Number Of Unsatisfied Clauses Research Articles

CHAMP: A multipass algorithm for Max Sat based on saver variables

In this paper, we introduce the concept of saver variables in Max Sat and demonstrate their contribution to the performance of solvers for this problem. We present two types of saver variables: high-rank savers and consensual savers. We show how to incorporate them in various ways into an iterated algorithm, CHAMP, for Max Sat. We conduct an extensive empirical evaluation on two collections of instances — instances from a past Max Sat competition and random instances. It turns out that, by using savers, the number of unsatisfied clauses may be reduced by more than 70% in some families. Moreover, a refined version CHAMP＋ of CHAMP improves the results even further. We show that by combining CHAMP＋ with CCLS, a state-of-the-art solver, we obtain better solutions for many Max Sat instances.

A Two-Phase Exact Algorithm for MAX-SAT and Weighted MAX-SAT Problems

We describe a two-phase algorithm for MAX-SAT and weighted MAX-SAT problems. In the first phase, we use the GSAT heuristic to find a good solution to the problem. In the second phase, we use an enumeration procedure based on the Davis-Putnam-Loveland algorithm, to find a provably optimal solution. The first heuristic stage improves the performance of the algorithm by obtaining an upper bound on the minimum number of unsatisfied clauses that can be used in pruning branches of the search tree. We compare our algorithm with an integer programming branch-and-cut algorithm. Our implementation of the two-phase algorithm is faster than the integer programming approach on many problems. However, the integer programming approach is more effective than the two-phase algorithm on some classes of problems, including MAX-2-SAT problems.