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

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.