Cut Selection For Benders Decomposition

TL;DR

This paper introduces a novel cut selection method for Benders decomposition based on polyhedral relations, enhancing cut quality and supporting facet-defining properties, thereby advancing the state-of-the-art in Benders cut generation.

Contribution

It proposes a new framework for Benders cut selection that unifies and extends existing methods, including generating facet-defining cuts as a special case.

Findings

Modified cuts are always supporting and mostly facet-defining.

The framework encompasses existing methods like the Conforti-Wolsey approach.

Improved cut quality potentially enhances Benders decomposition efficiency.

Abstract

In this paper, we present a new perspective on cut generation in the context of Benders decomposition. The approach, which is based on the relation between the alternative polyhedron and the reverse polar set, helps us to improve established cut selection procedures for Benders cuts, like the one suggested by Fischetti, Salvagnin, and Zanette [FSZ10]. Our modified version of that criterion produces cuts which are always supporting and, unless in rare special cases, facet-defining. We discuss our approach in relation to the state of the art in cut generation for Benders decomposition. In particular, we refer to Pareto-optimality and facet-defining cuts and observe that each of these criteria can be matched to a particular subset of parameterizations for our cut generation framework. As a consequence, our framework includes the method to generate facet-defining cuts proposed by Conforti and Wolsey [CW18] as a special case.