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An implementation of exact knapsack separation

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Abstract

Cutting planes have been used with great success for solving mixed integer programs. In recent decades, many contributions have led to successive improvements in branch-and-cut methods which incorporate cutting planes in branch and bound algorithm. Using advances that have taken place over the years on 0–1 knapsack problem, we investigate an efficient approach for 0–1 programs with knapsack constraints as local structure. Our approach is based on an efficient implementation of knapsack separation problem which consists of the four phases: preprocessing, row generation, controlling numerical errors and sequential lifting. This approach can be used independently to improve formulations with cutting planes generated or incorporated in branch and cut to solve a problem. We show that this approach allows us to efficiently solve large-scale instances of generalized assignment problem, multilevel generalized assignment problem, capacitated \(p\)-median problem and capacitated network location problem to optimality.

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Notes

  1. http://www-01.ibm.com/software/integration/optimization/cplex-optimizer/.

  2. http://miplib.zib.de/.

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Acknowledgments

The authors wish to thank Alberto Ceselli, Marcus Posta for their codes and test instances and Pasquale Avella for helpful comments.

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Authors and Affiliations

  1. Institute for System Dynamics and Control Theory, Siberian Branch of Russian Academy of Sciences, Lermontov Srt., 134, 664033, Irkutsk, Russia

    Igor Vasilyev

  2. Dipartimento di Ingegneria, Università del Sannio, Viale Traiano, 82100, Benevento, Italy

    Maurizio Boccia

  3. LAMIH - UMR CNRS 8530, Le Mont Houy - ISTV2, University of Valenciennes, 59313, Valenciennes Cedex 9, France

    Saïd Hanafi

Authors
  1. Igor Vasilyev
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  2. Maurizio Boccia
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  3. Saïd Hanafi
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Correspondence to Igor Vasilyev.

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Vasilyev, I., Boccia, M. & Hanafi, S. An implementation of exact knapsack separation. J Glob Optim 66, 127–150 (2016). https://doi.org/10.1007/s10898-015-0294-3

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