A Memetic Algorithm with Bucket Elimination for the Still Life Problem

  • José E. Gallardo
  • Carlos Cotta
  • Antonio J. Fernández
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3906)


Bucket elimination (BE) is an exact technique based on variable elimination, commonly used for solving constraint satisfaction problems. We consider the hybridization of BE with evolutionary algorithms endowed with tabu search. The resulting memetic algorithm (MA) uses BE as a mechanism for recombining solutions, providing the best possible child from the parental set. This MA is applied to the maximum density still life problem. Experimental tests indicate that the MA provides optimal or near-optimal results at an acceptable computational cost.


Tabu Search Constraint Programming Constraint Satisfaction Problem Memetic Algorithm Soft Constraint 


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  1. 1.
    Gardner, M.: The fantastic combinations of John Conway’s new solitaire game. Scientific American 223, 120–123 (1970)CrossRefGoogle Scholar
  2. 2.
    Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning Ways for your Mathematical Plays. Games in Particular, vol. 2. Academic Press, London (1982)MATHGoogle Scholar
  3. 3.
    Gardner, M.: On cellular automata, self-reproduction, the garden of Eden and the game of “life”. Scientific American 224, 112–117 (1971)CrossRefGoogle Scholar
  4. 4.
    Gardner, M.: Wheels, Life, and Other Mathematical Amusements. W.H. Freeman, New York (1983)MATHGoogle Scholar
  5. 5.
    Bosch, R., Trick, M.: Constraint programming and hybrid formulations for three life designs. In: CP-AI-OR, pp. 77–91 (2002)Google Scholar
  6. 6.
    Smith, B.M.: A dual graph translation of a problem in ‘life’. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 402–414. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  7. 7.
    Larrosa, J., Morancho, E., Niso, D.: On the practical use of variable elimination in constraint optimization problems: ‘still life’ as a case study. Journal of Artificial Intelligence Research 23, 421–440 (2005)MATHGoogle Scholar
  8. 8.
    Larrosa, J., Morancho, E.: Solving ‘still life’ with soft constraints and bucket elimination. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 466–479. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  9. 9.
    Bistarelli, S., Montanari, U., Rossi, F.: Semiring-based constraint satisfaction and optimization. Journal of the ACM 44, 201–236 (1997)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Dechter, R.: Bucket elimination: A unifying framework for reasoning. Artificial Intelligence 113, 41–85 (1999)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Radcliffe, N.: The algebra of genetic algorithms. Annals of Mathematics and Artificial Intelligence 10, 339–384 (1994)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Downey, R., Fellows, M.: Fixed parameter tractability and completeness I: Basic theory. SIAM Journal of Computing 24, 873–921 (1995)CrossRefMATHGoogle Scholar
  13. 13.
    Lehmann, E., D’Abrera, H.: Nonparametrics: Statistical Methods Based on Ranks. Prentice-Hall, Englewood Cliffs (1998)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • José E. Gallardo
    • 1
  • Carlos Cotta
    • 1
  • Antonio J. Fernández
    • 1
  1. 1.Dept. Lenguajes y Ciencias de la Computación, ETSI InformáticaUniversity of MálagaMálagaSpain

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