A Computational Status Update for Exact Rational Mixed Integer Programming

TL;DR

This paper presents a significantly improved exact rational mixed integer programming algorithm that integrates symbolic presolving, solution repair, and a faster LP solver, achieving substantial speedups and more solved instances.

Contribution

It introduces a revised framework for exact rational MIP solving with new algorithmic components and demonstrates improved performance on benchmark sets.

Findings

Average speedup of 6.6x over previous framework

Solved 2.8 times more instances within two hours

Enhanced algorithmic components lead to better computational behavior

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.