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Solving Bilevel Linear Programs Using Multiple Objective Linear Programming

Author

Listed:
  • J. Glackin

    (United States Military Academy)

  • J. G. Ecker

    (Rensselaer Polytechnic Institute)

  • M. Kupferschmid

    (Rensselaer Polytechnic Institute)

Abstract

We present an algorithm for solving bilevel linear programs that uses simplex pivots on an expanded tableau. The algorithm uses the relationship between multiple objective linear programs and bilevel linear programs along with results for minimizing a linear objective over the efficient set for a multiple objective problem. Results in multiple objective programming needed are presented. We report computational experience demonstrating that this approach is more effective than a standard branch-and-bound algorithm when the number of leader variables is small.

Suggested Citation

  • J. Glackin & J. G. Ecker & M. Kupferschmid, 2009. "Solving Bilevel Linear Programs Using Multiple Objective Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 140(2), pages 197-212, February.
    • Handle: RePEc:spr:joptap:v:140:y:2009:i:2:d:10.1007_s10957-008-9467-2
    DOI: 10.1007/s10957-008-9467-2
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    References listed on IDEAS

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    1. J. Fliege & L. N. Vicente, 2006. "Multicriteria Approach to Bilevel Optimization," Journal of Optimization Theory and Applications, Springer, vol. 131(2), pages 209-225, November.
    2. Serpil Sayin, 2000. "Optimizing Over the Efficient Set Using a Top-Down Search of Faces," Operations Research, INFORMS, vol. 48(1), pages 65-72, February.
    3. LeBlanc, Larry J. & Boyce, David E., 1986. "A bilevel programming algorithm for exact solution of the network design problem with user-optimal flows," Transportation Research Part B: Methodological, Elsevier, vol. 20(3), pages 259-265, June.
    4. Jesús Jorge, 2005. "A Bilinear Algorithm for Optimizing a Linear Function over the Efficient Set of a Multiple Objective Linear Programming Problem," Journal of Global Optimization, Springer, vol. 31(1), pages 1-16, January.
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    Cited by:

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    2. Ferdinard U. Ogbuisi & Yekini Shehu & Jen-Chih Yao, 2023. "Relaxed Single Projection Methods for Solving Bilevel Variational Inequality Problems in Hilbert Spaces," Networks and Spatial Economics, Springer, vol. 23(3), pages 641-678, September.
    3. Yanlai Song & Omar Bazighifan, 2022. "Regularization Method for the Variational Inequality Problem over the Set of Solutions to the Generalized Equilibrium Problem," Mathematics, MDPI, vol. 10(14), pages 1-20, July.
    4. Hecheng Li, 2015. "A genetic algorithm using a finite search space for solving nonlinear/linear fractional bilevel programming problems," Annals of Operations Research, Springer, vol. 235(1), pages 543-558, December.

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