Approximation algorithms on 0–1 linear knapsack problem with a single continuous variable

2013 ◽  
Vol 28 (4) ◽  
pp. 910-916 ◽  
Author(s):  
Chenxia Zhao ◽  
Xianyue Li
Keyword(s):  
Approximation Algorithms ◽  
Knapsack Problem ◽  
Continuous Variable

scholarly journals Reducing the 0-1 Knapsack Problem with a Single Continuous Variable to the Standard 0-1 Knapsack Problem

2012 ◽  
Vol 3 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Marcel Büther ◽  
Dirk Briskorn
Keyword(s):  
Knapsack Problem ◽  
Upper Bound ◽  
Original Problem ◽  
Natural Extension ◽  
Continuous Variable ◽  
Computational Effort ◽  
Objective Value ◽  
The One

The 0-1 knapsack problem with a single continuous variable (KPC) is a natural extension of the binary knapsack problem (KP), where the capacity is not any longer fixed but can be extended which is expressed by a continuous variable. This variable might be unbounded or restricted by a lower or upper bound, respectively. This paper concerns techniques in order to reduce several variants of KPC to KP which enables the authors to employ approaches for KP. The authors propose both, an equivalent reformulation and a heuristic one bringing along less computational effort. The authors show that the heuristic reformulation can be customized in order to provide solutions having an objective value arbitrarily close to the one of the original problem.

The 0-1 Knapsack problem with a single continuous variable

1999 ◽  
Vol 85 (1) ◽  
pp. 15-33 ◽  
Author(s):  
Hugues Marchand ◽  
Laurence A. Wolsey
Keyword(s):  
Knapsack Problem ◽  
Continuous Variable
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