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

• Published in: Mathematical methods of operations research (Heidelberg, Germany) Vol. 92; no. 1; pp. 107 - 132
• Main Authors: Schulze, Britta, Stiglmayr, Michael, Paquete, Luís, Fonseca, Carlos M, Willems, David, Ruzika, Stefan
• Format: Journal Article
• Language: English
• Published: Berlin, Heidelberg Springer 01.08.2020; Springer Berlin Heidelberg; Springer Nature B.V
• Subjects: 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
• DOI: 10.1007/s00186-020-00702-0

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...