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.
Highlights
Many planning problems require the synthesis of decisions of several interacting individuals or agencies
Zhang et al [27] presented an algorithm for solving decentralized bi-level multi-objective decision making (BL-MODM) problem with fuzzy demands by using -cut method
Assume that there are two-levels in a hierarchy structure with Upper-Level Decision Maker (ULDM) and Lower-Level Decision Maker (LLDM)
Summary
Many planning problems require the synthesis of decisions of several interacting individuals or agencies. Shih et al [19] extended Lai's concept by using non-compensatory max-min aggregation operator for solving multi-level optimization problem (MLOP). Sakawa et al [21] developed interactive FP for solving two-level linear fractional programming problems with fuzzy parameters in 2000. In 1997 Shi and Xia [23] studied the bi-level MultiObjective Decision Making (BL-MODM) problem and an interactive algorithm to solve such problem. In 2006 Abo-Sinna and Baky [26] presented balance space approach for non-linear BL-MODM problem. Zhang et al [27] presented an algorithm for solving decentralized BL-MODM problem with fuzzy demands by using -cut method. In 2003, Pal et al [29] presented a GP procedure for fuzzy multi-objective linear fractional programming problem.
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