Abstract
Weighted Partial MaxSAT (WPMS) is a well-known optimization variant of Boolean Satisfiability (SAT) that finds a wide range of practical applications. WPMS divides the formula in two sets of clauses: The hard clauses that must be satisfied and the soft clauses that can be falsified with a penalty given by their associated weight. However, some applications may require each original constraint to be modeled as a set or group of clauses. Then, the cost or penalty of falsifying one or several clauses of the same group is exactly the same. The resulting formalism is referred to as Group MaxSAT. This paper overviews Group MaxSAT, and shows how several optimization problems can be modeled as Group MaxSAT. Several encodings from Group MaxSAT to standard MaxSAT are formalized and refined. A comprehensive empirical study compares the performance of several MaxSAT solvers with the proposed encodings. The results indicate that, depending on the underlying MaxSAT solver and problem domain, the solver may perform better with a given encoding than with the others.