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A Computational Status Update for Exact Rational Mixed Integer Programming

Leon Eifler (eifler***at***zib.de)
Ambros Gleixner (gleixner***at***zib.de)

Abstract: The last milestone achievement for the roundoff-error-free solution of general mixed integer programs over the rational numbers was a hybrid-precision branch-and-bound algorithm published by Cook, Koch, Steffy, and Wolter in 2013. We describe a substantial revision and extension of this framework that integrates symbolic presolving, features an exact repair step for solutions from primal heuristics, employs a faster rational LP solver based on LP iterative refinement, and is able to produce independently verifiable certificates of optimality. We study the significantly improved performance and give insights into the computational behavior of the new algorithmic components. On the MIPLIB 2017 benchmark set, we observe an average speedup of 6.6x over the original framework and 2.8 times as many instances solved within a time limit of two hours.

Keywords: Mixed integer programming, exact computation, rational arithmetic, symbolic computations, correctness, certificate

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

Citation: ZR-21-04, Zuse Institute Berlin, Takustr. 7, 14195 Berlin, Germany, January/2021

Download: [PDF]

Entry Submitted: 01/22/2021
Entry Accepted: 01/22/2021
Entry Last Modified: 01/22/2021

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