Volume 5, Issue 3, September 2019, Page: 47-63
On Various Approaches for Bi-level Optimization Problems
Mohamed Aly El Sayed, Department of Basic Engineering Sciences, Benha University, ElQalyoubia, Egypt
Farahat Abdo Allah Farahat, Higher Technological Institute, Tenth of Ramadan City, Cairo, Egupt
Received: Sep. 23, 2019;       Accepted: Oct. 18, 2019;       Published: Oct. 25, 2019
DOI: 10.11648/j.ijmfs.20190503.11      View  21      Downloads  4
Abstract
In this paper we review some different basic approaches for solving bi-level optimization problems (BLOP). Firstly, the formulation and some basic concepts of such BLOP are presented. Secondly, some conventional approaches for solving the BLOP such as; vertex enumeration method, branch and bound algorithm, Karush Kuhn-Tucker (KKT) transformation are exhibited. The vertex enumeration based approaches which use the important characteristic that at least one global optimal solution is attained at an extreme point of the constraints set. The KKT approaches in which a BLOP is transformed into a single level problem that solves the upper level decision maker (ULDM) problem while including the lower level decision maker (LLDM) optimality conditions as extra constraints. Fuzzy programming approach mainly based on the fuzzy set theory. Finally, formulation of the bi-level multi-objective decision making (BL-MODM) problem and recently developed approaches, such as; fuzzy goal programming (FGP) and technique for order preference by similarity to ideal solution (TOPSIS) approach, for solving such problem are presented. Numerical illustrations are presented for each technique to ensure the applicability and efficiency.
Keywords
Bi-level Programming, Multi-objective Programming, KKT Transformation, FGP, TOPSIS
To cite this article
Mohamed Aly El Sayed, Farahat Abdo Allah Farahat, On Various Approaches for Bi-level Optimization Problems, International Journal of Management and Fuzzy Systems. Vol. 5, No. 3, 2019, pp. 47-63. doi: 10.11648/j.ijmfs.20190503.11
Copyright
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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