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Mathematical Problems in Engineering
Volume 2014, Article ID 737515, 8 pages
Research Article

An Evolutionary Algorithm Using Duality-Base-Enumerating Scheme for Interval Linear Bilevel Programming Problems

1Department of Mathematics, Qinghai Normal University, Xining 810008, China
2Business School, Nankai University, Tianjin 300070, China

Received 2 June 2014; Accepted 29 July 2014; Published 13 August 2014

Academic Editor: Yuping Wang

Copyright © 2014 Hecheng Li and Lei Fang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Interval bilevel programming problem is hard to solve due to its hierarchical structure as well as the uncertainty of coefficients. This paper is focused on a class of interval linear bilevel programming problems, and an evolutionary algorithm based on duality bases is proposed. Firstly, the objective coefficients of the lower level and the right-hand-side vector are uniformly encoded as individuals, and the relative intervals are taken as the search space. Secondly, for each encoded individual, based on the duality theorem, the original problem is transformed into a single level program simply involving one nonlinear equality constraint. Further, by enumerating duality bases, this nonlinear equality is deleted, and the single level program is converted into several linear programs. Finally, each individual can be evaluated by solving these linear programs. The computational results of 7 examples show that the algorithm is feasible and robust.