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Generating Efficient Solutions in Bilevel Multi-Objective Programming Problems

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Author(s): Calice Olivier Pieume | Patrice Marcotte | Laure Pauline Fotso | Patrick Siarry

Journal: American Journal of Operations Research
ISSN 2160-8830

Volume: 03;
Issue: 02;
Start page: 289;
Date: 2013;
Original page

Keywords: Multi-Objective Programming | Bilevel Programming | Efficient Solution | Efficient Edge | Hierarchical Systems

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.

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