A Performance Comparison of Chaotic Simulated Annealing Models for Solving the N-queen Problem

  • Terence Kwok
  • Kate A. Smith
Conference paper


Chaotic neural network models employing two chaotic simulated annealing (CSA) schemes, one with decaying self-couplings and the other with a decaying time-step, are used to solve the N-queen problem. Their optimisation performances are compared in terms of feasibility, efficiency, robustness and scalability in a two-parameter domain chosen for each model. Computational results show that the decaying self-coupling approach offers better feasibility, robustness and scalability, with efficiency being comparable for the two models. Correlation between feasibility and efficiency illustrates some chaotic search characteristics common to both models.


Travelling Salesman Problem Constraint Satisfaction Problem Hopfield Neural Network Chaotic Neural Network Hopfield Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Hopfield, J. J., Tank, D. W., (1985). “Neural” Computation of Decisions in Optimization Problems. Biol. Cybern., Vol. 52, pp. 141–152.MathSciNetMATHGoogle Scholar
  2. [2]
    Aihara, K., Takabe, T., Toyoda, M., (1990). Chaotic Neural Networks. Physics Letters A, Vol. 144, No. 6, 7, Mar., pp. 333–340.MathSciNetCrossRefGoogle Scholar
  3. [3]
    Hasegawa, M., Ikeguchi, T., Matozaki, T., (1995). Solving Combinatorial Optimization Problems by Nonlinear Neural Dynamics. Proc. IEEE Int. Conf. Neural Networks, Vol. 6, pp. 3140–3145.CrossRefGoogle Scholar
  4. [4]
    Nozawa, H., (1994). Solution of the Optimization Problem Using the Neural Network Model as a Globally Coupled Map. Towards the Harnessing of Chaos, pp. 99-114.Google Scholar
  5. [5]
    Yamada, T., Aihara, K., Kotani, M., (1993). Chaotic Neural Networks and The Travelling Salesman Problem. Proc. 1993 Int. Joint Conf. Neural Networks, Vol. 2, pp. 1549–1552.Google Scholar
  6. [6]
    Ishii, S., Sato, M. A., (1997). Chaotic Potts Spin Model for Combinatorial Optimization Problems. Neural Networks, Vol. 10, No. 5, pp. 941–963.CrossRefGoogle Scholar
  7. [7]
    Tokuda, I., Nagashima, T., Aihara, K., (1997). Global bifurcation Structure of Chaotic Neural Networks and its Application to Traveling Salesman Problems. Neural Networks, Vol. 10, No. 9, pp. 1673–1690.CrossRefGoogle Scholar
  8. [8]
    Asai H., Onodera, K., Kamio, T., Ninomiya, H., (1995). A Study of Hopfield Neural Networks with External Noises. Proc. IEEE Int. Conf. Neural Networks, Vol. 4, pp. 1584–1589.CrossRefGoogle Scholar
  9. [9]
    Hasegawa, M., Ikeguchi, T., Matozaki, T., Aihara, K., (1997). An Analysis on Additive Effects of Nonlinear Dynamics for Combinatorial Optimization. IEICE Trans. Fundamentals, Vol. E80-A, Iss. 1, pp. 206–213.Google Scholar
  10. [10]
    Hayakawa, Y., Marumoto, A., Sawada, Y., (1995). Effects of the Chaotic Noise on the Performance of a Neural Network Model for Optimization Problems. Physical Review E, Vol. 51, No. 4, Apr., pp. 2693–2696.CrossRefGoogle Scholar
  11. [11]
    Chen, L., Aihara, K., (1995). Chaotic Simulated Annealing by a Neural Network Model with Transient Chaos. Neural Networks, Vol. 8, No. 6, pp. 915–930.CrossRefGoogle Scholar
  12. [12]
    Chen, L., Aihara, K., (1997). Chaos and asymptotical stability in discrete-time neural networks. Physica D, Vol. 104, pp. 286–325.MathSciNetMATHCrossRefGoogle Scholar
  13. [13]
    Kwok, T., Smith, K. and Wang, L., (1998). Solving Combinatorial Optimization Problems by Chaotic Neural Networks. Intelligent Engineering Systems Through Artificial Neural Networks: Neural Networks, Fuzzy Logic, Evolutionary Programming, Data Mining, and Rough Sets, vol. 8. C. Dagli et al (eds.), pp. 317-322.Google Scholar
  14. [14]
    Wang, L., Smith, K., (1998). On Chaotic Simulated Annealing. IEEE Trans. Neural Networks, Vol. 9, No. 4, pp. 716–718.CrossRefGoogle Scholar
  15. [15]
    Wang, L., Smith, K., (1998). Chaos in the Discretized Analog Hopfield Neural Network and Potential Applications to Optimization. Proc. Int. Conf. Neural Networks, pp. 1679-1684.Google Scholar
  16. [16]
    Kwok, T., Smith, K., Wang, L., (1998). Incorporating Chaos into the Hopfield Neural Network for Combinatorial Optimization. 1998 World Multiconference on Systemics, Cybernetics and Informatics, Vol. 1, pp. 659–665.Google Scholar
  17. [17]
    Tagliarini, G. A., Page, E. W., (1987). Solving Constraint Satisfaction Problems with Neural Networks. Proc. IEEE Int. Conf. Neural Networks, III-741 — III-747.Google Scholar
  18. [18]
    Takefuji, Y., Szu, H., (1989). Design of Parallel Distributed Cauchy Machines. Proc. IJCNN, I-529-I-532.Google Scholar
  19. [19]
    Akiyama, Y., Yamashita, A., Kajiura, M., Aiso, H., (1989). Combinatorial Optimization with Gaussian Machines. IJCNN, Vol. 1, pp. I–533–I–540.Google Scholar

Copyright information

© Springer-Verlag London 2000

Authors and Affiliations

  • Terence Kwok
    • 1
  • Kate A. Smith
    • 1
  1. 1.School of Business Systems, Faculty of Information TechnologyMonash UniversityClaytonAustralia

Personalised recommendations