On Using Unsatisfiability for Solving Maximum Satisfiability

TL;DR

This paper analyzes and improves unsatisfiability-based MaxSAT algorithms, introducing key optimizations and a new algorithm that significantly enhance performance on practical instances by leveraging modern SAT solver capabilities.

Contribution

It provides a detailed analysis of existing algorithms, proposes optimizations, and introduces a new algorithm that outperforms previous methods on real-world MaxSAT problems.

Findings

Significant performance improvements on practical MaxSAT instances

Optimizations enhance scalability of unsatisfiability-based MaxSAT algorithms

Efficiency depends on modern SAT solvers' ability to prove unsatisfiability

Abstract

Maximum Satisfiability (MaxSAT) is a well-known optimization pro- blem, with several practical applications. The most widely known MAXS AT algorithms are ineffective at solving hard problems instances from practical application domains. Recent work proposed using efficient Boolean Satisfiability (SAT) solvers for solving the MaxSAT problem, based on identifying and eliminating unsatisfiable subformulas. However, these algorithms do not scale in practice. This paper analyzes existing MaxSAT algorithms based on unsatisfiable subformula identification. Moreover, the paper proposes a number of key optimizations to these MaxSAT algorithms and a new alternative algorithm. The proposed optimizations and the new algorithm provide significant performance improvements on MaxSAT instances from practical applications. Moreover, the efficiency of the new generation of unsatisfiability-based MaxSAT solvers becomes effectively indexed to the ability of modern SAT solvers to proving unsatisfiability and identifying unsatisfiable subformulas.