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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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    1. S Sinha, 2001. "A comment on Anandalingam (1988). A mathematical programming model of decentralized multi-level systems. J Opl Res Soc 39: 1021-1033," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 52(5), pages 594-596, May.
    2. Tomas Gal & Josef Nedoma, 1972. "Multiparametric Linear Programming," Management Science, INFORMS, vol. 18(7), pages 406-422, March.
    3. Sakawa, Masatoshi & Nishizaki, Ichiro & Hitaka, Masatoshi, 1999. "Interactive fuzzy programming for multi-level 0-1 programming problems through genetic algorithms," European Journal of Operational Research, Elsevier, vol. 114(3), pages 580-588, May.
    4. Pramanik, Surapati & Roy, Tapan Kumar, 2007. "Fuzzy goal programming approach to multilevel programming problems," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1151-1166, January.
    5. D. J. White, 1997. "Penalty Function Approach to Linear Trilevel Programming," Journal of Optimization Theory and Applications, Springer, vol. 93(1), pages 183-197, April.
    6. Richard Oberdieck & Martina Wittmann-Hohlbein & Efstratios Pistikopoulos, 2014. "A branch and bound method for the solution of multiparametric mixed integer linear programming problems," Journal of Global Optimization, Springer, vol. 59(2), pages 527-543, July.
    7. GAL, Thomas & NEDOMA, Jozef, 1972. "Multiparametric linear programming," LIDAM Reprints CORE 115, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Dempe, Stephan & Kalashnikov, Vyacheslav & Rios-Mercado, Roger Z., 2005. "Discrete bilevel programming: Application to a natural gas cash-out problem," European Journal of Operational Research, Elsevier, vol. 166(2), pages 469-488, October.
    9. Gerald Brown & Matthew Carlyle & Javier Salmerón & Kevin Wood, 2006. "Defending Critical Infrastructure," Interfaces, INFORMS, vol. 36(6), pages 530-544, December.
    10. Nuno Faísca & Pedro Saraiva & Berç Rustem & Efstratios Pistikopoulos, 2009. "A multi-parametric programming approach for multilevel hierarchical and decentralised optimisation problems," Computational Management Science, Springer, vol. 6(4), pages 377-397, October.
    11. James T. Moore & Jonathan F. Bard, 1990. "The Mixed Integer Linear Bilevel Programming Problem," Operations Research, INFORMS, vol. 38(5), pages 911-921, October.
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