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Connections Between Single-Level and Bilevel Multiobjective Optimization

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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.

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Authors and Affiliations

  1. Department of Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland

    Sauli Ruuska, Kaisa Miettinen & Margaret M. Wiecek

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  1. Sauli Ruuska
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  2. Kaisa Miettinen
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  3. Margaret M. Wiecek
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Correspondence to Sauli Ruuska.

Additional information

Communicated by Patrice Marcotte.

M.M. Wiecek is on sabbatical leave from Department of Mathematical Sciences, Clemson University, Clemson, SC, USA.

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Ruuska, S., Miettinen, K. & Wiecek, M.M. Connections Between Single-Level and Bilevel Multiobjective Optimization. J Optim Theory Appl 153, 60–74 (2012). https://doi.org/10.1007/s10957-011-9943-y

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