Connections Between Single-Level and Bilevel Multiobjective Optimization

  • Sauli Ruuska
  • Kaisa Miettinen
  • Margaret M. Wiecek
Article

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.

Keywords

Two-level optimization Multiobjective programming Multicriteria optimization Binary relations 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Sauli Ruuska
    • 1
  • Kaisa Miettinen
    • 1
  • Margaret M. Wiecek
    • 1
  1. 1.Department of Mathematical Information TechnologyUniversity of JyväskyläJyväskyläFinland

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