On the Practical use of Variable Elimination in Constraint Optimization Problems: 'Still-life' as a Case Study

TL;DR

This paper explores the practical application of variable elimination in solving the complex still-life problem, demonstrating its effectiveness when combined with other methods and achieving new state-of-the-art results.

Contribution

It introduces novel ways to apply variable elimination to constraint optimization, including as a standalone method, integrated with search, and for generating lower bounds.

Findings

Successfully solved the n=20 still-life instance.

Variable elimination outperforms other approaches in this context.

Combining variable elimination with search enhances problem-solving capabilities.

Abstract

Variable elimination is a general technique for constraint processing. It is often discarded because of its high space complexity. However, it can be extremely useful when combined with other techniques. In this paper we study the applicability of variable elimination to the challenging problem of finding still-lifes. We illustrate several alternatives: variable elimination as a stand-alone algorithm, interleaved with search, and as a source of good quality lower bounds. We show that these techniques are the best known option both theoretically and empirically. In our experiments we have been able to solve the n=20 instance, which is far beyond reach with alternative approaches.