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The Knapsack Problem and Its Variants: Formulations and Solution Methods

In: The Palgrave Handbook of Operations Research

Author

Listed:
  • Christophe Wilbaut

    (University Polytechnique Hauts-de-France
    INSA Hauts-de-France)

  • Saïd Hanafi

    (University Polytechnique Hauts-de-France
    INSA Hauts-de-France)

  • Igor Machado Coelho

    (Universidade do Estado do Rio de Janeiro
    Universidade Federal Fluminense)

  • Abilio Lucena

    (Programa de Engenharia de Sistemas e Computação, Universidade Federal do Rio de Janeiro)

Abstract

The Knapsack Problem is among the most well-known and widely studied optimization problems. Given a set of items, each item with an associated weight, the problem asks for a subset of items with a total weight no larger than an available capacity and which maximizes a corresponding measure of profit. The problem appears in distinct versions and also in accompanying variants to these versions, each version being defined by a different type of objective function. Every variant, in turn, imposes some additional requirements on item selection. In this chapter we review a subset of these variants, with a focus on recent papers that bring interesting new applications for the problem.

Suggested Citation

  • Christophe Wilbaut & Saïd Hanafi & Igor Machado Coelho & Abilio Lucena, 2022. "The Knapsack Problem and Its Variants: Formulations and Solution Methods," Springer Books, in: Saïd Salhi & John Boylan (ed.), The Palgrave Handbook of Operations Research, chapter 0, pages 105-151, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-96935-6_4
    DOI: 10.1007/978-3-030-96935-6_4
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