On Optimization Modulo Theories, MaxSMT and Sorting Networks

Abstract: Optimization Modulo Theories (OMT) is an extension of SMT which allows for finding models that optimize given objectives. (Partial weighted) MaxSMT --or equivalently OMT with Pseudo-Boolean objective functions, OMT+PB-- is a very-relevant strict subcase of OMT. We classify existing approaches for MaxSMT or OMT+PB in two groups: MaxSAT-based approaches exploit the efficiency of state-of-the-art MAXSAT solvers, but they are specific-purpose and not always applicable; OMT-based approaches are general-purpose, but they suffer from intrinsic inefficiencies on MaxSMT/OMT+PB problems. We identify a major source of such inefficiencies, and we address it by enhancing OMT by means of bidirectional sorting networks. We implemented this idea on top of the OptiMathSAT OMT solver. We run an extensive empirical evaluation on a variety of problems, comparing MaxSAT-based and OMT-based techniques, with and without sorting networks, implemented on top of OptiMathSAT and {\nu}Z. The results support the effectiveness of this idea, and provide interesting insights about the different approaches.