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

Artikel

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Journal: Mathematical Methods of Operations Research ; ISSN: 1432-5217 ; Volume: 92 ; Year: 2020 ; Issue: 1 ; Pages: 107-132 ; Berlin, Heidelberg: Springer

Classification and Topics

• Classification: Wirtschaft
• Subject: Quadratic knapsack problem ; Approximation algorithm ; Multiobjective combinatorial optimization ; Hypervolume

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Schulze, Britta ; Stiglmayr, Michael ; Paquete, Luís ; Fonseca, Carlos M. ; Willems, David ; Ruzika, Stefan
• Event: Veröffentlichung
• (who): Springer
• (where): Berlin, Heidelberg
• (when): 2020

Further information

• DOI: doi:10.1007/s00186-020-00702-0
• Last update: 10.03.2025, 11:43 AM CET