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

Author

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  • Styliani Avraamidou

    (Centre for Process Systems Engineering, Imperial College London
    Texas A & M Energy Institute, Artie McFerrin Department of Chemical Engineering, Texas A & M University)

  • Efstratios N. Pistikopoulos

    (Texas A & M Energy Institute, Artie McFerrin Department of Chemical Engineering, Texas A & M University)

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.

Suggested Citation

  • Styliani Avraamidou & Efstratios N. Pistikopoulos, 2019. "Multi-parametric global optimization approach for tri-level mixed-integer linear optimization problems," Journal of Global Optimization, Springer, vol. 74(3), pages 443-465, July.
    • Handle: RePEc:spr:jglopt:v:74:y:2019:i:3:d:10.1007_s10898-018-0668-4
    DOI: 10.1007/s10898-018-0668-4
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    References listed on IDEAS

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