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Generating Efficient Solutions in Bilevel Multi-Objective Programming Problems
Department of Mathematics, Faculty of Science, University of Yaoundé I, Yaoundé, Cameroon
Department of Computer Science and Operations Research, University of Montreal, Montreal, Canada
Department of Computer Sciences, Faculty of Science, University of Yaoundé I, Yaoundé, Cameroon
LISSI, Faculty of Sciences and Technology, University of Paris XII Val-de-Marne, Créteil, France
- 1 Department of Mathematics, Faculty of Science, University of Yaoundé I, Yaoundé, Cameroon
- 2 Department of Computer Science and Operations Research, University of Montreal, Montreal, Canada
- 3 Department of Computer Sciences, Faculty of Science, University of Yaoundé I, Yaoundé, Cameroon
- 4 LISSI, Faculty of Sciences and Technology, University of Paris XII Val-de-Marne, Créteil, France
American Journal of Operations Research·Volume 03 (2013)·Pages 289–298·Published 28 March 2013·DOI10.4236/ajor.2013.32026
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Abstract
In this paper, we address bilevel multi-objective programming problems ( BMPP ) in which the decision maker at each level has multiple objective functions conflicting with each other. Given a BMPP , we show how to construct two artificial multiobjective programming problems such that any point that is efficient for both the two problems is an efficient solution of the BMPP . Some necessary and sufficient conditions for which the obtained result is applicable are provided. A complete procedure of the implementation of an algorithm for generating efficient solutions for the linear case of BMPP is presented. A numerical example is provided to illustrate how the algorithm operates.
KeywordsMulti-Objective ProgrammingBilevel ProgrammingEfficient SolutionEfficient EdgeHierarchical Systems
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