Solving Sudoku with the GAuGE System

  • Miguel Nicolau
  • Conor Ryan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3905)


This paper presents an evolutionary approach to solving Sudoku puzzles. Sudoku is an interesting problem because it is a challenging logical puzzle that has previously only been solved by computers using various brute force methods, but it is also an abstract form of a timetabling problem, and is scalably difficult. A different take on the problem, motivated by the desire to be able to generalise it, is presented. The GAuGE system was applied to the problem, and the results obtained show that its mapping process is well suited for this class of problems.


Timetabling Problem Grammatical Evolution Successful Instruction Genotypic Level Brute Force Search 
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. 1.
    Bagley, J.D.: The Behaviour of Adaptive Systems which Employ Genetic and Correlation Algorithms. PhD Thesis, University of Michigan (1967)Google Scholar
  2. 2.
    Felgenhauer, B., Jarvis, F.: Enumerating Possible Sudoku Grids. Technical Report pm1afj/sudoku/ (2005),
  3. 3.
    Frantz, D.R.: Non-linearities in Genetic Adaptive Search. PhD Thesis, University of Michigan (1972)Google Scholar
  4. 4.
    Goldberg, D.E., Korb, B., Deb, K.: Messy genetic algorithms: Motivation, analysis, and first results. Complex Systems 3(5), 493–530 (1989)MathSciNetMATHGoogle Scholar
  5. 5.
    Goldberg, D.E., Deb, K., Kargupta, H., Harik, G.: Rapid, Accurate Optimization of Difficult Problems Using Fast Messy Genetic Algorithms. In: Forrest, S. (ed.) Proceedings of the Fifth International Conference on Genetic Algorithms, pp. 56–64. Morgan Kaufmann Publishers, San Francisco (1993)Google Scholar
  6. 6.
    Harik, G.: Learning Gene Linkage to Efficiently Solve Problems of Bounded Difficulty Using Genetic Algorithms. Doctoral Dissertation, University of Illinois (1997)Google Scholar
  7. 7.
    Holland, J.H.: Adaptation in Natural and Artificial Systems, 2nd edn. University of Michigan Press (1992)Google Scholar
  8. 8.
    Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Evolution. MIT Press, Cambridge (1992)MATHGoogle Scholar
  9. 9.
    Nicolau, M., Ryan, C.: How Functional Dependency Adapts to Salience Hierarchy in the GAuGE System. In: Ryan, C., Soule, T., Keijzer, M., Tsang, E.P.K., Poli, R., Costa, E. (eds.) EuroGP 2003. LNCS, vol. 2610, pp. 153–163. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  10. 10.
    Nicolau, M., Auger, A., Ryan, C.: Functional dependency and degeneracy: Detailed analysis of the gAuGE system. In: Liardet, P., Collet, P., Fonlupt, C., Lutton, E., Schoenauer, M. (eds.) EA 2003. LNCS, vol. 2936, pp. 15–26. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  11. 11.
    Ohnishi, K., Sastry, K., Chen, Y.-P., Goldberg, D.: Inducing Sequentiality Using Grammatical Genetic Codes. In: Deb, K., et al. (eds.) GECCO 2004. LNCS, vol. 3102, pp. 1426–1437. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  12. 12.
    Oliver, I.M., Smith, D.J., Holland, J.R.C.: A Study of Permutation Crossover Operators on the Travelling Salesman Problem. In: Grefenstette, J.J. (ed.) Proceedings of the Second International Conference on Genetic Algorithms, pp. 224–230. Lawrence Erlbaum Associates, Mahwah (1987)Google Scholar
  13. 13.
    O’Neill, M., Ryan, C.: Grammatical Evolution - Evolving programs in an arbitrary language. Kluwer Academic Publishers, Dordrecht (2003)MATHGoogle Scholar
  14. 14.
    Ryan, C., Nicolau, M., O’Neill, M.: Genetic Algorithms using Grammatical Evolution. In: Foster, J.A., Lutton, E., Miller, J., Ryan, C., Tettamanzi, A.G.B. (eds.) EuroGP 2002. LNCS, vol. 2278, pp. 278–287. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  15. 15.
    Satoh, H., Yamamura, M., Kobayashi, S.: Minimal Generation Gap Model for GAs Considering Both Exploration and Exploitation. In: Proceedings of the 4th International Conference on Fuzzy Systems, Neural Networks and Soft Computing, vol. 2, pp. 494–497. World Scientific, Singapore (1996)Google Scholar
  16. 16.
  17. 17.
    Vorderman, C.: Carol Vorderman’s How To Do Sudoku. Ebury Press (2005)Google Scholar
  18. 18.
  19. 19.
  20. 20.
    Yato, T., Seta, T.: Complexity and Completeness of Finding Another Solution and its Application to Puzzles. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences 86(5), 1052–1060 (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Miguel Nicolau
    • 1
  • Conor Ryan
    • 1
  1. 1.Biocomputing and Developmental Systems Group, Department of Computer Science and Information SystemsUniversity of LimerickIreland

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