A probabilistic comparison of the strength of split, triangle, and quadrilateral cuts (extended version)
Optimization and Control
2011-02-04 v2
Abstract
We consider mixed integer linear sets defined by two equations involving two integer variables and any number of non-negative continuous variables. The non-trivial valid inequalities of such sets can be classified into split, type 1, type 2, type 3, and quadrilateral inequalities. We use a strength measure of Goemans to analyze the benefit from adding a non-split inequality on top of the split closure. Applying a probabilistic model, we show that the importance of a type 2 inequality decreases with decreasing lattice width, on average. Our results suggest that this is also true for type 3 and quadrilateral inequalities.
Keywords
Cite
@article{arxiv.1009.5253,
title = {A probabilistic comparison of the strength of split, triangle, and quadrilateral cuts (extended version)},
author = {Alberto Del Pia and Christian Wagner and Robert Weismantel},
journal= {arXiv preprint arXiv:1009.5253},
year = {2011}
}