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Title of Journal: Math Program

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Abbravation: Mathematical Programming

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Springer Berlin Heidelberg

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DOI

10.1016/j.ab.2014.02.015

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1436-4646

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Using cuts for mixed integer knapsack sets to gene

Authors: Sujeevraja Sanjeevi Sina Masihabadi Kiavash Kianfar
Publish Date: 2015/10/30
Volume: 159, Issue: 1-2, Pages: 571-583
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Abstract

Based on a bijective mapping between two mixed integer sets we introduce a new perspective on developing cuts for the mixed integer polyhedral conic MIPC set by establishing a onetoone correspondence between the cuts for this set and those for a related mixed integer knapsack MIK set The face/facetdefining properties of the corresponding cuts are identical for their respective sets We further show that the cut generation approach for the MIPC set resulting from this new perspective always produces cuts that dominate those generated based on any of the two individual MIK constraints corresponding to the MIPC constraint Our computational results show this dominance can be quite significant As a special case of this new perspective the conic MIR inequality of Atamtürk  and Narayanan for the MIPC set and its properties can be directly derived from the MIR inequality for the MIK set and its properties We also generalize these cuts to the nstep conic MIR inequalities which are directly derived form the nstep MIR inequalities for the MIK set

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