Weight-Based Variable Ordering in the Context of High-Level Consistencies

TL;DR

This paper explores how to effectively update weights in the dom/wdeg heuristic when applying high-level consistencies like singleton and relational, proposing and empirically testing several strategies for improved variable ordering.

Contribution

It introduces new strategies for updating weights in dom/wdeg under high-level consistencies and provides a comprehensive empirical evaluation and recommendations.

Findings

Certain weight update strategies outperform others in practice.

Empirical results favor specific strategies for singleton and relational consistencies.

Recommendations improve the effectiveness of dom/wdeg in high-level consistency contexts.

Abstract

Dom/wdeg is one of the best performing heuristics for dynamic variable ordering in backtrack search [Boussemart et al., 2004]. As originally defined, this heuristic increments the weight of the constraint that causes a domain wipeout (i.e., a dead-end) when enforcing arc consistency during search. "The process of weighting constraints with dom/wdeg is not defined when more than one constraint lead to a domain wipeout [Vion et al., 2011]." In this paper, we investigate how weights should be updated in the context of two high-level consistencies, namely, singleton (POAC) and relational consistencies (RNIC). We propose, analyze, and empirically evaluate several strategies for updating the weights. We statistically compare the proposed strategies and conclude with our recommendations.