Volume 55, Number 5, September-October 2021
|Page(s)||2915 - 2939|
|Published online||13 October 2021|
Hierarchical multilevel optimization with multiple-leaders multiple-followers setting and nonseparable objectives
Department of Mathematics, Addis Ababa University, P.O.Box 1176, Addis Ababa, Ethiopia
2 Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, P/Bag 16, Palapye, Botswana
* Corresponding author: firstname.lastname@example.org
Accepted: 18 September 2021
Hierarchical multilevel multi-leader multi-follower problems are non-cooperative decision problems in which multiple decision-makers of equal status in the upper-level and multiple decision-makers of equal status are involved at each of the lower-levels 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 only for two level cases. In this paper, we have considered hierarchical multilevel multi-leader multi-follower problems 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. We have proposed a solution algorithm to such problems by equivalent reformulation as a hierarchical multilevel problem involving single decision maker at all levels of the hierarchy. Then, we applied a multi-parametric algorithm to solve the resulting single leader single followers problem.
Mathematics Subject Classification: 91A65 / 91A06 / 91A10 / 90C26
Key words: Hierarchical game / multi-leader multi-follower / Stackelberg game / Nash game / equivalent reformulation / multi-parametric algorithm
© The authors. Published by EDP Sciences, ROADEF, SMAI 2021
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