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Verifying integer programming results. (English) Zbl 1418.90176
Eisenbrand, Friedrich (ed.) et al., Integer programming and combinatorial optimization. 19th international conference, IPCO 2017, Waterloo, ON, Canada, June 26–28, 2017. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 10328, 148-160 (2017).
Summary: Software for mixed integer linear programming can return incorrect results for a number of reasons, one being the use of inexact floating-point arithmetic. Even solvers that employ exact arithmetic may suffer from programming or algorithmic errors, motivating the desire for a way to produce independently verifiable certificates of claimed results. Due to the complex nature of state-of-the-art MIP solution algorithms, the ideal form of such a certificate is not entirely clear. This paper proposes such a certificate format designed with simplicity in mind, which is composed of a list of statements that can be sequentially verified using a limited number of inference rules. We present a supplementary verification tool for compressing and checking these certificates independently of how they were created. We report computational results on a selection of MIP instances from the literature. To this end, we have extended the exact rational version of the MIP solver SCIP to produce such certificates.
For the entire collection see [Zbl 1364.90010].

90C11 Mixed integer programming
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