Chaotic Neurodynamics in the Frequency Assignment Problem

  • K. Dorkofikis
  • N. M. Stephens
Conference paper


The frequency assignment problem belongs to the quite difficult to deal with class of NP (nondeterministic polynomial) - hard combinatorial optimization problems [3]. Its computational complexity directs researchers in the field at developing efficient techniques for finding solutions realizing minimum (or maximum) values of an objective function subject to a set of, often conflicting, constraints. To seek an optimal (or near optimal) solution, many methods have been proposed, such as dynamic programming methods, branch and bound methods, etc., and, lately, some heuristic algorithms relating to physical and biological phenomena. They include tabu search, genetic algorithms, simulated annealing and artificial neural networks [4]. We propose a Hop-field neural network model with chaotic neurodynamics to overcome the obstacle of local minima in the energy function and obtain optimal solutions in less iterations than the time-consuming convergent dynamics.


Chaotic Neural Network Hopfield Network Frequency Assignment Problem Channel Assignment Problem Hard Combinatorial Optimization Problem 
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  1. [1]
    D.H. Ackley, G.E. Hinton, and T.J. Sejnowski. A learning algorithm for Boltzmann machines. Cognitive Science, 9:147–169, 1985.CrossRefGoogle Scholar
  2. [2]
    D.J. Amit, H. Gutfreund, and H. Sompolinsky. Spin-glass models for neural networks. Physical Review, A(32):1007–1018, 1986.MathSciNetGoogle Scholar
  3. [3]
    D.J. Castelino, S. Hurley, and N.M. Stephens. A tabu search algorithm for frequency assignment. Annals of Ops Res, 63:301–319, 1996.MATHCrossRefGoogle Scholar
  4. [4]
    Euclid cepa 6 project proposal. RTP 6.4 combinatorial algorithms for military applications, project specification. appendix 3, Scholar
  5. [5]
    L. Clen. Application of chaotic simulation and self-organizing neural net to power system voltage stability monitoring. In Second Int. Forums on Applications of Neural Networks to Power Systems, 7B1. Yokohama, Japan, 1993.Google Scholar
  6. [6]
    L. Clen and K. Aihara. Chaotic Simulated Annealing for Combinatorial Optimization, volume 1, pages 319–322. 1994.Google Scholar
  7. [7]
    L. Clen and K. Aihara. Transient Chaotic Neural Networks and Chaotic Simulated Annealing, pages 347–352. 1994.Google Scholar
  8. [8]
    L. Clen and K. Aihara. Chaotic simulated annealing by a neural network model with transient chaos. Neural Networks, 8(6):915–930, 1995.CrossRefGoogle Scholar
  9. [9]
    N. Funabiki and Y. Takefuji. A neural network parallel algorithm for channel assignment problems in cellular radio networks. IEEE Trans. Veh. Technol., 41(4):430–437, 1992.CrossRefGoogle Scholar
  10. [10]
    A. Gamst and W. Rave. On frequency assignment in mobile automatic telephone systems. In Proc. GLOBECOM’ 82 1982, pages 57–64, May 1978.Google Scholar
  11. [11]
    J.J. Hopfield. Neural networks and physical systems with emergent collective computational abilities. In Proceedings of the National Academy of Sciences’ 79, pages 2554–2558, 1982.Google Scholar
  12. [12]
    J.J. Hopfield and D.W. Tank. Neural computation of decisions in optimization problems. Biological Cybernetics, 52:141–152, 1985.MathSciNetMATHGoogle Scholar
  13. [13]
    T. Kasahara and M. Nakagawa. Parameter-controlled chaos neural networks. Electronics and Communications in Japan, Part 3, 78(7), 1995.Google Scholar
  14. [14]
    Y. Takefuji and K.C. Lee. Artificial neural networks for four-coloring map problems and k-colorability problems. IEEE Trans. Circuit systems, 38(3):326–333, March 1991.CrossRefGoogle Scholar
  15. [15]
    J. Tani. Proposal of chaotic steepnest descent method for neural networks and analysis of their dynamics. Trans. Inst. Electron. Inf. Commun., J74-A-8:1208–1215, 1991.Google Scholar

Copyright information

© Springer-Verlag Wien 1998

Authors and Affiliations

  • K. Dorkofikis
    • 1
  • N. M. Stephens
    • 1
  1. 1.Goldsmiths UniversityLondonUK

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