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

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.

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Acknowledgements

We are grateful to the Department of Chemical Engineering and the Faculty of Engineering of Imperial College London for an EPSRC-funded Doctoral Training Partnership (DTP) studentship. Financial support from Texas A&M University and Texas A&M Energy Institute is also gratefully acknowledged.

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Correspondence to Efstratios N. Pistikopoulos.

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Avraamidou, S., Pistikopoulos, E.N. Multi-parametric global optimization approach for tri-level mixed-integer linear optimization problems. J Glob Optim 74, 443–465 (2019) doi:10.1007/s10898-018-0668-4

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Keywords

  • Multi-level mixed-integer optimization
  • Hierarchical optimization
  • Tri-level optimization
  • Multi-parametric programming