Hierarchical Multilevel Multi-Leader Multi-Follower Problem Multi-Parametric Solution Approach

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Addis Ababa University


Hierarchical multilevel multi-leader multi-follower games are non-cooperative decision problems in which multiple decision-makers of equal status in the upperlevel andmultiple decision-makers of equal status are involved at each of the lowerlevels of the hierarchy. Much of solution methods proposed so far on the topic are either model specific which may work only for a particular sub-class of problems or are based on some strong assumptions and mainly for two level cases. In this dissertation we have proposed a multi-parametric programming based solution approach for hierarchical multilevel multi-leader multi-follower games in which the objective functions contain separable and non-separable terms (but the non-separable terms can be written as a factor of two functions, a function which depends on other level decision variables and a function which is common to all objectives across the same level) and shared constraint. The proposed solution approach transforms a hierarchical multilevel multi-leader multi-follower game into multilevel game involving a single decision maker at each level of the hierarchy. In addition, a solution algorithm for bilevel optimization problems whose lower-level problem involves convex nonlinear constraints is also developed. The solution algorithm recasts the lower-level problem as a multi-parametric problem and employs an equivalent barrier problem reformulation. The solution obtained with this method is shown to be exact if the lower-level problem and the nonlinear constraints can be expressed by a polynomial of utmost degree three with followers’ variable and upto quadratic in the variable of the leader.



Bilevel Optimization, Hierarchical Multilevel, Multi-Leader Multifollower, Multi-Parametric Programming, Barrier Method, Nonlinear Constraints, Exact Solutions