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Journal of Applied Mathematics
Volume 2012, Article ID 626717, 13 pages
Research Article

An Improved Particle Swarm Optimization for Solving Bilevel Multiobjective Programming Problem

1State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
2School of Information and Mathematics, Yangtze University, Jingzhou 434023, China
3College of Mathematics and Computer Sciences, Huanggang Normal University, Huanggang 438000, China

Received 4 December 2011; Revised 21 January 2012; Accepted 5 February 2012

Academic Editor: Debasish Roy

Copyright © 2012 Tao Zhang et al. 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.


An improved particle swarm optimization (PSO) algorithm is proposed for solving bilevel multiobjective programming problem (BLMPP). For such problems, the proposed algorithm directly simulates the decision process of bilevel programming, which is different from most traditional algorithms designed for specific versions or based on specific assumptions. The BLMPP is transformed to solve multiobjective optimization problems in the upper level and the lower level interactively by an improved PSO. And a set of approximate Pareto optimal solutions for BLMPP is obtained using the elite strategy. This interactive procedure is repeated until the accurate Pareto optimal solutions of the original problem are found. Finally, some numerical examples are given to illustrate the feasibility of the proposed algorithm.