Conflict Directed Variable Selection Strategies for Constraint Satisfaction Problems

Abstract

It is well known that the order in which variables are instantiated by a backtracking search algorithm can make an enormous difference to the search effort in solving CSPs. Among the plethora of heuristics that have been proposed in the literature to efficiently order variables during search, a significant recently proposed class uses the learning-from-failure approach. Prime examples of such heuristics are the wdeg and dom/wdeg heuristics of Boussemart et al. which store and exploit information about failures in the form of constraint weights. The efficiency of all the proposed conflict-directed heuristics is due to their ability to learn though conflicts encountered during search. As a result, they can guide search towards hard parts of the problem and identify contentious constraints. Such heuristics are now considered as the most efficient general purpose variable ordering heuristic for CSPs. In this paper we show how information about constraint weights can be used in order to create several new variants of the wdeg and dom/wdeg heuristics. The proposed conflict-driven variable ordering heuristics have been tested over a wide range of benchmarks. Experimental results show that they are quite competitive compared to existing ones and in some cases they can increase efficiency.