, Volume 153, Issue 1, pp 60-74
Date: 21 Oct 2011

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.

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