Verifying Integer Programming Results

  • 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.

Export metadata

Additional Services

Share in Twitter Search Google Scholar
Author:Kevin K. H. Cheung, Ambros GleixnerORCiD, Daniel E. Steffy
Document Type:In Proceedings
Parent Title (English):F. Eisenbrand and J. Koenemann, eds., Integer Programming and Combinatorial Optimization: 19th International Conference, IPCO 2017
First Page:148
Last Page:160
Year of first publication:2017