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The maximum density still life problem (MDSLP) is a hard constraintoptimization problem based on Conway's game of life. It is a prime example ofweighted constrained optimization problem that has been recently tackled in theconstraint-programming community. Bucket elimination (BE) is a completetechnique commonly used to solve this kind of constraint satisfaction problem.When the memory required to apply BE is too high, a heuristic method based onit (denominated mini-buckets) can be used to calculate bounds for the optimalsolution. Nevertheless, the curse of dimensionality makes these techniquesunpractical for large size problems. In response to this situation, we presenta memetic algorithm for the MDSLP in which BE is used as a mechanism forrecombining solutions, providing the best possible child from the parental set.Subsequently, a multi-level model in which this exact/metaheuristic hybrid isfurther hybridized with branch-and-bound techniques and mini-buckets isstudied. Extensive experimental results analyze the performance of these modelsand multi-parent recombination. The resulting algorithm consistently findsoptimal patterns for up to date solved instances in less time than currentapproaches. Moreover, it is shown that this proposal provides new best knownsolutions for very large instances.

Finding Still Lifes with Memetic/Exact Hybrid Algorithms