Finding Still Lifes with Memetic/Exact Hybrid Algorithms

TL;DR

This paper introduces a hybrid memetic algorithm combining exact and heuristic methods to efficiently find optimal still life patterns in the maximum density still life problem, outperforming existing approaches especially on large instances.

Contribution

It presents a novel hybrid memetic algorithm that integrates bucket elimination and branch-and-bound techniques for solving large instances of the MDSLP, achieving new best solutions.

Findings

Consistently finds optimal solutions for benchmark instances.

Outperforms current methods in solving large instances.

Provides new best known solutions for very large problems.

Abstract

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