Skip to main content
SpringerLink
Log in

Dynamic characteristic of a multiple chaotic neural network and its application

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Based on chaotic neural network, a multiple chaotic neural network algorithm combining two different chaotic dynamics sources in each neuron is proposed. With the effect of self-feedback connection and non-linear delay connection weight, the new algorithm can contain more powerful chaotic dynamics to search the solution domain globally in the beginning searching period. By analyzing the dynamic characteristic and the influence of cooling schedule in simulated annealing, a flexible parameter tuning strategy being able to promote chaotic dynamics convergence quickly is introduced into our algorithm. We show the effectiveness of the new algorithm in two difficult combinatorial optimization problems, i.e., a traveling salesman problem and a maximum clique problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Aihara K (2002) Chaos engineering and its application to parallel distributed processing with chaotic neural networks. Proc IEEE 90:919–930

    Article  Google Scholar 

  • Cao Y, Liu S, Liu X (2006) Optimization of SF/sub 6/ circuit breaker based on chaotic neural network. IEEE Trans Magn 42:1151–1154

    Article  Google Scholar 

  • Chen L, Aihara K (1995) Chaotic simulated annealing by a neural network model with transient chaos. Neural Netw 8(6):915–930

    Article  Google Scholar 

  • Hansel D, Sompolinsky H (1992) Synchronization and computation in a chaotic neural network. Phys Rev Lett 68:5

    Article  Google Scholar 

  • Hasegawa M, Ikeguchi T, Matozaki T, Aihara K (1995) Solving combinatorial optimization problems by nonlinear neural dynamics. In: Proceedings of ICNN95 - international conference on neural networks, pp 3140–3145

  • He Y (2002) Chaotic simulated annealing with decaying chaotic noise. IEEE Trans Neural Netw 13(6):1526–1531

    Article  Google Scholar 

  • Hopfield JJ, Tank DW (1985) Neural computation of decisions in optimization problems. Biol Cybern 52:141–152

    MathSciNet  MATH  Google Scholar 

  • Hopfield JJ, Tank DW (1986) Computing with neural circuits: a model. Science 233:624–633

    Article  Google Scholar 

  • Jagota A (1995) Approximating maximum clique with a Hopfield network. IEEE Trans Neural Netw 6(3):724–735

    Google Scholar 

  • Klotz A, Brauer K. (1999) A small-size neural network for computing with strange attractors. Neural Netw 12:601–607

    Article  Google Scholar 

  • Kwok T, Smith KA (2000) Experimental analysis of chaotic neural network models for combinatorial optimization under a unifying framework. Neural Netw 13:731–744

    Article  Google Scholar 

  • Lin JS (2001) Annealed chaotic neural network with nonlinear self-feedback and its application to clustering problem. Pattern Recognit 34:1093–1104

    Article  MATH  Google Scholar 

  • Lysetskiy M, Zurada JM (2004) Bifurcating neuron: computation and learning. Neural Netw 17:225–232

    Article  MATH  Google Scholar 

  • Nozawa H (1992) A neural-network model as a globally coupled map and applications based on chaos. Chaos 2(3):377–386

    Article  MathSciNet  MATH  Google Scholar 

  • Ohta M (2002) Chaotic neural networks with reinforced self-feedbacks and its application to N-Queen problem. Math Comput Simul 59(4):305–317

    Article  MATH  Google Scholar 

  • Potapov A, Ali MK (2000) Robust chaos in neural networks. Phys Lett A 277:310–322

    Article  MathSciNet  MATH  Google Scholar 

  • Potvin JY (1993) The traveling salesman problem: a neural network perspective. ORSA J Comput 5:328–348

    Article  MATH  Google Scholar 

  • Tokuda I, Nagashima T, Aihara K (1997) Global bifurcation structure of chaotic neural networks and its application to traveling salesman problems. Neural Netw 10:1673–1690

    Article  Google Scholar 

  • Tokuda I, Aihara K, Nagashima T (1998) Adaptive annealing for chaotic optimization. Phys Rev E 58(4):5157–5160

    Article  MathSciNet  Google Scholar 

  • Wang L, Smith K (1998) On chaotic simulated annealing. IEEE Trans Neural Netw 9:716–718

    Article  Google Scholar 

  • Wang L, Li S, Tian F, Fu X (2004) A noisy chaotic neural network for solving combinatorial optimization problems: stochastic Chaotic simulated annealing. IEEE Trans Syst Man Cybern Part B Cybern 34(5):2119–2125

    Article  Google Scholar 

  • Wang LP, Liu W, Shi H (2008) Noisy chaotic neural networks with variable thresholds for the frequency assignment problem in satellite communications. IEEE Trans Syst Man Cybern Part C Rev Appl 38(2):209–217

    Article  MATH  Google Scholar 

  • Wang LP, Liu W, Shi H (2009) Delay-constrained multicast routing using the noisy chaotic neural networks. IEEE Trans Comput 58(1):82–89

    Article  MathSciNet  Google Scholar 

  • Xu YQ, Sun M, Zhang JH (2006) A model of wavelet chaotic neural network with applications in optimization. In: Proceedings 6th World Congr. Intell. Control Autom, China 1:2901–2905

  • Yang G, Tang Z, Zhang Z, Zhu Y (2007) A flexible annealing chaotic neural network to maximum clique problem. Int J Neural Syst 17(3):183–192

    Article  Google Scholar 

  • Yang G., Yi J, Vairappan C, Tang Z (2008) A flexible annealing strategy for chaotic neural network to maximum clique problem. Int J Innov Comput Inf Control 4(4):981–993

    Google Scholar 

  • Yi J, Yang G, Zhang Z, Tang Z (2009) An improved elastic net method with time-dependent parameters for traveling salesman problem. Int J Innov Comput Inf Control 5(4):1089–1100

    Google Scholar 

  • Zhao L, Sun M, Cheng J, Xu Y (2009) A novel chaotic neural network with the ability to characterize local features and its application. IEEE Trans Neural Netw 20(4)

  • Zhou CS, Chen T (2000) Chaotic neural networks and chaotic annealing. Neurocomputing 30:293–300

    Article  Google Scholar 

Download references

Acknowledgments

This research was partially supported by the grants from the Natural Science Foundation of China (No. 61003205, No. 71001103); Zhejiang Provincial Natural Science Foundation of China (No. Y1101062); the Fundamental Research Funds for the Central Universities,and the Research Funds of Renmin University of China (No. 10XNF036).

Author information

Authors and Affiliations

  1. Key Laboratory of Data Engineering and Knowledge Engineering, Renmin University of China, MOE, Beijing, 100872, People’s Republic of China

    Gang Yang

  2. Department of Computer Science and Technology, Zhejiang University of Technology, Chaowang Road 18, Hangzhou, 310026, Zhejiang Province, People’s Republic of China

    Junyan Yi

Authors
  1. Gang Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Junyan Yi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gang Yang.

Additional information

Communicated by Y. Jin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yang, G., Yi, J. Dynamic characteristic of a multiple chaotic neural network and its application. Soft Comput 17, 783–792 (2013). https://doi.org/10.1007/s00500-012-0948-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-012-0948-8

Keywords

Search

Navigation