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

Styliani Avraamidou () and Efstratios N. Pistikopoulos ()
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Styliani Avraamidou: Centre for Process Systems Engineering, Imperial College London
Efstratios N. Pistikopoulos: Texas A & M Energy Institute, Artie McFerrin Department of Chemical Engineering, Texas A & M University

Journal of Global Optimization, 2019, vol. 74, issue 3, No 2, 443-465

Abstract: 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 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10898-018-0668-4

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