Hierarchical Multilevel Multi-Leader Multi-Follower Problem Multi-Parametric Solution Approach
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Date
2022-04-07
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Addis Ababa University
Abstract
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.
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Keywords
Bilevel Optimization, Hierarchical Multilevel, Multi-Leader Multifollower, Multi-Parametric Programming, Barrier Method, Nonlinear Constraints, Exact Solutions