Multi-parametric global optimization approach for tri-level mixed-integer linear optimization problems

Multi-parametric global optimization approach for tri-level mixed-integer linear optimization... 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) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Global Optimization Springer Journals

Multi-parametric global optimization approach for tri-level mixed-integer linear optimization problems

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Publisher
Springer US
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Mathematics; Optimization; Operations Research/Decision Theory; Real Functions; Computer Science, general
ISSN
0925-5001
eISSN
1573-2916
D.O.I.
10.1007/s10898-018-0668-4
Publisher site
See Article on Publisher Site

Abstract

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

Journal of Global OptimizationSpringer Journals

Published: May 31, 2018

References

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