KKT transformation approach for multi-objective multi-level linear programming problems

A neural network for solving nonlinear multilevel programming problems

“…The most popular approach to solve the nested MLP optimization problems is using the KKT conditions and transforms the original problem to its first level auxiliary problem [10] .The lower level conditions become the rigid constraints of thehigher level DM. So the lower level gains importance.…”

“…Hsu-Shih Shih [9] proposed a fuzzy approach for solving the multiobjective and multilevel knapsack problems. Surabhi Sinha [10] give the mathematical formulation and corresponding development by KKT transformation when DMs have absolute control over certain decision variables but some variables may be shared and hence controlled by two or more DMs.…”

GIS-modelling based coal-fired power plant site identification and selection

“…Complex models are difficult to solve using exact techniques as bi-level programming problems are known to be NP-hard problems [22,23], and therefore many methods have been developed to deal with these bi-level programming problems [24][25][26]. Bi-level decision makers depend partly on a degree of interaction or cooperation [25,26].…”

Model, solution concept, and Kth-best algorithm for linear trilevel programming

“…There have been many approaches and algorithms proposed for solving BLP problems since the field caught the attention of researchers in the mid-1970s, including the well-known KuhnTucker approach [6,18], the Branch-and-bound algorithm [8,18], penalty function approach [34], the Kth-best approach [13,10], and also genetic algorithm [12,22]. Furthermore, some fuzzy BLP models and approaches [29,27,35], multi-follower BLP [23,24,25], and multi-objective BLP models and approaches [17,28,30,36] have been recently developed to deal with more complex cases of bi-level decision problems.…”

“…The follower's decision, with the corresponding levels of optimality and decision powers, is submitted to and modified by the leader with considerations of overall benefit for the organization and distribution of decision power until a best preferred solution is reached. Subsequently, Sinha and Sinha [30] proposed a Karush-Kuhn-Tucker (KKT) transformation method for multi-level linear programming problems, wherein some subsets of decision variables were under the exclusive domain of the decision makers as some other subsets of decision variables are also common to two or more decision makers on different levels and/or on various divisions on a level. Although these LTLP methods and algorithms have been developed, the solution concepts, including the solution existence for LTLP problems, have not been well developed in the literature.…”