## Abstract

*Maximum Satisfiability* (MaxSAT) is an optimization version of SAT, and many real world applications can be naturally encoded as such. Solving MaxSAT is an important problem from both a theoretical and a practical point of view. In recent years, there has been considerable interest in developing efficient algorithms and several families of algorithms have been proposed. This paper overviews recent approaches to handle MaxSAT and presents a survey of MaxSAT algorithms based on iteratively calling a SAT solver which are particularly effective to solve problems arising in industrial settings. First, classic algorithms based on iteratively calling a SAT solver and updating a *bound* are overviewed. Such algorithms are referred to as *iterative* MaxSAT algorithms. Then, more sophisticated algorithms that additionally take advantage of *unsatisfiable cores* are described, which are referred to as *core-guided* MaxSAT algorithms. Core-guided MaxSAT algorithms use the information provided by unsatisfiable cores to *relax clauses on demand* and to create simpler constraints. Finally, a comprehensive empirical study on non-random benchmarks is conducted, including not only the surveyed algorithms, but also other state-of-the-art MaxSAT solvers. The results indicate that (i) core-guided MaxSAT algorithms in general abort in less instances than classic solvers based on iteratively calling a SAT solver and that (ii) core-guided MaxSAT algorithms are fairly competitive compared to other approaches.

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Morgado, A., Heras, F., Liffiton, M. *et al.* Iterative and core-guided MaxSAT solving: A survey and assessment.
*Constraints* **18**, 478–534 (2013). https://doi.org/10.1007/s10601-013-9146-2

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DOI: https://doi.org/10.1007/s10601-013-9146-2