On the rectangular knapsack problem: approximation of a specific quadratic knapsack problem - Britta Schulze; Michael Stiglmayr; Luís Paquete; Carlos M. Fonseca; David Willems; Stefan Ruzika (Mathematical Methods of Operations Research, 2020)
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.
Keywords: 330; Quadratic knapsack problem; Approximation algorithm; Multiobjective combinatorial optimization; Hypervolume