The Knapsack Problem and Its Variants: Formulations and Solution Methods

Christophe Wilbaut (), Saïd Hanafi (), Igor Machado Coelho () and Abilio Lucena ()
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Christophe Wilbaut: University Polytechnique Hauts-de-France
Saïd Hanafi: University Polytechnique Hauts-de-France
Igor Machado Coelho: Universidade do Estado do Rio de Janeiro
Abilio Lucena: Programa de Engenharia de Sistemas e Computação, Universidade Federal do Rio de Janeiro

Chapter Chapter 4 in The Palgrave Handbook of Operations Research, 2022, pp 105-151 from Springer

Abstract: 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.

Date: 2022
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DOI: 10.1007/978-3-030-96935-6_4

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