Weight-Aware Core Extraction in SAT-Based MaxSAT Solving

Maximum satisfiability (MaxSAT) is today a competitive approach to tackling NP-hard optimization problems in a variety of AI and industrial domains. A great majority of the modern state-of-the-art MaxSAT solvers are core-guided, relying on a SAT solver to iteratively extract unsatisfiable cores of the soft clauses in the working formula and ruling out the found cores via adding cardinality constraints into the working formula until a solution is found. In this work we propose weight-aware core extraction (WCE) as a refinement to the current common approach of core-guided solvers. WCE integrates knowledge of soft clause weights into the core extraction process, and allows for delaying the addition of cardinality constraints into the working formula. We show that WCE noticeably improves in practice the performance of PMRES, one of the recent core-guided MaxSAT algorithms using soft cardinality constraints, and explain how the approach can be integrated into other core-guided algorithms.