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The Strength of Multi-row Aggregation Cuts for Sign-pattern Integer Programs

Santanu S. Dey(santanu.dey***at***isye.gatech.edu)
Andres Iroume(airoume.gatech***at***gmail.com)
Guanyi Wang(gwang93***at***gatech.edu)

Abstract: In this paper, we study the strength of aggregation cuts for sign-pattern integer programs (IPs). Sign-pattern IPs are a generalization of packing IPs and are of the form {x \in Z^n | Ax <=b, x >= 0} where for a given column j, A_{ij} is either non-negative for all i or non-positive for all i. Our first result is that the aggregation closure for such sign-pattern IPs can be 2-approximated by the original 1-row closure. This generalizes a result for packing IPs. On the other hand, unlike in the case of packing IPs, we show that the multi-row aggregation closure cannot be well approximated by the original multi-row closure. Therefore for these classes of integer programs general aggregated multi-row cutting planes can perform significantly better than just looking at cuts from multiple original constraints.

Keywords: Cutting-plane, Aggregation, Multi-row cuts

Category 1: Integer Programming (Cutting Plane Approaches )

Citation:

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Entry Submitted: 11/18/2017
Entry Accepted: 11/19/2017
Entry Last Modified: 11/18/2017

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