Computing Equivalent Transformations for Combinatorial Optimization by Branch-and-Bound Search

Abstract

Branch-and-Bound search is a basic algorithm for solving combinatorial optimization problems. Here we introduce a new lower-bounding methodology that can be incorporated into any branch-and-bound solver, and demonstraint its use on the MaxSAT constraint optimization problem. The approach is to adapt a “minimum-height equivalent transformation” framework that was first developed in the context of computer vision. We present efficient algorithms to realize this framework within the MaxSAT domain, and demonstrate their feasibility by implementing them within the state-of-the-art maxsatz solver. We evaluate the solver on test sets from the 2009 MaxSAT competition; we observe a basic performance tradeoff whereby the (quadratic) time cost of computing the transformations may or may not be worthwhile in exchange for better bounds and more frequent pruning. For specific test sets, the trade-off does result in significant improvement in both prunings and overall run-time.