Optimizing with minimum satisfiability

Authors:
Chu Min Li;Zhu Zhu;Felip Manyí;Laurent Simon
Affiliations:
MIS, Université de Picardie Jules Verne, 5 Rue du Moulin Neuf, 80000 Amiens, France and Huazhong University of Science and Technology, Wuhan, China;MIS, Université de Picardie Jules Verne, 5 Rue du Moulin Neuf, 80000 Amiens, France;Artificial Intelligence Research Institute (IIIA), Spanish Scientific Research Council (CSIC), Campus UAB, 08193 Bellaterra, Spain;LRI/INRIA Futurs, Parc Club Université, Batiment G, 4, rue Jacques Monod, 91893 Orsay, France
Venue:
Artificial Intelligence
Year:
2012

Citing 15
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Abstract

MinSAT is the problem of finding a truth assignment that minimizes the number of satisfied clauses in a CNF formula. When we distinguish between hard and soft clauses, and soft clauses have an associated weight, then the problem, called Weighted Partial MinSAT, consists in finding a truth assignment that satisfies all the hard clauses and minimizes the sum of weights of satisfied soft clauses. In this paper we describe a branch-and-bound solver for Weighted Partial MinSAT equipped with original upper bounds that exploit both clique partitioning algorithms and MaxSAT technology. Then, we report on an empirical investigation that shows that solving combinatorial optimization problems by reducing them to MinSAT is a competitive generic problem solving approach when solving MaxClique and combinatorial auction instances. Finally, we investigate an interesting correlation between the minimum number and the maximum number of satisfied clauses on random CNF formulae.