# Deepest Cuts for Benders Decomposition

@inproceedings{Hosseini2021DeepestCF, title={Deepest Cuts for Benders Decomposition}, author={Mojtaba Hosseini and John G. Turner}, year={2021} }

Since its inception, Benders Decomposition (BD) has been successfully applied to a wide range of large-scale mixed-integer (linear) problems. The key element of BD is the derivation of Benders cuts, which are often not unique. In this paper, we introduce a novel unifying Benders cut selection technique based on a geometric interpretation of cut “depth”, produce deepest Benders cuts based on `p-norms, and study their properties. Specifically, we show that deepest cuts resolve infeasibility…

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An algorithmic strategy that utilizes a preemptively small perturbation of the right-hand-side of the Benders subproblem to generate maximal nondominated Benders cuts, as well as a complimentary strategy that generates an additional cut in each iteration via an alternative emphasis on decision variable weights are proposed.

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It is demonstrated that using split cuts within the cut-and-project framework can significantly improve the performance of Benders decomposition and yield stronger relaxations in general when using multiple split disjunctions.

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A successive projections algorithm onto the reverse polar is proposed that computes the decomposition of the deepest cut into facet-defining cuts, which are deep in a well-defined geometrical sense, and facet- Defining cuts.

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