Influence of CNF Encodings of AtMost-1 Constraints on UNSAT-based PMSAT Solvers

Partial maximum Boolean satisfiability (Partial MaxSAT or PMSAT) is an optimization variant of Boolean Satisability (SAT). It asks to find a variable assignment that satisfies all hard clauses and the maximum number of soft clauses in a Boolean formula. Several exact PMSAT solvers have been developed since the introduction of the MaxSAT evaluations in 2006, based mainly on the DavisPutnam-LogemannLoveland (DPLL) procedure and branch and bound (B&B) algorithms. One recent approach that provides an alternative to B&B algorithms is based on unsatisfiable (UNSAT) core identification. All PMSAT algorithms based on UNSAT identification are dependent on two essential external components: (1) a cardinality constraint encoder for encoding AtMost-1 constraints into conjunctive normal form (CNF); and (2) a SAT solver. Ensuring the effectiveness of both components directly affects the performance of the PMSAT solver. Whereas great advances have been made in PMSAT algorithms based on UNSAT core identification, only a few research work has been conducted to understand the influence of CNF encoding methods on the performance of PMSAT solvers. In this paper, we investigate the influence of three CNF encoding methods for AtMost-1 constraints on an UNSAT-based PMSAT solver. We implement the solver using the pairwise, parallel, and sequential encodings, and evaluate its performance on industrial instances. The experimental results show the impact of the CNF encoding method on the performance of the PMSAT solver. Overall, the best results were obtained with the sequential encoding.

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