutions. Proceedings of IEEE World Congress on Computational Intelligence 7, 4514–4517 (1994)
Chen, L., Aihara, K.: Chaotic Simulated Annealing by a Neural Network Model with Transient Chaos. Neural Networks 8, 915–930 (1995)
Gu, S.S., Yu, S.N.: A Chaotic Neural Network for the Maximum Clique Problem. In: Tawfik, A.Y., Goodwin, S.D. (eds.) Canadian AI 2004. LNCS (LNAI), vol. 3060, pp. 391–405. Springer, Heidelberg (2004)
Xie, C.Q., He, C.: Simulated Annealing Mechanics in Chaotic Neural Networks. Journal of Shanghai Jiaotong University 37, 36–39 (2003)
Kang, B., Li, X.Y., Lu, B.C.: Improved Simulated AnnealingMechanics in Transiently Chaotic Neural Network. In: Proceedings of 2004 IEEE International Conference on Communications, Circuits and Systems, vol. 2, pp. 1057–1060 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gu, S. (2005). An Improved Transiently Chaotic Neural Network for Solving the K-Coloring Problem. In: Wang, J., Liao, X., Yi, Z. (eds) Advances in Neural Networks – ISNN 2005. ISNN 2005. Lecture Notes in Computer Science, vol 3496. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427391_120
Download citation
DOI: https://doi.org/10.1007/11427391_120
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25912-1
Online ISBN: 978-3-540-32065-4
eBook Packages: Computer ScienceComputer Science (R0)