Exploring the Numerics of Branch-and-Cut for Mixed Integer Linear Optimization

  • We investigate how the numerical properties of the LP relaxations evolve throughout the solution procedure in a solver employing the branch-and-cut algorithm. The long-term goal of this work is to determine whether the effect on the numerical conditioning of the LP relaxations resulting from the branching and cutting operations can be effectively predicted and whether such predictions can be used to make better algorithmic choices. In a first step towards this goal, we discuss here the numerical behavior of an existing solver in order to determine whether our intuitive understanding of this behavior is correct.

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Author:Matthias MiltenbergerORCiD, Ted Ralphs, Daniel Steffy
Document Type:In Proceedings
Parent Title (English):Operations Research Proceedings 2017
First Page:151
Last Page:157
Publisher:Springer International Publishing
Year of first publication:2018
Published in:Operations Research Proceedings 2017