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

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, th...

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Veröffentlicht in:Journal of global optimization Jg. 74; H. 3; S. 443 - 465
Hauptverfasser: Avraamidou, Styliani, Pistikopoulos, Efstratios N.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 15.07.2019
Springer
Springer Nature B.V
Schlagworte:
Algorithms
Analysis
Computer Science
Continuity (mathematics)
Global optimization
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Tri-level optimization
Multi-parametric programming
Multi-level mixed-integer optimization
Hierarchical optimization
ISSN:0925-5001, 1573-2916
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Beschreibung
Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-018-0668-4