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Strengthened Benders Cuts for Stochastic Integer Programs with Continuous Recourse

Merve Bodur (mbodur***at***wisc.edu)
Sanjeeb Dash (sanjeebd***at***us.ibm.com)
Oktay Gunluk (gunluk***at***us.ibm.com)
James Luedtke (jrluedt1***at***wisc.edu)

Abstract: With stochastic integer programming as the motivating application, we investigate techniques to use integrality constraints to obtain improved cuts within a Benders decomposition algorithm. We compare the effect of using cuts in two ways: (i) cut-and-project, where integrality constraints are used to derive cuts in the extended variable space, and Benders cuts are then used to project the resulting improved relaxation, and (ii) project-and-cut, where integrality constraints are used to derive cuts directly in the Benders reformulation. For the case of split cuts, we demonstrate that although these approaches yield equivalent relaxations when considering a single split disjunction, cut-and-project yields stronger relaxations in general when using multiple split disjunctions. Computational results illustrate that the difference can be very large, and demonstrate that using split cuts within the cut-and-project framework can significantly improve the performance of Benders decomposition.

Keywords: Two-stage stochastic integer programs, Benders decomposition, Split cuts

Category 1: Stochastic Programming

Category 2: Integer Programming (Cutting Plane Approaches )

Category 3: Integer Programming ((Mixed) Integer Linear Programming )

Citation: University of Wisconsin-Madison, IBM Research, March, 2014.

Download: [PDF]

Entry Submitted: 03/02/2014
Entry Accepted: 03/02/2014
Entry Last Modified: 04/10/2017

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