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Verifying Integer Programming Results

Kevin K.H. Cheung (kevin.cheung***at***carleton.ca)
Ambros Gleixner (gleixner***at***zib.de)
Daniel E. Steffy (steffy***at***oakland.edu)

Abstract: 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.

Keywords: correctness, verification, proof, certificate, optimality, infeasibility, mixed-integer linear programming

Category 1: Integer Programming ((Mixed) Integer Linear Programming )

Citation: ZIB-Report 16-58, Zuse Institute Berlin, Takustr. 7, 14195 Berlin, November 2016

Download: [PDF]

Entry Submitted: 11/24/2016
Entry Accepted: 11/24/2016
Entry Last Modified: 01/01/2019

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