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 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Berlin, Heidelberg
Springer
01.08.2020
Springer Berlin Heidelberg Springer Nature B.V |
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| ISSN: | 1432-5217, 1432-2994, 1432-5217 |
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| Abstract | 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. |
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| AbstractList | 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. 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. |
| Author | Willems, David Stiglmayr, Michael Ruzika, Stefan Paquete, Luís Fonseca, Carlos M Schulze, Britta |
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| CitedBy_id | crossref_primary_10_1016_j_cor_2021_105693 crossref_primary_10_1145_3453474 crossref_primary_10_1007_s00186_022_00788_8 crossref_primary_10_1016_j_asoc_2023_111073 crossref_primary_10_1016_j_cor_2021_105349 crossref_primary_10_1007_s11081_020_09586_9 crossref_primary_10_1016_j_cor_2025_107140 crossref_primary_10_1109_ACCESS_2020_3009318 |
| Cites_doi | 10.1162/EVCO_a_00157 10.1287/ijoc.2015.0678 10.1023/A:1009898604624 10.1007/BF01585164 10.1016/0377-2217(94)00229-0 10.1137/110820762 10.1287/ijoc.1050.0172 10.1016/S0377-2217(03)00244-3 10.1016/S0167-6377(02)00122-0 10.1287/ijoc.11.2.125 10.1016/j.dam.2006.08.007 10.1007/978-3-540-24777-7 10.1287/mnsc.17.3.200 10.1016/S0377-2217(97)00414-1 10.1016/j.ejor.2011.10.049 10.1007/s00453-008-9248-1 10.1016/j.orl.2016.05.005 10.1007/BFb0056872 10.6028/NBS.IR.75-737 10.1007/978-1-4613-0303-9_27 |
| ContentType | Journal Article |
| Copyright | The Author(s) 2020 The Author(s) 2020. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
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| Snippet | In this article, we introduce the rectangular knapsack problem as a special case of the quadratic knapsack problem consisting in the maximization of the... In this article, we introduce the rectangular knapsack problem as a special case of the quadratic knapsack problem consisting in the maximization of the... |
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| SubjectTerms | 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 |
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| Title | On the rectangular knapsack problem: approximation of a specific quadratic knapsack problem |
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| Volume | 92 |
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