With stochastic integer programming as the motivating application, we investigate techniques to use integrality information to obtain improved cuts within a Benders decomposition algorithm. We consider two options: (i) cut-and-project, where integrality information is 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 information is used to derive cuts directly in the projected space defined by Benders cuts. We analyze the use of split cuts in these two approaches, and demonstrate that although they yield equivalent relaxations when considering a single split, cut-and-project yields stronger relaxations in general when using multiple splits. Computational results illustrate that the difference can be very large, and demonstrate that using split cuts within the cut-and-project framework can significantly outperform other general purpose methods.
By: Merve Bodur, Sanjeeb Dash, Oktay Günlük, James Luedtke
Published in: RC25427 in 2013
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