The strength of multi-row models

We develop a method for computing facet-defining valid inequalities for any mixed-integer set PJ . While our practical implementation does not return only facet-defining inequalities, it is able to find a separating cut whenever one exists. The separator is not comparable in speed with the specific cutting-plane generators used in branch-and-cut solvers, but it is general-purpose. We can thus use it to compute cuts derived from any reasonably small relaxation PJ of a general mixedinteger problem, even when there exists no specific implementation for computing cuts with PJ . Exploiting this, we evaluate, from a computational perspective, the usefulness of cuts derived from several types of multi-row relaxations. In particular, we present results with four different strengthenings of the two-row intersection cut model, and multi-row models with up to fifteen rows. We conclude that only fully-strengthened two-row cuts seem to offer a significant advantage over two-row intersecti...

• Type: Journal
• Year: 2015
• Where: MPC
• Authors: Quentin Louveaux, Laurent Poirrier, Domenico Salvagnin
• Keywords: Mathematics, MPC 2015