Maximum Satisfiability

Maximum Satisfiability extends SAT from deciding whether all Boolean constraints can hold to finding an assignment that satisfies the largest number or total weight of clauses, often while preserving hard constraints. Solvers use branch-and-bound and SAT-based core-guided methods, alongside local search and reductions that encode other optimization problems as weighted MaxSAT. These methods support scheduling and configuration as well as structured reasoning and explanations, and are tested on crafted and industrial benchmark instances. A central challenge is balancing scalability with proof of optimality: the strongest solver family can depend on the problem’s structure and encoding.