Local Max-Resolution in Branch and Bound Solvers for Max-SAT

Abstract

One of the most critical components of Branch & Bound (BnB) solvers for Max-SAT is the estimation of the lower bound. At each node of the search tree, they detect inconsistent subsets (IS) of the formula by unit propagation based methods and apply a treatment on them. Depending on the structure of the IS, current best performing BnB solvers transform them by several max-resolution steps and keep the changes in the sub-part of the sub tree or simply remove the clauses of these subsets from the formula and restore them before the next decision. The formula obtained after this last treatment is not equivalent to the original one and the number of detectable remaining inconsistencies may be reduced. In this paper, instead of applying such a removal, we propose to fully exploit all the inconsistent subsets by applying the well-known max-resolution inference rule to transform them locally in the current node of the search tree. The expected benefits of this transformation are an accurate lower bound estimation and the reduction of the number of decisions needed to solve an instance. We show experimentally the interest of our approach on weighted and unweighted Max-SAT instances and discuss the obtained results.