A Hierarchical Particle Swarm Optimization for Solving Bilevel Programming Problems

  • Xiangyong Li
  • Peng Tian
  • Xiaoping Min
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4029)


The bilevel programming problem (BLPP) has proved to be a NP-hard problem. In this paper, we propose a hierarchial particle swarm optimization (PSO) for solving general BLPPs. Unlike most traditional algorithms designed for specific versions or based on specific assumptions, the proposed method is a hierarchical algorithm framework, which solves the general bilevel programming problems directly by simulating the decision process of bilevel programming. The solving general BLPPs is transformed to solve the upper-level and lower-level problems iteratively by two variants of PSO. The variants of PSO are built to solve upper-level and lower-level constrained optimization problems. The experimental results compared with those of other methods show that the proposed algorithm is a competitive method for solving general BLPPs.


Bilevel Programming Bilevel Programming Problem Standard Particle Swarm Optimization Trust Region Algorithm Linear Bilevel Programming 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Dempe, S.: Foundations of Bilevel Programming. In: Nonconvex optimization and its application, vol. 61, Kluwer Academic Publishers, Dordrecht (2002)Google Scholar
  2. 2.
    Colson, B., Marcotte, P., Savard, G.: Bilevel programming: A survey. 4OR: Quarterly Journal of the Belgian, French and Italian Operations Research Societies 3, 87–107 (2005)CrossRefMathSciNetMATHGoogle Scholar
  3. 3.
    Chiou, S.W.: Bilevel programming for the continuous transport network design problem. Transportation Research Part B: Methodological 39, 383 (2005)Google Scholar
  4. 4.
    Shi, C., Lu, J., Zhang, G.: An extended kuhn-tucker approach for linear bilevel programming. Applied Mathematics and Computation 162, 63 (2005)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Shih, H., Lai, Y., Lee, E.: Fuzzy apporach for multi-level programming problems. Computers and Operations Research 23, 773–791 (1983)MathSciNetGoogle Scholar
  6. 6.
    Marcotte, P., Savard, G., Zhu, D.L.: A trust region algorithm for nonlinear bilevel programming. Operations Research Letters 29, 179 (2001)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Wang, Y., Jiao, Y., Li, H.: An evolutionary algorithm for solving nonlinear bilevel programming based on a new constraint-handling scheme. IEEE Transactions on Systems, Man, and Cybernetics, Part C 35, 221 (2005)CrossRefGoogle Scholar
  8. 8.
    Sahin, K.H., Ciric, A.R.: A dual temperature simulated annealing approach for solving bilevel programming problems. Computers and Chemical Engineering 23, 25 (1998)CrossRefGoogle Scholar
  9. 9.
    Genderau, M., Marcotte, P., Savard, G.: A hybrid tabu-ascent algorithm for the linear bilevel programming problem. Journal of Global Optimization 8, 217–233 (1996)CrossRefGoogle Scholar
  10. 10.
    Kennedy, J., Eberhart, R., Shi, Y.: Swarm intelligence. Morgan Kaufmann Publisher, San Francisco (2001)Google Scholar
  11. 11.
    Powell, D., Skolnick, M.M.: Using genetic algorithms in engineering design optimization with non-linear constraints. In: Proceedings of the Fifth International Conference on Genetic Algorithms, Los Altos, CA, Morgan Kaufmann, San Francisco (1993)Google Scholar
  12. 12.
    Shi, Y., Eberhart, R.: A modified particle swarm optimizer. In: Proceedings of IEEE World Congress on Computational Intelligence 1998, pp. 69–73 (1998)Google Scholar
  13. 13.
    Aiyoshi, E., Shimizu, K.: A solution method for the static constrained stackelberg problem via penalty method. IEEE Transactions on Automatic Control 29, 1111–1114 (1984)CrossRefMathSciNetMATHGoogle Scholar
  14. 14.
    Shimizu, K., Aiyoshi, E.: A new computational method for syackelberg and min-max problems by use of a penalty method. IEEE Transaction on Autommatic Control AC-26, 460–466 (1981)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Bard, J.: Convex two-level optimization. Mathematical Programming 40, 15–27 (1988)CrossRefMathSciNetMATHGoogle Scholar
  16. 16.
    Calvete, H.I., Gale, C.: Theory and methodology: The bilevel linear/linear fractional programming problem. European Journal of Operation Research 114, 188–197 (1999)CrossRefMATHGoogle Scholar
  17. 17.
    Outrata, J.V.: On the numerical solution of a class of stackelberg problems. Zeitschrift Fur Operation Research 34, 255–278 (1990)MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Xiangyong Li
    • 1
  • Peng Tian
    • 1
  • Xiaoping Min
    • 2
  1. 1.Antai College of Economics & ManagementShanghai Jiaotong UniversityShanghaiP.R. China
  2. 2.School of FinanceJiangxi University of Finance and EconomicsNanchangP.R. China

Personalised recommendations