Heuristics Guided by the Quality of solutions in Weighted CSP

Weighted Constraint Satisfaction Problems (WCSP) are used to model and to solve some constraint optimization problems. WCSPs are often solved by complete or partial tree search strategies combined with filtering. For these methods, variable ordering heuristic (MinDom/FutDeg) and value ordering heuristic (MinAC) are considered to be the most efficient ones. In this paper, we propose a new value ordering heuristic for WCSP based on the quality of solutions. The H-Quality of an assignment estimates its capacity to occur in solutions of “good” quality. Then, we propose several variable ordering heuristics also based on H-Quality. Experiments using Limited Discrepancy Search on random WCSP instances and CELAR benchmarks show that our value ordering clearly outperforms MinAC on most instances. Our variable ordering heuristics outperforms MinDom/FutDeg on random instances having high connectivity. For CELAR instances, no heuristic always outperforms the other ones.