| Issue |
Math. Model. Nat. Phenom.
Volume 5, Number 7, 2010
JANO9 – The 9th International Conference on Numerical Analysis and Optimization
|
|
|---|---|---|
| Page(s) | 116 - 121 | |
| DOI | https://doi.org/10.1051/mmnp/20105719 | |
| Published online | 26 August 2010 | |
Integer Programming Formulation of the Bilevel Knapsack Problem
LAMIH-SIADE, University of Valenciennes,
France
* Corresponding author: E-mail:
said.hanafi@univ-valenciennes.fr
The Bilevel Knapsack Problem (BKP) is a hierarchical optimization problem in which the feasible set is determined by the set of optimal solutions of parametric Knapsack Problem. In this paper, we propose two stages exact method for solving the BKP. In the first stage, a dynamic programming algorithm is used to compute the set of reactions of the follower. The second stage consists in solving an integer program reformulation of BKP. We show that the integer program reformulation is equivalent to the BKP. Numerical results show the efficiency of our method compared with those obtained by the algorithm of Moore and Bard
Mathematics Subject Classification: 65K05 / 90C30
Key words: Bilevel programming / Knapsack problem / dynamic programming / branch-and-bound
© EDP Sciences, 2010
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.