Abstract
AbstractIn 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 et al. (Math Program Ser B 124(1–2):175–182, 2010). 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 parametrizations for our cut generation framework. As a consequence, our framework covers the method to generate facet-defining cuts proposed by Conforti and Wolsey (Math Program Ser A 178:1–20, 2018) as a special case. We conclude the paper with a computational evaluation of the proposed cut selection method. For this, we use different instances of a capacity expansion problem for the european power system.
Funder
Bundesministerium für Wirtschaft und Energie
TUM International Graduate School of Science and Engineering
Technische Universität München
Publisher
Springer Science and Business Media LLC
Subject
Management Science and Operations Research,General Mathematics,Software
Cited by
4 articles.
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