TITLE:
Generating Efficient Solutions in Bilevel Multi-Objective Programming Problems
AUTHORS:
Calice Olivier Pieume, Patrice Marcotte, Laure Pauline Fotso, Patrick Siarry
KEYWORDS:
Multi-Objective Programming; Bilevel Programming; Efficient Solution; Efficient Edge; Hierarchical Systems
JOURNAL NAME:
American Journal of Operations Research,
Vol.3 No.2,
March
29,
2013
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.