A Computational Status Update for Exact Rational Mixed Integer Programming

The last milestone achievement for the round-off-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 floating-point 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.

Automated summary

This study presents a significant advancement in solving general mixed integer programs over the rational numbers, achieving a substantial performance improvement. The new framework outperforms the original framework on the MIPLIB 2017 benchmark set, solving instances faster and more efficiently.