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.

Additional Metadata
Keywords Certificate, Correctness, Infeasibility, Mixed-integer linear programming, Optimality, Proof, Verification
Persistent URL dx.doi.org/10.1007/978-3-319-59250-3_13
Series Lecture Notes in Computer Science
Citation
Cheung, K, Gleixner, A. (Ambros), & Steffy, D.E. (Daniel E.). (2017). Verifying integer programming results. In Lecture Notes in Computer Science. doi:10.1007/978-3-319-59250-3_13