From MiniZinc to Optimization Modulo Theories, and Back (Extended Version)

Optimization Modulo Theories (OMT) is an extension of SMT that allows for finding models that optimize objective functions. In this paper we aim at bridging the gap between Constraint Programming (CP) and OMT, in both directions. First, we have extended the OMT solver OptiMathSAT with a FlatZinc interface -- which can also be used as a FlatZinc-to-OMT encoder for other OMT solvers. This allows OMT tools to be used in combination with mzn2fzn on the large amount of CP problems coming from the MiniZinc community. Second, we have introduced a tool for translating SMT and OMT problems on the linear arithmetic and bit-vector theories into MiniZinc. This allows MiniZinc solvers to be used on a large amount of SMT/OMT problems. We have discussed the main issues we had to cope with in either directions. We have performed an extensive empirical evaluation comparing three state-of-the-art OMT-based tools with many state-of-the-art CP tools on (i) CP problems coming from the MiniZinc challenge, and (ii) OMT problems coming mostly from formal verification. This analysis also allowed us to identify some criticalities, in terms of efficiency and correctness, one has to cope with when addressing CP problems with OMT tools, and vice versa.