scholarly journals A New Optimization Model for the Sustainable Development: Quadratic Knapsack Problem with Conflict Graphs

2017 ◽  
Vol 9 (2) ◽  
pp. 236 ◽  
Author(s):  
Xiaochuan Shi ◽  
Lei Wu ◽  
Xiaoliang Meng
Keyword(s):  
Sustainable Development ◽  
Knapsack Problem ◽  
Optimization Model ◽  
The Sustainable Development ◽  
Quadratic Knapsack Problem ◽  
Conflict Graphs ◽  
Quadratic Knapsack

On the continuous quadratic knapsack problem

1992 ◽  
Vol 55 (1-3) ◽  
pp. 99-108 ◽  
Author(s):  
A. G. Robinson ◽  
N. Jiang ◽  
C. S. Lerme
Keyword(s):  
Knapsack Problem ◽  
Quadratic Knapsack Problem ◽  
Quadratic Knapsack

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

2020 ◽  
Vol 92 (1) ◽  
pp. 107-132 ◽  
Author(s):  
Britta Schulze ◽  
Michael Stiglmayr ◽  
Luís Paquete ◽  
Carlos M. Fonseca ◽  
David Willems ◽  
...  
Keyword(s):  
Knapsack Problem ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Approximation Ratio ◽  
Experimental Results ◽  
Cardinality Constraint ◽  
Quadratic Knapsack Problem ◽  
Problem Instances ◽  
Quadratic Knapsack ◽  
Special Case

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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