Using Learnt Clauses in maxsat

Abstract

MAXSAT is an optimization version of SAT capable of expressing a variety of practical problems. MAXSAT solvers have been designed to take advantage of many of the successful techniques of SAT solvers. However, the most important technique of modern SAT solvers, clause learning, has not been utilized since learnt clauses cannot be soundly added to a MAXSAT theory. In this paper we present a new method that allows SAT clause learning to be exploited in a MAXSAT solver without losing soundness. We present techniques for learning clauses during a branch and bound (B&B) MAXSAT search, a process that is more complicated than standard clause learning. To exploit these learnt clauses we develop a connection between them and bounds that can be used during B&B. This connection involves formulating a hitting set problem and finding bounds on its optimal solution. We present some new techniques for generating useful hitting set bounds and also show how linear and integer programs can be exploited for this purpose, opening the door for a hybrid approach to solving MAXSAT.