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Approximate solutions to the multiple-choice knapsack problem by multiobjectivization and Chebyshev scalarization

Author

Listed:
  • Ewa M. Bednarczuk
  • Ignacy Kaliszewski
  • Janusz Miroforidis

Abstract

The method BISSA, proposed by Bednarczuk, Miroforidis, and Pyzel, provides approximate solutions to the multiple-choice knapsack problem. To fathom the optimality gap that is left by BISSA, we present a method that starts from the BISSA16 solution and it is able to provide a better approximation and in consequence a tighter optimality gap. Like BISSA, the new method is based on the multiobjectivization of the multiple-choice knapsack problem but instead of the linear scalarization used in BISSA, it makes use of the Chebyshev scalarization. We validate the new method on the same set of problems as the one used to validate BISSA.

Suggested Citation

  • Ewa M. Bednarczuk & Ignacy Kaliszewski & Janusz Miroforidis, 2024. "Approximate solutions to the multiple-choice knapsack problem by multiobjectivization and Chebyshev scalarization," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 34(4), pages 53-66.
    • Handle: RePEc:wut:journl:v:34:y:2024:i:4:p:53-66:id:3
    DOI: 10.37190/ord240403
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    References listed on IDEAS

    as
    1. Ignacy Kaliszewski, 2006. "Soft Computing For Complex Multiple Criteria Decision Making," International Series in Operations Research and Management Science, Springer, number 978-0-387-30177-8, July-Dece.
    2. Ignacy Kaliszewski & Janusz Miroforidis & Dmitry Podkopaev, 2016. "Multiple Criteria Decision Making by Multiobjective Optimization," International Series in Operations Research and Management Science, Springer, number 978-3-319-32756-3, July-Dece.
    3. Ewa M. Bednarczuk & Janusz Miroforidis & Przemysław Pyzel, 2018. "A multi-criteria approach to approximate solution of multiple-choice knapsack problem," Computational Optimization and Applications, Springer, vol. 70(3), pages 889-910, July.
    4. Matthias Ehrgott, 2005. "Multicriteria Optimization," Springer Books, Springer, edition 0, number 978-3-540-27659-3, March.
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