IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v74y2019i3d10.1007_s10898-018-0668-4.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-018-0668-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10898-018-0668-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Dai, Jingqi & Li, Zongmin, 2023. "An equilibrium approach towards sustainable operation of a modern coal chemical industrial park," Omega, Elsevier, vol. 120(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Richard Oberdieck & Nikolaos A. Diangelakis & Styliani Avraamidou & Efstratios N. Pistikopoulos, 2017. "On unbounded and binary parameters in multi-parametric programming: applications to mixed-integer bilevel optimization and duality theory," Journal of Global Optimization, Springer, vol. 69(3), pages 587-606, November.
    2. Fakhry, Ramy & Hassini, Elkafi & Ezzeldin, Mohamed & El-Dakhakhni, Wael, 2022. "Tri-level mixed-binary linear programming: Solution approaches and application in defending critical infrastructure," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1114-1131.
    3. Iosif Pappas & Nikolaos A. Diangelakis & Efstratios N. Pistikopoulos, 2021. "The exact solution of multiparametric quadratically constrained quadratic programming problems," Journal of Global Optimization, Springer, vol. 79(1), pages 59-85, January.
    4. William M. Kroshl & Shahram Sarkani & Thomas A Mazzuchi, 2015. "Efficient Allocation of Resources for Defense of Spatially Distributed Networks Using Agent‐Based Simulation," Risk Analysis, John Wiley & Sons, vol. 35(9), pages 1690-1705, September.
    5. Tilahun, Surafel Luleseged, 2019. "Feasibility reduction approach for hierarchical decision making with multiple objectives," Operations Research Perspectives, Elsevier, vol. 6(C).
    6. Patrice Gaillardetz & Saeb Hachem, 2019. "Risk-Control Strategies," Papers 1908.02228, arXiv.org.
    7. Matteo Fischetti & Ivana Ljubić & Michele Monaci & Markus Sinnl, 2019. "Interdiction Games and Monotonicity, with Application to Knapsack Problems," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 390-410, April.
    8. J. Spjøtvold & P. Tøndel & T. A. Johansen, 2007. "Continuous Selection and Unique Polyhedral Representation of Solutions to Convex Parametric Quadratic Programs," Journal of Optimization Theory and Applications, Springer, vol. 134(2), pages 177-189, August.
    9. Filippi, Carlo & Romanin-Jacur, Giorgio, 2002. "Multiparametric demand transportation problem," European Journal of Operational Research, Elsevier, vol. 139(2), pages 206-219, June.
    10. Liu, Shaonan & Kong, Nan & Parikh, Pratik & Wang, Mingzheng, 2023. "Optimal trauma care network redesign with government subsidy: A bilevel integer programming approach," Omega, Elsevier, vol. 119(C).
    11. Goldlücke, Susanne & Kranz, Sebastian, 2012. "Infinitely repeated games with public monitoring and monetary transfers," Journal of Economic Theory, Elsevier, vol. 147(3), pages 1191-1221.
    12. Amir Akbari & Paul I. Barton, 2018. "An Improved Multi-parametric Programming Algorithm for Flux Balance Analysis of Metabolic Networks," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 502-537, August.
    13. Stephan Helfrich & Arne Herzel & Stefan Ruzika & Clemens Thielen, 2022. "An approximation algorithm for a general class of multi-parametric optimization problems," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1459-1494, October.
    14. Losada, Chaya & Scaparra, M. Paola & O’Hanley, Jesse R., 2012. "Optimizing system resilience: A facility protection model with recovery time," European Journal of Operational Research, Elsevier, vol. 217(3), pages 519-530.
    15. F. Borrelli & A. Bemporad & M. Morari, 2003. "Geometric Algorithm for Multiparametric Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 118(3), pages 515-540, September.
    16. Chaya Losada & M. Scaparra & Richard Church & Mark Daskin, 2012. "The stochastic interdiction median problem with disruption intensity levels," Annals of Operations Research, Springer, vol. 201(1), pages 345-365, December.
    17. Leonardo Lozano & J. Cole Smith, 2017. "A Value-Function-Based Exact Approach for the Bilevel Mixed-Integer Programming Problem," Operations Research, INFORMS, vol. 65(3), pages 768-786, June.
    18. Charitopoulos, Vassilis M. & Dua, Vivek, 2017. "A unified framework for model-based multi-objective linear process and energy optimisation under uncertainty," Applied Energy, Elsevier, vol. 186(P3), pages 539-548.
    19. 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.
    20. Martina Wittmann-Hohlbein & Efstratios Pistikopoulos, 2013. "On the global solution of multi-parametric mixed integer linear programming problems," Journal of Global Optimization, Springer, vol. 57(1), pages 51-73, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jglopt:v:74:y:2019:i:3:d:10.1007_s10898-018-0668-4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.