Generating Efficient Solutions in Bilevel Multi-Objective Programming Problems

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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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