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A note on upper bounds to the robust knapsack problem with discrete scenarios

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Published
<mark>Journal publication date</mark>12/2014
<mark>Journal</mark>Annals of Operations Research
Issue number1
Volume223
Number of pages9
Pages (from-to)461-469
Publication StatusPublished
Early online date24/05/14
<mark>Original language</mark>English

Abstract

We consider the knapsack problem in which the objective function is uncertain, and given by a finite set of possible realizations. The resulting robust optimization problem is a max–min problem that follows the pessimistic view of optimizing the worst-case behavior. Several branch-and-bound algorithms have been proposed in the recent literature. In this short note, we show that by using a simple upper bound that is tailored to balance out the drawbacks of the current best approach based on surrogate relaxation, computation times improve by up to an order of magnitude. Additionally, one can make use of any upper bound for the classic knapsack problem as an upper bound for the robust problem.