J Glob Optim https://doi.org/10.1007/s10898-018-0668-4 Multi-parametric global optimization approach for tri-level mixed-integer linear optimization problems 1,2 2 Styliani Avraamidou · Efstratios N. Pistikopoulos Received: 2 July 2017 / Accepted: 23 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract In this work, we present a novel algorithm for the global solution of tri-level mixed- integer linear optimization problems containing both integer and continuous variables at all three optimization levels. Based on multi-parametric theory and our earlier results for bi- level programming problems, the main idea of the algorithm is to recast the lower levels of the tri-level optimization problem as multi-parametric programming problems, in which the optimization variables (continuous and integer) of all the upper level problems, are considered as parameters at the lower levels. The resulting parametric solutions are then substituted into the corresponding higher-level problems sequentially. The algorithm is illustrated through numerical examples, along with implementation and computational studies. Keywords Multi-level mixed-integer optimization · Hierarchical optimization · Tri-level optimization · Multi-parametric programming 1 Introduction Optimization problems involving multiple decision makers at different decision levels are referred to as multi-level programming problems. In the case of tri-level programming, the ﬁrst decision maker (upper level; leader)
Journal of Global Optimization – Springer Journals
Published: May 31, 2018
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