Optimization Modulo Non-linear Arithmetic via Incremental Linearization

Abstract

Incremental linearization is a conceptually simple, yet effective, technique that we have recently proposed for solving SMT problems on the theories of non-linear arithmetic over the reals and the integers. Optimization Modulo Theories (OMT) is an important extension of SMT which allows for finding models that optimize given objective functions. In this paper, we show how incremental linearization can be extended to OMT in a simple way, producing an incomplete though effective OMT procedure. We describe the main ideas and algorithms, we provide an implementation within the OptiMathSAT OMT solver, and perform an empirical evaluation. The results support the effectiveness of the approach.

OMTPlan: A Tool for Optimal Planning Modulo Theories

“…We discussed the internal work-flow of OMTPlan and explained its main functionalities. Notably, OMTPlan can be used to convert PDDL problems into SMT-LIB format, thus enabling fruitful interactions between the planning and SMT/OMT communities [3]. We reported numeric experiments that demonstrate the capabilities of OMTPlan.…”

“…• benchmarking: benchmarks developed by the planning community can be used to test OMT solvers, as done, e.g. in [3].…”

“…The current implementation of OMTPlan relies on Z3/νZ [4] to construct and solve planning formulas. 3 However other OMT solvers could be used for the latter step via a compilation to SMT-LIB.…”

“…Besides offering solving capabilities, OMTPlan can also act as a translator from PDDL [5], the standard language of planning, to SMT-LIB [1] thus providing a new source of challenging benchmarks for the automated reasoning community -see, e.g. [3] for such an application of the tool. The planner is open-sourced under a GNU General Public License, version 3 (GPL-3.0).…”