On Various Approaches for Bi-level Optimization Problems
Mohamed Aly El Sayed,
Farahat Abdo Allah Farahat
Issue:
Volume 5, Issue 3, September 2019
Pages:
47-63
Received:
23 September 2019
Accepted:
18 October 2019
Published:
25 October 2019
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.
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 ar...
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