Abstract
An efficient neural network technique is presented for the solution of binary constraint satisfaction problems. The method is based on the application of a double-update technique to the operation of the discrete Hopfield-type neural network that can be constructed for the solution of such problems. This operation scheme ensures that the network moves only between consistent states, such that each problem variable is assigned exactly one value, and leads to a fast and efficient search of the problem state space. Extensions of the proposed method are considered in order to include several optimisation criteria in the search. Experimental results concerning many real-size instances of the Radio Links Frequency Assignment Problem demonstrate very good performance.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E. Aarts and J. Korst, Simulated Annealing and Boltzmann Machines, A Stochastic Approach to Combinatorial Optimization and Neural Computing, John Wiley & Sons: Chichester, 1989.
D. Abramson, “A very high speed architecture for simulated annealing,” Computer, vol. 25, pp. 27–36, 1992.
H. Adorf and M. Johnston, “A discrete stochastic neural network algorithm for constraint satisfaction problems,” Proc. Int. Joint Conf. on Neural Networks, San Diego, CA, June 1990, vol. 3, pp. 917–924.
J. Bitner and E. Reingold, “Backtracking programming techniques,” Communications of the ACM, vol. 18, pp. 651–656, 1975.
A. Bouju, J.F. Boyce, C.H.D. Dimitropoulos, G. vom Scheidt, J.G. Taylor, A. Likas, G. Papageorgiou, and A. Stafylopatis, “Intelligent search for the radio links frequency assisgnment problem,” Proc. Int. Conf. on Digital Signal Processing (DSP'95), Limassol, Cyprus, June 1995, vol. 1, pp. 408–414.
K. Chiba, F. Takahata, and M. Nohara, “Theory and performance of frequency assignment schemes for carriers with different bandwidths under demand assignment SCPC/FDMA operation,” IEICE Trans. Commun., vol. E75-B, pp. 476–486, 1992.
A. de Gloria, P. Faraboschi, and S. Ribella, “A dedicated massively parallel architecture for the boltzmann machine,” Parallel Computing, vol. 18, pp. 57–73, 1992.
R. Dorne and J.K. Hao, “An evolutionaty approach for frequency assignment in cellular radio networks,” Proc. IEEE Intl. Conf. on Evolutionary Computation (ICEC'95), Perth, Australia, 1995.
M. Duque-Antón, D. Kunz, and B. Rüber “Channel assignment for cellular radio using simulated annealing,” IEEE Trans. on Vehicular Technology, vol. 42, pp. 14–21, 1993.
N. Funabiki and Y. Takefuji, “A neural network parallel algorithm for channel assignment problems in cellular radio networks,” IEEE Trans. on Vehicular Technology, vol. 41, pp. 430–437, 1992.
M. Garey and D. Johnson, Computers and Intractability: A Guide to the Theory of NP-completeness, W.H. Freeman and Company: San Francisco, 1979.
L. Gislén, C. Peterson, and B. Söderberg, “Complex scheduling with potts neural networks,” Neural Computation, vol. 4, pp. 805–831, 1992.
F. Glover, “Tabu search part I,” ORSA J. Comput., vol. 1, pp. 190–206, 1989.
F. Glover, “Tabu search part II,” ORSA J. Comput., vol. 2, pp. 4–32, 1990.
J.K. Hao and R. Dorne, “Study of genetic search for the frequency assignment problem,” Proc French Nat. Conf. on Artificial Evolution (EA'95), Brest, France (Lecture Notes in Computer Science, Springer-Verlag), Sept. 1995.
J. Hopfield, “Neural networks and physical systems with emergent collective computational abilities,” Proc. Nat. Academy of Sciences USA, vol. 79, pp. 2554–2558, 1982.
J.J. Hopfield and D.W. Tank, “Neural computation of decisions in optimization problems,” Biological Cybernetics, vol. 52, pp. 141–152, 1985.
Y. Kamp and M. Hasler, Recursive Neural Networks for Associative Memory, John Wiley & Sons: Chichester, 1990.
S. Kirkpatrick, C.D. Gellat Jr., and M.P. Vecchi, “Optimization by simulated annealing,” Science, vol. 220, pp. 671–689, 1983.
D. Kontoravdis, A. Likas, and A. Stafylopatis, “Embedding knowledge into stochastic learning automata for fast solution of binary constraint satisfaction problems,” Proc. Europ. Symp. on Artificial Neural Networks (ESANN'93), Brussels, April 1993, pp. 21–26.
V. Kumar, “Algorithms for constraint satisfaction problems: A survey,” The AI Magazine, vol. 13, pp. 32–44, 1992.
D. Kunz, “Channel assignment for cellular radio using neural networks,” IEEE Trans. on Vehicular Technology, vol. 40, pp. 188–193, 1991.
A. Likas and A. Stafylopatis, “Group updates and multiscaling: An efficient neural network approach to combinatorial optimization,” IEEE Transactions on Systems, Man and Cybernetics, Part B: Cybernetics, vol. 26, pp. 222–232, 1996.
Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag, 1992.
M. Ohlsson, C. Peterson, and B. Söderberg, “Neural networks for optimization problems with inequality constraints: The knapsack problem,” Neural Computation, vol. 5, pp. 331–339, 1993.
A. Raychaudhuri, “Optimal multiple interval assignments in frequency assignment and traffic phasing,” Discrete Applied Mathematics, vol. 40, pp. 319–332, 1992.
F. Ricci, “Constraint reasoning with learning automata,” Proc. 3rd Workshop of AI*IA Interest Group in Automatic Learning, Rome, May 1992.
J.C. Spall, “Multivariate stochastic approximation using a simultaneous perturbation gradient approximation,” IEEE Trans. Automatic Control, vol. 37, pp. 332–341, 1992.
H.A. Stone and J.M. Stone, “Efficient search techniques—An empirical study of the N-queens problem,” IBM Journal on Research and Development, vol. 31, pp. 464–474, 1987.
M. Skubiszewski, “A hardware emulator for binary neural networks,” Proc. Int. Neural Network Conf., Paris, July 1990, vol. 2, pp. 555–558.
M. Skubiszewski, “An exact hardware implementation of the boltzmann machine,” Research Report, DEC Paris Research Laboratory, 1992.
G. Tagliarini and E. Page, “Solving constraint satisfaction problems with neural networks,” Proc. Int. Conf. on Neural Networks, San Diego, CA, June 1987, vol. 3, pp. 741–747.
Y. Takefuji and H. Szu, “Design of parallel distributed cauchy machines,” Proc. Int. Joint Conf. on Neural Networks, Washington DC, June 1989, vol. 1, pp. 529–532.
M.A. Thathachar and P.S. Sastry, “Relaxation labeling with learning automata,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 8, pp. 256–268, 1986.
E. Tsang, Foundations of Constraint Satisfaction, Academic Press, 1993.
G.V. Wilson and G.S. Pawley, “On the stability of the TSP algorithm of hopfield and tank,” Biological Cybernetics, vol. 58, pp. 63–70, 1988.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Likas, A., Papageorgiou, G. & Stafylopatis, A. A Connectionist Approach for Solving Large Constraint Satisfaction Problems. Applied Intelligence 7, 215–225 (1997). https://doi.org/10.1023/A:1008272531960
Issue Date:
DOI: https://doi.org/10.1023/A:1008272531960