 On linear bilevel problems with multiple objectives at the lower levelHerminia I. Calvete and Carmen Galé Omega, 2011, vol. 39, issue 1, 33-40 Abstract: Bilevel programming problems provide a framework to deal with decision processes involving two decision makers with a hierarchical structure. They are characterized by the existence of two optimization problems in which the constraint region of the upper level problem is implicitly determined by the lower level optimization problem. This paper focuses on bilevel problems for which the lower level problem is a linear multiobjective program and constraints at both levels define polyhedra. This bilevel problem is reformulated as an optimization problem over a nonconvex region given by a union of faces of the polyhedron defined by all constraints. This reformulation is obtained when dealing with efficient solutions as well as weakly efficient solutions for the lower level problem. Assuming that the upper level objective function is quasiconcave, then an extreme point exists which solves the problem. An exact and a metaheuristic algorithm are developed and their performance is analyzed and compared. Keywords: Bilevel; optimization; Multiobjective; optimization; Efficient; solution; Weakly; efficient; solution; Genetic; algorithm (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:jomega:v:39:y:2011:i:1:p:33-40 Ordering information: This journal article can be ordered from Access Statistics for this article Omega is currently edited by B. Lev More articles in Omega from Elsevier |
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