Skip to main content

A Particle Swarm Optimization Based Algorithm for Fuzzy Bilevel Decision Making with Objective-Shared Followers

  • Conference paper
Simulated Evolution and Learning (SEAL 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5361))

Included in the following conference series:

Abstract

A bilevel decision problem may have multiple followers as the lower decision units and have fuzzy demands simultaneously. This paper focuses on problems of fuzzy linear bilevel decision making with multiple followers who share a common objective but have different constraints (FBOSF). Based on the ranking relationship among fuzzy sets defined by cut set and satisfactory degree, a FBOSF model is presented and a particle swarm optimization based algorithm is developed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Von Stackelberg, H.: Theory of the Market Economy. Oxford University Press, New York (1952)

    Google Scholar 

  2. Bard, J.F.: Practical bilevel optimization: algorithms and applications. Kluwer Academic Publishers, Boston (1998)

    Book  MATH  Google Scholar 

  3. Yu, H., Dang, C., Wang, S.: Game theoretical analysis of buy-it-now price auctions. International Journal of Information Technology and Decision Making 5(3), 557–581 (2006)

    Article  Google Scholar 

  4. Hobbs, B.F., Metzler, B., Pang, J.S.: Strategic gaming analysis for electric power system: an mpec approach. IEEE Transactions on Power System 15, 637–645 (2000)

    Article  Google Scholar 

  5. Zhang, G., Lu, J.: Model and approach of fuzzy bilevel decision making for logistics planning problem. Journal of Enterprise Information Management 20(2), 178–197 (2007)

    Article  MathSciNet  Google Scholar 

  6. Amat, J., McCarl, B.: A representation and economic interpretation of a two-level programming problem. Journal of the Operational Research Society 32, 783–792 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  7. Feng, C., Wen, C.: Bi-level and multi-objective model to control traffic flow into the disaster area post earthquake. Journal of the Eastern Asia Society for Transportation Studies 6, 4253–4268 (2005)

    Google Scholar 

  8. Gao, Y., Zhang, G., Lu, J., Gao, S.: A bilevel model for railway train set organizing optimization. In: 2007 International Conference on Intelligent Systems and Knowledge Engineering (ISKE 2007), pp. 777–782. Atlantis Press (2007)

    Google Scholar 

  9. Bard, J.F., Moore, J.T.: A branch and bound algorithm for the bilevel programming problem. SIAM Journal on Scientific and Statistical Computing 11, 281–292 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  10. Shi, C., Lu, J., Zhang, G.: An extended kth-best approach for linear bilevel programming. Applied Mathematics and Computation 164(3), 843–855 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  11. Lu, J., Shi, C., Zhang, G., Ruan, D.: An extended branch and bound algorithm for bilevel multi-follower decision making in a referential-uncooperative situation. International Journal of Information Technology and Decision Making 6(2), 371–388 (2007)

    Article  MATH  Google Scholar 

  12. Shi, C., Lu, J., Zhang, G.: An extended kuhn-tucker approach for linear bilevel programming. Applied Mathematics and Computation 162, 51–63 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  13. Shi, C., Lu, J., Zhang, G., Zhou, H.: An extended branch and bound algorithm for linear bilevel programming. Applied Mathematics and Computation 180(2), 529–537 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  14. Li, X., Tian, P., Min, X.: A hierarchical particle swarm optimization for solving bilevel programming problems. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS, vol. 4029, pp. 1169–1178. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  15. White, D., Anandalingam, G.: A penalty function approach for solving bi-level linear programs. Journal of Global Optimization (3), 397–419 (1993)

    Google Scholar 

  16. Gao, Y., Zhang, G., Lu, J.: A particle swarm optimization based algorithm for fuzzy bilevel decision making. In: IEEE International Conference on Fuzzy Systems, pp. 1452–1457 (2008)

    Google Scholar 

  17. Lu, J., Shi, C., Zhang, G.: On bilevel multi-follower decision making: General framework and solutions. Information Sciences 176(11), 1607–1627 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  18. Kitayama, S., Yasuda, K.: A method for mixed integer programming problems by particle swarm optimization. Electrical Engineering in Japan 157(2), 40–49 (2006)

