The quadratic knapsack problem

The quadratic knapsack problem is a relevant NP-hard combinatorial optimization problem, inspired, since the Seventies, by a number of real-world applications. After its formal definition in 1980, it was subject to intensive research, especially in the last two decades. No recent review on this prob...

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Bibliographic Details
Published inEuropean journal of operational research Vol. 326; no. 1; pp. 1 - 12
Main Authors Galli, Laura, Martello, Silvano, Toth, Paolo
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.10.2025
Subjects
Approximation
Computational results
Exact solution
Heuristics
Linearization
Metaheuristics
Quadratic knapsack problem
Upper bounds
Approximation
Upper bounds
Metaheuristics
Computational results
Heuristics
Quadratic knapsack problem
Linearization
Exact solution
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Summary:The quadratic knapsack problem is a relevant NP-hard combinatorial optimization problem, inspired, since the Seventies, by a number of real-world applications. After its formal definition in 1980, it was subject to intensive research, especially in the last two decades. No recent review on this problem appeared in the literature after a well-known survey, published in 2007 but updated to 2003. The purpose of this work is to provide a thorough overview of classical and recent results on the quadratic knapsack problem. We examine mathematical models, linearizations and reformulations. We review upper bounds, exact algorithms, heuristic and metaheuristic approaches, and provide a comparison of their computational performance. •Linearizations.•Upper bounds.•Exact algorithms.•Approximation algorithms and Heuristics.•Computational results.
ISSN:0377-2217
DOI:10.1016/j.ejor.2024.12.032