## Verifying Integer Programming Results

Please always quote using this URN: urn:nbn:de:0297-zib-61044
• 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 MILP solution algorithms, the ideal form of such a certificate is not entirely clear. This paper proposes such a certificate format, illustrating its capabilities and structure through examples. The certificate format is designed with simplicity in mind and is composed of a list of statements that can be sequentially verified using a limited number of simple yet powerful 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 mixed-integer linear programming instances from the literature. To this end, we have extended the exact rational version of the MIP solver SCIP to produce such certificates.

Author: Kevin K. H. Cheung, Ambros Gleixner, Daniel E. Steffy ZIB-Report correctness, verification, proof, certificate, optimality, infeasibility, mixed-integer linear programming 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C11 Mixed integer programming 2016/11/20 ZIB-Report (16-58) 1438-0064

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