    Article  Google Scholar 

  19. Sakawa, M., Nishizaki, I., Uemura, Y.: Interactive fuzzy programming for multilevel linear programming problems with fuzzy parameters. Fuzzy Sets and Systems 109, 3–19 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  20. Zhang, G., Lu, J., Dillon, T.: An approximation kuhn-tucker approach for fuzzy linear bilevel decision making problems. In: Jain, L., Wren, G. (eds.) Intelligent Decision Making. Springer, Heidelberg (2007)

    Google Scholar 

  21. Zhang, G., Lu, J., Dillon, T.: Kth-best algorithm for fuzzy bilevel programming. In: Proceedings of International Conference on Intelligent Systems and Knowledge Engineering, Shanghai (2006)

    Google Scholar 

  22. Zhang, G., Lu, J., Dillon, T.: An approximation branch-and-bound algorithm for fuzzy bilevel decision making problems. In: Proceedings of The 1st International Symposium Advances in Artificial Intelligence and Applications, Poland (2006)

    Google Scholar 

  23. Gao, Y., Zhang, G., Lu, J., Zeng, X.: A λ−cut approximate approach to supporting fuzzy goal based bilevel decision making in risk management. In: The First International Conference on Risk Analysis and Crisis Response, pp. 132–137. Atlantis Press (2007)

    Google Scholar 

  24. Lu, J., Shi, C., Zhang, G., Dillon, T.: Model and extended kuhn-tucker approach for bilevel multi-follower decision making in a referential-uncooperative situation. International Journal of Global Optimization 38(4), 597–608 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  25. Mathieu, R., Pittard, L., Anandalingam, G.: Genetic algorithm based approach to bi-level linear programming. Recherche Operationnelle 28(1), 1–21 (1994)

    MathSciNet  MATH  Google Scholar 

  26. Pei, Z., Tian, S., Huang, H.: A novel method for solving nonlinear bilevel programming based on hybrid particle swarm optimization. In: The 8th International Conference on Signal Processing, vol. 3 (2006)

    Google Scholar 

  27. Zhao, Z., Gu, X.: Particle swarm optimization based algorithm for bilevel programming problems. In: 2006 6th International Conference on Intelligent Systems Design and Applications (2006)

    Google Scholar 

  28. Oduguwa, V., Roy, R.: Bi-level optimisation using genetic algorithm. In: Proceedings of the 2002 IEEE International Conference on Artificial Intelligence Systems, ICAIS 2002 (2002)

    Google Scholar 

  29. Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: Proc IEEE International Conference on Neural Networks, pp. 1942–1948 (1995)

    Google Scholar 

  30. Eberhart, R., Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings Sixth International Symposium on Micro Machine and Human Science (1995)

    Google Scholar 

  31. Parsopoulos, K.E., Vrahatis, M.N.: Recent approaches to global optimization problems through particle swarm optimization. Natural Computing 1, 235–306 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  32. Zhang, J.-R., Zhang, J., Lok, T.-M., Lyu, M.R.: A hybrid particle swarm optimization-back-propagation algorithm for feedforward neural network training. Applied Mathematics and Computation 185(2), 1026–1037 (2007)

    Article  MATH  Google Scholar 

  33. Ho, S.L., Yang, S., Ni, G., Lo, E.W.C., Wong, H.C.: A particle swarm optimization-based method for multiobjective design optimizations. IEEE Transactions On Magnetics 41(5), 557–581 (2005)

    Google Scholar 

  34. Eberhart, R.C., Simpson, P., Dobbins, R.: Computational Intelligence PC Tools. Academic Press, London (1996)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gao, Y., Zhang, G., Lu, J. (2008). A Particle Swarm Optimization Based Algorithm for Fuzzy Bilevel Decision Making with Objective-Shared Followers. In: Li, X., et al. Simulated Evolution and Learning. SEAL 2008. Lecture Notes in Computer Science, vol 5361. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89694-4_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-89694-4_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89693-7

  • Online ISBN: 978-3-540-89694-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics