IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v90y2024i4d10.1007_s10898-024-01422-z.html
   My bibliography  Save this article

Robust bilevel optimization for near-optimal lower-level solutions

Author

Listed:
  • Mathieu Besançon

    (Université Grenoble Alpes, Inria, LIG)

  • Miguel F. Anjos

    (University of Edinburgh
    GERAD)

  • Luce Brotcorne

    (Centre Inria de l’Université de Lille, Inria, France and UMR 9189 - CRIStAL, Univ. Lille, CNRS)

Abstract

Bilevel optimization problems embed the optimality of a subproblem as a constraint of another optimization problem. We introduce the concept of near-optimality robustness for bilevel optimization, protecting the upper-level solution feasibility from limited deviations from the optimal solution at the lower level. General properties and necessary conditions for the existence of solutions are derived for near-optimal robust versions of general bilevel optimization problems. A duality-based solution method is defined when the lower level is convex, leveraging the methodology from the robust and bilevel literature. Numerical results assess the efficiency of exact and heuristic methods and the impact of valid inequalities on the solution time.

Suggested Citation

  • Mathieu Besançon & Miguel F. Anjos & Luce Brotcorne, 2024. "Robust bilevel optimization for near-optimal lower-level solutions," Journal of Global Optimization, Springer, vol. 90(4), pages 813-842, December.
  • Handle: RePEc:spr:jglopt:v:90:y:2024:i:4:d:10.1007_s10898-024-01422-z
    DOI: 10.1007/s10898-024-01422-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-024-01422-z
    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/s10898-024-01422-z?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. Christoph Buchheim & Dorothee Henke, 2022. "The robust bilevel continuous knapsack problem with uncertain coefficients in the follower’s objective," Journal of Global Optimization, Springer, vol. 83(4), pages 803-824, August.
    2. Beck, Yasmine & Ljubić, Ivana & Schmidt, Martin, 2023. "A survey on bilevel optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 311(2), pages 401-426.
    3. Gabrel, Virginie & Murat, Cécile & Thiele, Aurélie, 2014. "Recent advances in robust optimization: An overview," European Journal of Operational Research, Elsevier, vol. 235(3), pages 471-483.
    4. M. Hosein Zare & Osman Y. Özaltın & Oleg A. Prokopyev, 2018. "On a class of bilevel linear mixed-integer programs in adversarial settings," Journal of Global Optimization, Springer, vol. 71(1), pages 91-113, May.
    5. Holger Scheel & Stefan Scholtes, 2000. "Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity," Mathematics of Operations Research, INFORMS, vol. 25(1), pages 1-22, February.
    6. Still, G., 1999. "Generalized semi-infinite programming: Theory and methods," European Journal of Operational Research, Elsevier, vol. 119(2), pages 301-313, December.
    7. M. Hosein Zare & Oleg A. Prokopyev & Denis Sauré, 2020. "On Bilevel Optimization with Inexact Follower," Decision Analysis, INFORMS, vol. 17(1), pages 74-95, March.
    8. Benoît Legat & Oscar Dowson & Joaquim Dias Garcia & Miles Lubin, 2022. "MathOptInterface: A Data Structure for Mathematical Optimization Problems," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 672-689, March.
    9. S. Siddiqui & S. Gabriel, 2013. "An SOS1-Based Approach for Solving MPECs with a Natural Gas Market Application," Networks and Spatial Economics, Springer, vol. 13(2), pages 205-227, June.
    10. Rahmaniani, Ragheb & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2017. "The Benders decomposition algorithm: A literature review," European Journal of Operational Research, Elsevier, vol. 259(3), pages 801-817.
    11. Stephan Dempe, 2020. "Bilevel Optimization: Theory, Algorithms, Applications and a Bibliography," Springer Optimization and Its Applications, in: Stephan Dempe & Alain Zemkoho (ed.), Bilevel Optimization, chapter 0, pages 581-672, Springer.
    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. Faraji, Jamal & Allard, Julien & Vallée, François & De Grève, Zacharie, 2025. "On the limited observability of energy community members: An uncertainty-aware near-optimal bilevel programming approach," Applied Energy, Elsevier, vol. 381(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. Beck, Yasmine & Ljubić, Ivana & Schmidt, Martin, 2023. "A survey on bilevel optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 311(2), pages 401-426.
    2. Stein, Oliver, 2012. "How to solve a semi-infinite optimization problem," European Journal of Operational Research, Elsevier, vol. 223(2), pages 312-320.
    3. Birbil, S.I. & Bouza, G. & Frenk, J.B.G. & Still, G.J., 2003. "Equilibrium Constrained Optimization Problems," Econometric Institute Research Papers ERS-2003-085-LIS, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    4. Zhang, Fang & Lu, Jian & Hu, Xiaojian & Meng, Qiang, 2023. "Integrated deployment of dedicated lane and roadside unit considering uncertain road capacity under the mixed-autonomy traffic environment," Transportation Research Part B: Methodological, Elsevier, vol. 174(C).
    5. Ilker Birbil, S. & Gürkan, G. & Listes, O.L., 2004. "Simulation-Based Solution of Stochastic Mathematical Programs with Complementarity Constraints : Sample-Path Analysis," Discussion Paper 2004-25, Tilburg University, Center for Economic Research.
    6. Birbil, S.I. & Bouza, G. & Frenk, J.B.G. & Still, G.J., 2003. "Equilibrium Constrained Optimization Problems," ERIM Report Series Research in Management ERS-2003-085-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    7. Joaquim Dias Garcia & Guilherme Bodin & Alexandre Street, 2024. "BilevelJuMP.jl: Modeling and Solving Bilevel Optimization Problems in Julia," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 327-335, March.
    8. Yasmine Beck & Daniel Bienstock & Martin Schmidt & Johannes Thürauf, 2023. "On a Computationally Ill-Behaved Bilevel Problem with a Continuous and Nonconvex Lower Level," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 428-447, July.
    9. Darshan Chauhan & Avinash Unnikrishnan & Stephen D. Boyles & Priyadarshan N. Patil, 2024. "Robust maximum flow network interdiction considering uncertainties in arc capacity and resource consumption," Annals of Operations Research, Springer, vol. 335(2), pages 689-725, April.
    10. Benita, Francisco & López-Ramos, Francisco & Nasini, Stefano, 2019. "A bi-level programming approach for global investment strategies with financial intermediation," European Journal of Operational Research, Elsevier, vol. 274(1), pages 375-390.
    11. Lou, Yingyan & Yin, Yafeng & Lawphongpanich, Siriphong, 2010. "Robust congestion pricing under boundedly rational user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 15-28, January.
    12. Ilker Birbil, S. & Gürkan, G. & Listes, O.L., 2004. "Simulation-Based Solution of Stochastic Mathematical Programs with Complementarity Constraints : Sample-Path Analysis," Other publications TiSEM ab097838-6408-404d-aaeb-f, Tilburg University, School of Economics and Management.
    13. G. Constante-Flores & A. J. Conejo & S. Constante-Flores, 2022. "Solving certain complementarity problems in power markets via convex programming," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 465-491, October.
    14. Ş. İlker Birbil & Gül Gürkan & Ovidiu Listeş, 2006. "Solving Stochastic Mathematical Programs with Complementarity Constraints Using Simulation," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 739-760, November.
    15. Julia Grübel & Richard Krug & Martin Schmidt & Winnifried Wollner, 2023. "A Successive Linear Relaxation Method for MINLPs with Multivariate Lipschitz Continuous Nonlinearities," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 1077-1117, September.
    16. Jann Michael Weinand & Kenneth Sorensen & Pablo San Segundo & Max Kleinebrahm & Russell McKenna, 2020. "Research trends in combinatorial optimisation," Papers 2012.01294, arXiv.org.
    17. Chiou, Suh-Wen, 2024. "A learning optimization for resilience enhancement of risk-informed traffic control system with hazardous materials transportation under uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 252(C).
    18. Birbil, S.I. & Bouza, G. & Frenk, J.B.G. & Still, G., 2006. "Equilibrium constrained optimization problems," European Journal of Operational Research, Elsevier, vol. 169(3), pages 1108-1127, March.
    19. Xiaoqi Yang & Zhangyou Chen & Jinchuan Zhou, 2016. "Optimality Conditions for Semi-Infinite and Generalized Semi-Infinite Programs Via Lower Order Exact Penalty Functions," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 984-1012, June.
    20. Cambier, Adrien & Chardy, Matthieu & Figueiredo, Rosa & Ouorou, Adam & Poss, Michael, 2022. "Optimizing subscriber migrations for a telecommunication operator in uncertain context," European Journal of Operational Research, Elsevier, vol. 298(1), pages 308-321.

    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:90:y:2024:i:4:d:10.1007_s10898-024-01422-z. 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.