On the rectangular knapsack problem: approximation of a specific quadratic knapsack problem

In this article, we introduce the rectangular knapsack problem as a special case of the quadratic knapsack problem consisting in the maximization of the product of two separate knapsack profits subject to a cardinality constraint. We propose a polynomial time algorithm for this problem that provides...

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Veröffentlicht in:Mathematical methods of operations research (Heidelberg, Germany) Jg. 92; H. 1; S. 107 - 132
Hauptverfasser: Schulze, Britta, Stiglmayr, Michael, Paquete, Luís, Fonseca, Carlos M, Willems, David, Ruzika, Stefan
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin, Heidelberg Springer 01.08.2020
Springer Berlin Heidelberg
Springer Nature B.V
Schlagworte:
Algorithms
Approximation
Approximation algorithm
Business and Management
Calculus of Variations and Optimal Control; Optimization
Hypervolume
Knapsack problem
Mathematical analysis
Mathematics
Mathematics and Statistics
Multiobjective combinatorial optimization
Operations research
Operations Research/Decision Theory
Original Article
Polynomials
Quadratic knapsack problem
Multiobjective combinatorial optimization
Approximation algorithm
Quadratic knapsack problem
Hypervolume
ISSN:1432-5217, 1432-2994, 1432-5217
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Zusammenfassung:In this article, we introduce the rectangular knapsack problem as a special case of the quadratic knapsack problem consisting in the maximization of the product of two separate knapsack profits subject to a cardinality constraint. We propose a polynomial time algorithm for this problem that provides a constant approximation ratio of 4.5. Our experimental results on a large number of artificially generated problem instances show that the average ratio is far from theoretical guarantee. In addition, we suggest refined versions of this approximation algorithm with the same time complexity and approximation ratio that lead to even better experimental results.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1432-5217
1432-2994
1432-5217
DOI:10.1007/s00186-020-00702-0