Learning Nobetter Clauses in Max-SAT Branch and Bound Solvers

Branch and Bound solvers for Max-SAT are very efficient on random and some crafted instances, as shown in the recent Max-SAT Evaluation results. However, on structured instances (particularly on the ones issued from industrial applications), they are significantly outperformed by other types of Max-SAT solvers. In the SAT context, CDLC solvers perform very well on industrial instances. One of the main reasons of this efficiency is the learning mechanism of nogood clauses, which has been introduced more than fifteen years ago. It allows solvers to learn from their failure with a twofold objective: limit redundancies and lead the exploration to the most promising areas of the search space. We propose in this paper a similar mechanism, which we call nobetter clause learning, adapted to BnB Max-SAT solvers. The results we have obtained show gains on industrial instances. These results call for more work in this direction, to further improve the quality of the information learned and make a better exploitation of them.