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Constraint Programming and Hybrid Formulations for Three Life Designs

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Abstract

Conway's game of Life provides an interesting testbed for exploring issues in formulation, symmetry, and optimization with constraint programming and hybrid constraint programming/integer programming methods. We consider three Life pattern-creation problems: finding maximum density still-Lifes, finding smallest immediate predecessor patterns, and finding period-2 oscillators. For the first two problems, integrating integer programming and constraint programming approaches provides a much better solution procedure than either individually. For the final problem, the constraint programming formulation provides the better approach.

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Authors and Affiliations

  1. Department of Mathematics, Oberlin College, Oberlin, OH, USA

    Robert Bosch

  2. Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, PA, USA

    Michael Trick

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  1. Robert Bosch
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  2. Michael Trick
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Bosch, R., Trick, M. Constraint Programming and Hybrid Formulations for Three Life Designs. Annals of Operations Research 130, 41–56 (2004). https://doi.org/10.1023/B:ANOR.0000032569.86938.2f

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  • DOI: https://doi.org/10.1023/B:ANOR.0000032569.86938.2f

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