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Connections Between Single-Level and Bilevel Multiobjective Optimization

Author

Listed:
  • Sauli Ruuska

    (University of Jyväskylä)

  • Kaisa Miettinen

    (University of Jyväskylä)

  • Margaret M. Wiecek

    (University of Jyväskylä)

Abstract

The relationship between bilevel optimization and multiobjective optimization has been studied by several authors, and there have been repeated attempts to establish a link between the two. We unify the results from the literature and generalize them for bilevel multiobjective optimization. We formulate sufficient conditions for an arbitrary binary relation to guarantee equality between the efficient set produced by the relation and the set of optimal solutions to a bilevel problem. In addition, we present specially structured bilevel multiobjective optimization problems motivated by real-life applications and an accompanying binary relation permitting their reduction to single-level multiobjective optimization problems.

Suggested Citation

  • Sauli Ruuska & Kaisa Miettinen & Margaret M. Wiecek, 2012. "Connections Between Single-Level and Bilevel Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 60-74, April.
    • Handle: RePEc:spr:joptap:v:153:y:2012:i:1:d:10.1007_s10957-011-9943-y
    DOI: 10.1007/s10957-011-9943-y
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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. Alexander Engau & Margaret M. Wiecek, 2008. "Interactive Coordination of Objective Decompositions in Multiobjective Programming," Management Science, INFORMS, vol. 54(7), pages 1350-1363, July.
    3. 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.
    4. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    5. I. Nishizaki & M. Sakawa, 1999. "Stackelberg Solutions to Multiobjective Two-Level Linear Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 161-182, October.
    6. Guangquan Zhang & Jie Lu & Tharam Dillon, 2008. "Solution Concepts and an Approximation Kuhn–Tucker Approach for Fuzzy Multiobjective Linear Bilevel Programming," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Athanasios Migdalas & Leonidas Pitsoulis (ed.), Pareto Optimality, Game Theory And Equilibria, pages 457-480, Springer.
    7. 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.
    8. H. Bonnel & J. Morgan, 2006. "Semivectorial Bilevel Optimization Problem: Penalty Approach," Journal of Optimization Theory and Applications, Springer, vol. 131(3), pages 365-382, December.
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