Connections Between Single-Level and Bilevel Multiobjective Optimization

• Published in: Journal of optimization theory and applications Vol. 153; no. 1; pp. 60 - 74
• Main Authors: Ruuska, Sauli, Miettinen, Kaisa, Wiecek, Margaret M.
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.04.2012; Springer Nature B.V
• Subjects: Applications of Mathematics; Calculus of Variations and Optimal Control; Optimization; Decision making; Engineering; Joints; Links; Mathematical programming; Mathematics; Mathematics and Statistics; Multicriteria; Multiobjective programming; Objectives; Operations Research/Decision Theory; Optimization; Reduction; Sabbatical leave; Studies; Theory of Computation; Two-level optimization; Two-level optimization; Binary relations; Multicriteria optimization; Multiobjective programming
• ISSN: 0022-3239; 1573-2878; 1573-2878
• DOI: 10.1007/s10957-011-9943-y

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.