Biological Cybernetics

, Volume 66, Issue 4, pp 375–379 | Cite as

A neural network designed to solve the N-Queens Problem

  • Jacek Mandziuk
  • Bohdan Macuk


In this paper we discuss the Hopfield neural network designed to solve the N-Queens Problem (NQP). Our network exhibits good performance in escaping from local minima of energy surface of the problem. Only in approximately 1% of trials it settles in a false stable state (local minimum of energy). Extenive simulations indicate that the network is efficient and less sensitive to changes of its initial energy (potentials of neurons). Two strategies employed to achieve the solution and results of computer simulation are presented. Some theoretical remarks about convergence of the network are added.


Neural Network Energy Surface Computer Simulation Stable State Local Minimum 
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.


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  1. Angéniol B, De La Croix Vaubois G, Le Texier JY (1988) Self-organizing feature maps and the Travelling Salesman Problem. Neural Networks 1:289–293Google Scholar
  2. Bizzarri AR (1991) Convergence properties of a modified HopfieldTank model. Biol Cybern 64:293–300Google Scholar
  3. Brandt RD, Wang Y, Laub AJ, Mitra SK (1988) Alternative networks for solving the Traveling Salesman Problem and the List-Matching Problem. ICNN, pp 333–340Google Scholar
  4. Fort JC (1988) Solving a combinatorial problem via self-organizing process: an application of the Kohonen algorithm to the Traveling Salesman Problem. Biol Cybern 59:33–40Google Scholar
  5. Grossberg S (1988) Nonlinear neural networks: principles, mechanisms, and architectures. Neural Networks 1:17–61Google Scholar
  6. Hopfield JJ (1984) Neurons with graded response have collective computational properties like those of two-state neurons. Proc Natl Acad Sci USA 81:3088–3092Google Scholar
  7. Hopfield JJ, Tank DW (1985) “Neural” computation of decisions in optimization problems. Biol Cybern 52:141–152Google Scholar
  8. Kohonen T (1984) Self-organization and associative memory. Springer, Berlin Heidelberg New YorkGoogle Scholar
  9. Lippman RP (1987) An introduction to computing with neural nets. IEEE ASSP Mag, April:4–22Google Scholar
  10. Shackleford JB (1989) Neural data structures: programming with neurons. Hewlett-Packard J, June:69–28Google Scholar
  11. Yao KC, Chavel P, Meyrueis P (1989) Perspective of a neural optical solution to the Traveling Salesman optimization Problem. SPIE, Vol 1134, Optical Pattern Recognition 11, pp 17–25Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Jacek Mandziuk
    • 1
  • Bohdan Macuk
    • 1
  1. 1.Institute of MathematicsWarsaw University of TechnologyWarszawaPoland

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