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Reducing the complexity of the knapsack linear integer problem by reformulation techniques

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Listed:
  • Elias Munapo

    (North West University)

  • Santosh Kumar

    (RMIT University
    University of Melbourne)

Abstract

The paper presents reformulation techniques to reduce the complexity of a knapsack linear integer problem. Reformulation significantly reduces the number of standard branch and bound sub-problems required to verify optimality. Computational results of the various technique are given to compare the number of branch and bound iterations on some selected knapsack linear integer problems before and after the reformulation.

Suggested Citation

  • Elias Munapo & Santosh Kumar, 2021. "Reducing the complexity of the knapsack linear integer problem by reformulation techniques," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 12(6), pages 1087-1093, December.
    • Handle: RePEc:spr:ijsaem:v:12:y:2021:i:6:d:10.1007_s13198-021-01232-6
    DOI: 10.1007/s13198-021-01232-6
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    References listed on IDEAS

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    1. Simon, Jay & Apte, Aruna & Regnier, Eva, 2017. "An application of the multiple knapsack problem: The self-sufficient marine," European Journal of Operational Research, Elsevier, vol. 256(3), pages 868-876.
    2. Fampa, M. & Lubke, D. & Wang, F. & Wolkowicz, H., 2020. "Parametric convex quadratic relaxation of the quadratic knapsack problem," European Journal of Operational Research, Elsevier, vol. 281(1), pages 36-49.
    3. Wu, Zhengtian & Jiang, Baoping & Karimi, Hamid Reza, 2020. "A logarithmic descent direction algorithm for the quadratic knapsack problem," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    4. Cynthia Barnhart & Christopher A. Hane & Pamela H. Vance, 2000. "Using Branch-and-Price-and-Cut to Solve Origin-Destination Integer Multicommodity Flow Problems," Operations Research, INFORMS, vol. 48(2), pages 318-326, April.
    5. Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser & Martin W. P. Savelsbergh & Pamela H. Vance, 1998. "Branch-and-Price: Column Generation for Solving Huge Integer Programs," Operations Research, INFORMS, vol. 46(3), pages 316-329, June.
    6. Martello, Silvano & Monaci, Michele, 2020. "Algorithmic approaches to the multiple knapsack assignment problem," Omega, Elsevier, vol. 90(C).
    7. Elias Munapo, 2019. "The equal tendency algorithm: a new heuristic for the reliability model," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(5), pages 918-924, October.
    8. Zouache, Djaafar & Moussaoui, Abdelouahab & Ben Abdelaziz, Fouad, 2018. "A cooperative swarm intelligence algorithm for multi-objective discrete optimization with application to the knapsack problem," European Journal of Operational Research, Elsevier, vol. 264(1), pages 74-88.
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    Cited by:

    1. Elias Munapo & Joshua Chukwuere & Trust Tawanda, 2023. "Solving Linear Integer Models with Variable Bounding," Forecasting, MDPI, vol. 5(2), pages 1-10, May.

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