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OptiMathSAT: A Tool for Optimization Modulo Theories

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Abstract

Optimization Modulo Theories (\(\text {OMT}\)) is an extension of SMT which allows for finding models that optimize given objectives. OptiMathSAT is an OMT solver which allows for solving a list of optimization problems on SMT formulas with linear objective functions—on the Boolean, the rational and the integer domains, and on their combination thereof—including (partial weighted) MaxSMT . Multiple and heterogeneous objective functions can be combined together and handled either independently, or lexicographically, or in linear or min–max /max–min combinations. OptiMathSAT provides an incremental interface, it supports both an extended version of the SMT-LIBv2 language and a subset of the FlatZinc language, and can be interfaced via an API. In this paper we describe OptiMathSAT and its usage in full detail.

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Notes

  1. In the famous Zeno’s paradox, Achilles never reaches the tortoise for a similar reason.

  2. This observation is empirical and based on our experience with \(\text {OMT}\) (\(\mathcal {LIRA}\)) (see, e.g., [70, 71, 73]).

  3. As in [31], by “continuous relaxation”—henceforth simply “relaxation”—we mean that the integrality constraints on the integer variables are relaxed, so that they can take fractional values.

  4. Notice that the Linear, Max–Min and Min–Max combinations of objectives are handled instead by the Optimization Context block because this consists in a simple encoding, see Sect. 2.5.

  5. This is a purely syntactic sugar extension for easiness of use.

  6. Notice that SMT-LIBv2 makes available the define-fun command, which can be used to achieve similar goals. The “id” attribute was introduced over arbitrary objectives for consistency with the case of MaxSMT/PB goals defined with assert-soft. It also makes it simpler to identify objectives recombination at the implementation level, which may allow for introducing new techniques exploiting this knowledge in the future.

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    Roberto Sebastiani & Patrick Trentin

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This paper describes OptiMathSAT 1.4.2, which is the latest version available when it was submitted.

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Sebastiani, R., Trentin, P. OptiMathSAT: A Tool for Optimization Modulo Theories. J Autom Reasoning 64, 423–460 (2020). https://doi.org/10.1007/s10817-018-09508-6

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