Skip to main content

Performance-Enhancing Bifurcations in a Self-organising Neural Network

  • Conference paper
  • First Online:
Computational Methods in Neural Modeling (IWANN 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2686))

Included in the following conference series:

Abstract

The self-organising neural network with weight normalisation (SONN-WN) for solving combinatorial optimisation problems (COPs) is investigated in terms of its performance and dynamical characteristics. A simplified computational model of the weight normalisation process is constructed, which reveals symmetry-breaking bifurcations in a typical node outside the winning neighbourhood. Experimental results with the N-queen problem show that bifurcations can enhance solution qualities in a consistent manner. A mechanism based on the weights’ transient trajectories is proposed to account for the neural network’s capacity to escape local minima.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Kohonen, T.: Self-organized Formation of Topologically Correct Feature Maps. Biol. Cybern., Vol. 43. (1982) 59–69

    Article  MATH  MathSciNet  Google Scholar 

  2. Smith, K. A.: Neural Networks for Combinatorial Optimisation: A Review of More Than a Decade of Research. INFORMS Journal on Computing, Vol. 11, No. 1. (1999) 15–34

    Article  MATH  MathSciNet  Google Scholar 

  3. Durbin, R., Willshaw, D.: An Analogue Approach to the Travelling Salesman Problem Using an Elastic Net Method. Nature, Vol. 326. (1987) 689–691

    Article  Google Scholar 

  4. Fort, J. C.: Solving a Combinatorial Problem via Self-Organizing Process: An Application of the Kohonen Algorithm to the Travelling Salesman Problem. Biol. Cybern., Vol. 59. (1988) 33–40

    Article  MATH  MathSciNet  Google Scholar 

  5. Favata, F., Walker, R.: A Study of the Application of Kohonen-Type Neural Networks to the Travelling Salesman Problem. Biol. Cybern., Vol. 64. (1991) 463–468

    Article  MATH  Google Scholar 

  6. Smith, K. A., Palaniswami, M., Krishnamoorthy, M.: A Hybrid Neural Approach to Combinatorial Optimization. Computers Ops. Res., Vol. 23. (1996) 597–610

    Article  MATH  MathSciNet  Google Scholar 

  7. Smith, K. A.: Neural Techniques for Combinatorial Optimization with Applications. IEEE Trans. Neural Networks, Vol. 9, No. 6. (1998) 1301–1318

    Article  Google Scholar 

  8. Guerrero, F., Lozano, S., Smith. K. A., Canca, D., Kwok, T.: Manufacturing Cell Formation Using a New Self-Organizing Neural Network. Computers & Industrial Engineering, Vol. 42. (2002) 377–382

    Article  Google Scholar 

  9. Van den Bout, D. E., Miller, T. K.: Improving the Performance of the Hopfield-Tank Neural Network Through Normalization and Annealing. Biol. Cybern., Vol. 62. (1989) 129–139

    Article  Google Scholar 

  10. Peterson, C., Söderberg, B.: A New Method for Mapping Optimization Problems onto Neural Networks. Int. Jnl. Neural Systems, Vol. 1, No. 1. (1989) 3–22

    Article  Google Scholar 

  11. Kwok, T., Smith, K. A.: Improving the Optimisation Performance of a Self-Organising Neural Network with Weight Normalisation. Proc. Int. ICSC Congress on Intelligent Systems & Applications (ISA’2000), Paper no. 1513-285. (2000)

    Google Scholar 

  12. Kwok, T.: Characteristic Updating-Normalisation Dynamics of a Self-Organising Neural Network for Enhanced Combinatorial Optimisation. Proc. 9th Int. Conf. Neural Information Processing, Vol. 3. (2002) 1146–1152

    Google Scholar 

  13. Kwok, T.: Nonlinear System Dynamics in the Normalisation Process of a Self-Organising Neural Network for Combinatorial Optimisation. In: Lecture Notes in Computer Science, Vol. 2084. Springer-Verlag, Berlin (2001) 733–740

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kwok, T., Smith, K.A. (2003). Performance-Enhancing Bifurcations in a Self-organising Neural Network. In: Mira, J., Álvarez, J.R. (eds) Computational Methods in Neural Modeling. IWANN 2003. Lecture Notes in Computer Science, vol 2686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44868-3_50

Download citation

  • DOI: https://doi.org/10.1007/3-540-44868-3_50

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40210-7

  • Online ISBN: 978-3-540-44868-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics