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A restarted estimation of distribution algorithm for solving sudoku puzzles

Author

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  • Maire Sylvain

    (Laboratoire des Sciences de l'Information et des Systemes (LSIS), UMR6168, ISITV, Universite de Toulon et du Var, Avenue G. Pompidou, BP 56, 83262 La Valette du Var cedex, France)

  • Prissette Cyril

    (Laboratoire des Sciences de l'Information et des Systemes (LSIS), UMR6168, ISITV, Universite de Toulon et du Var, Avenue G. Pompidou, BP 56, 83262 La Valette du Var cedex, France)

Abstract

In this paper, we describe a stochastic algorithm to solve sudoku puzzles. Our method consists in computing probabilities for each symbol of each cell updated at each step of the algorithm using estimation of distributions algorithms (EDA). This update is done using the empirical estimators of these probabilities for a fraction of the best puzzles according to a cost function. We develop also some partial restart techniques in the RESEDA algorithm to obtain a convergence for the most difficult puzzles. Our algorithm is tested numerically on puzzles with various levels of difficulty starting from very easy ones to very hard ones including the famous puzzle AI Escargot. The CPU times vary from few hundreds of a second for the easy ones to about one minute for the most difficult one.

Suggested Citation

  • Maire Sylvain & Prissette Cyril, 2012. "A restarted estimation of distribution algorithm for solving sudoku puzzles," Monte Carlo Methods and Applications, De Gruyter, vol. 18(2), pages 147-160, January.
    • Handle: RePEc:bpj:mcmeap:v:18:y:2012:i:2:p:147-160:n:3
    DOI: 10.1515/mcma-2012-0004
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