Abstract
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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Acknowledgements
The work for this article has been partly conducted within the Research Campus Modal funded by the German Federal Ministry of Education and Research (fund number 05M14ZAM). The support of Lehigh University is also gratefully acknowledged.
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Miltenberger, M., Ralphs, T., Steffy, D.E. (2018). Exploring the Numerics of Branch-and-Cut for Mixed Integer Linear Optimization. In: Kliewer, N., Ehmke, J., Borndörfer, R. (eds) Operations Research Proceedings 2017. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-89920-6_21
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DOI: https://doi.org/10.1007/978-3-319-89920-6_21
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