Maximum Satisfiability (MaxSAT) is an optimization variant of the Boolean Satisfiability (SAT) problem. In general, MaxSAT algorithms perform a succession of SAT solver calls to reach an optimum solution making extensive use of cardinality constraints. Many of these algorithms are non-incremental in nature, i.e. at each iteration the formula is rebuilt and no knowledge is reused from one iteration to another. In this paper, we exploit the knowledge acquired across iterations using novel schemes to use cardinality constraints in an incremental fashion. We integrate these schemes with several MaxSAT algorithms. Our experimental results show a significant performance boost for these algo- rithms as compared to their non-incremental counterparts. These results suggest that incremental cardinality constraints could be beneficial for other constraint solving domains.
Core-guided algorithms proved to be effective on industrial instances of MaxSAT, the optimization variant of the satisfiability problem for propositional formulas. These algorithms work by iteratively checking satisfiability of a formula that is relaxed at each step by using the information provided by unsatisfiable cores. The paper introduces a new core-guided algorithm that adds cardinality constraints for each detected core, but also limits the number of literals in each constraint in order to control the number of refutations in subsequent satisfiability checks. The performance gain of the new algorithm is assessed on the industrial instances of the 2014 MaxSAT Evaluation.
We propose a new approach that exploits the good properties of core-guided and model-guided MaxSAT solvers. In particular, we show how to effectively exploit the structure of unsatisfiable cores in MaxSAT instances. Experimental results on industrial instances show that the proposed approach outperforms both complete and incomplete state-of-the-art MaxSAT solvers at the last international MaxSAT Evaluation in terms of robustness and total number of solved instances.
Incomplete MaxSAT solving aims to quickly find a solution that attempts to minimize the sum of the weights of the unsatisfied soft clauses without providing any optimality guarantees. In this paper, we propose two approximation strategies for improving incomplete MaxSAT solving. In one of the strategies, we cluster the weights and approximate them with a representative weight. In another strategy, we break up the problem of minimizing the sum of weights of unsatisfiable clauses into multiple minimization subproblems. Experimental results show that approximation strategies can be used to find better solutions than the best incomplete solvers in the MaxSAT Evaluation 2017.
Pseudo-Boolean constraints, also known as 0-1 Integer Linear Constraints, are used to model many real-world problems. A common approach to solve these constraints is to encode them into a SAT formula. The runtime of the SAT solver on such formula is sensitive to the manner in which the given pseudo-Boolean constraints are encoded. In this paper, we propose generalized Totalizer encoding (GTE), which is an arc-consistency preserving extension of the Totalizer encoding to pseudo-Boolean constraints. Unlike some other encodings, the number of auxiliary variables required for GTE does not depend on the magnitudes of the coefficients. Instead, it depends on the number of distinct combinations of these coefficients. We show the superiority of GTE with respect to other encodings when large pseudo-Boolean constraints have low number of distinct coefficients. Our experimental results also show that GTE remains competitive even when the pseudo-Boolean constraints do not have this characteristic.