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Multi-cover Inequalities for Totally-Ordered Multiple Knapsack Sets

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Integer Programming and Combinatorial Optimization (IPCO 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12707))

Abstract

We propose a method to generate cutting-planes from multiple covers of knapsack constraints. The covers may come from different knapsack inequalities if the weights in the inequalities form a totally-ordered set. Thus, we introduce and study the structure of a totally-ordered multiple knapsack set. The valid multi-cover inequalities we derive for its convex hull have a number of interesting properties. First, they generalize the well-known (1, k)-configuration inequalities. Second, they are not aggregation cuts. Third, they cannot be generated as a rank-1 Chvátal-Gomory cut from the inequality system consisting of the knapsack constraints and all their minimal covers. Finally, we provide conditions under which the inequalities are facet-defining for the convex hull of the totally-ordered knapsack set.

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Acknowledgements

A. Del Pia is partially funded by ONR grant N00014-19-1-2322. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the Office of Naval Research. J. Linderoth and H. Zhu are in part supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research (ASCR) under Contract DEAC02-06CH11347.

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Authors and Affiliations

  1. Department of Industrial and Systems Engineering, University of Wisconsin-Madison, Madison, USA

    Alberto Del Pia, Jeff Linderoth & Haoran Zhu

  2. Wisconsin Institute for Discovery, Madison, USA

    Alberto Del Pia & Jeff Linderoth

Authors
  1. Alberto Del Pia
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  2. Jeff Linderoth
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  3. Haoran Zhu
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Correspondence to Haoran Zhu .

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Editors and Affiliations

  1. Georgia Institute of Technology, Atlanta, GA, USA

    Mohit Singh

  2. Cornell University, Ithaca, NY, USA

    David P. Williamson

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Del Pia, A., Linderoth, J., Zhu, H. (2021). Multi-cover Inequalities for Totally-Ordered Multiple Knapsack Sets. In: Singh, M., Williamson, D.P. (eds) Integer Programming and Combinatorial Optimization. IPCO 2021. Lecture Notes in Computer Science(), vol 12707. Springer, Cham. https://doi.org/10.1007/978-3-030-73879-2_14

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  • DOI: https://doi.org/10.1007/978-3-030-73879-2_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-73878-5

  • Online ISBN: 978-3-030-73879-2

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