IDEAS home Printed from https://ideas.repec.org/a/inm/orijoc/v36y2024i2p327-335.html
   My bibliography  Save this article

BilevelJuMP.jl: Modeling and Solving Bilevel Optimization Problems in Julia

Author

Listed:
  • Joaquim Dias Garcia

    (PSR, Rio de Janeiro, Rio de Janeiro 22250-040, Brazil; LAMPS at Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Rio de Janeiro 22451-900, Brazil)

  • Guilherme Bodin

    (PSR, Rio de Janeiro, Rio de Janeiro 22250-040, Brazil; LAMPS at Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Rio de Janeiro 22451-900, Brazil)

  • Alexandre Street

    (LAMPS at Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Rio de Janeiro 22451-900, Brazil)

Abstract

In this paper, we present BilevelJuMP.jl, a new Julia package to support bilevel optimization within the JuMP framework. The package is a Julia library that enables the user to describe both upper and lower-level optimization problems using the JuMP algebraic syntax. Because of the generality and flexibility that our library inherits from JuMP’s syntax, our package allows users to model bilevel optimization problems with conic constraints in the lower level and all constraints supported by JuMP in the upper level including conic, quadratic, and nonlinear constraints. Moreover, the models defined with the syntax from BilevelJuMP.jl can be solved by multiple techniques that are based on reformulations as mathematical programs with equilibrium constraints (MPEC). Manipulations on the original problem data are possible due to MathOptInterface.jl’s structures and Dualization.jl features. Hence, the proposed package allows quick modeling, deployment, and thereby experimenting with bilevel models based on off-the-shelf mixed-integer linear programming and nonlinear solvers.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:orijoc:v:36:y:2024:i:2:p:327-335
    DOI: 10.1287/ijoc.2022.0135
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/ijoc.2022.0135
    Download Restriction: no
    File URL: https://libkey.io/10.1287/ijoc.2022.0135?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
    ---><---

    References listed on IDEAS

    as
    1. Martine Labbé & Patrice Marcotte & Gilles Savard, 1998. "A Bilevel Model of Taxation and Its Application to Optimal Highway Pricing," Management Science, INFORMS, vol. 44(12-Part-1), pages 1608-1622, December.
    2. Pietro Belotti & Pierre Bonami & Matteo Fischetti & Andrea Lodi & Michele Monaci & Amaya Nogales-Gómez & Domenico Salvagnin, 2016. "On handling indicator constraints in mixed integer programming," Computational Optimization and Applications, Springer, vol. 65(3), pages 545-566, December.
    3. David Pozo & Enzo Sauma & Javier Contreras, 2017. "Basic theoretical foundations and insights on bilevel models and their applications to power systems," Annals of Operations Research, Springer, vol. 254(1), pages 303-334, July.
    4. Jerome Bracken & James T. McGill, 1974. "Defense Applications of Mathematical Programs with Optimization Problems in the Constraints," Operations Research, INFORMS, vol. 22(5), pages 1086-1096, October.
    5. 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.
    6. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    7. M. Hosein Zare & Juan S. Borrero & Bo Zeng & Oleg A. Prokopyev, 2019. "A note on linearized reformulations for a class of bilevel linear integer problems," Annals of Operations Research, Springer, vol. 272(1), pages 99-117, January.
    8. Vyacheslav V. Kalashnikov & Stephan Dempe & Gerardo A. Pérez-Valdés & Nataliya I. Kalashnykova & José-Fernando Camacho-Vallejo, 2015. "Bilevel Programming and Applications," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-16, March.
    9. Oscar Dowson & Lea Kapelevich, 2021. "SDDP.jl : A Julia Package for Stochastic Dual Dynamic Programming," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 27-33, January.
    10. 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.
    11. Thomas Kleinert & Martin Schmidt, 2023. "Why there is no need to use a big-M in linear bilevel optimization: a computational study of two ready-to-use approaches," Computational Management Science, Springer, vol. 20(1), pages 1-12, December.
    12. Miles Lubin & Iain Dunning, 2015. "Computing in Operations Research Using Julia," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 238-248, May.
    13. Dajun Yue & Jiyao Gao & Bo Zeng & Fengqi You, 2019. "A projection-based reformulation and decomposition algorithm for global optimization of a class of mixed integer bilevel linear programs," Journal of Global Optimization, Springer, vol. 73(1), pages 27-57, January.
    Full references (including those not matched with items on IDEAS)

    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. Çalcı, Baturay & Leibowicz, Benjamin D. & Bard, Jonathan F. & Jayadev, Gopika G., 2024. "A bilevel approach to multi-period natural gas pricing and investment in gas-consuming infrastructure," Energy, Elsevier, vol. 303(C).
    2. Rahman Khorramfar & Osman Y. Özaltın & Karl G. Kempf & Reha Uzsoy, 2022. "Managing Product Transitions: A Bilevel Programming Approach," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2828-2844, September.
    3. 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).
    4. Juan S. Borrero & Oleg A. Prokopyev & Denis Sauré, 2019. "Sequential Interdiction with Incomplete Information and Learning," Operations Research, INFORMS, vol. 67(1), pages 72-89, January.
    5. 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.
    6. Nicoletti, Jack & You, Fengqi, 2020. "Multiobjective economic and environmental optimization of global crude oil purchase and sale planning with noncooperative stakeholders," Applied Energy, Elsevier, vol. 259(C).
    7. Ankur Sinha & Zhichao Lu & Kalyanmoy Deb & Pekka Malo, 2020. "Bilevel optimization based on iterative approximation of multiple mappings," Journal of Heuristics, Springer, vol. 26(2), pages 151-185, April.
    8. Allan Peñafiel Mera & Chandra Balijepalli, 2020. "Towards improving resilience of cities: an optimisation approach to minimising vulnerability to disruption due to natural disasters under budgetary constraints," Transportation, Springer, vol. 47(4), pages 1809-1842, August.
    9. Steven Gabriel & Sauleh Siddiqui & Antonio Conejo & Carlos Ruiz, 2013. "Solving Discretely-Constrained Nash–Cournot Games with an Application to Power Markets," Networks and Spatial Economics, Springer, vol. 13(3), pages 307-326, September.
    10. Zhao, Ning & You, Fengqi, 2019. "Dairy waste-to-energy incentive policy design using Stackelberg-game-based modeling and optimization," Applied Energy, Elsevier, vol. 254(C).
    11. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    12. Polyxeni-Margarita Kleniati & Claire Adjiman, 2014. "Branch-and-Sandwich: a deterministic global optimization algorithm for optimistic bilevel programming problems. Part I: Theoretical development," Journal of Global Optimization, Springer, vol. 60(3), pages 425-458, November.
    13. Beraldi, Patrizia & Khodaparasti, Sara, 2023. "Designing electricity tariffs in the retail market: A stochastic bi-level approach," International Journal of Production Economics, Elsevier, vol. 257(C).
    14. Liu, Shaonan & Wang, Mingzheng & Kong, Nan & Hu, Xiangpei, 2021. "An enhanced branch-and-bound algorithm for bilevel integer linear programming," European Journal of Operational Research, Elsevier, vol. 291(2), pages 661-679.
    15. M. Köppe & M. Queyranne & C. T. Ryan, 2010. "Parametric Integer Programming Algorithm for Bilevel Mixed Integer Programs," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 137-150, July.
    16. Martin Weibelzahl & Alexandra Märtz, 2020. "Optimal storage and transmission investments in a bilevel electricity market model," Annals of Operations Research, Springer, vol. 287(2), pages 911-940, April.
    17. Xi, Haoning & Aussel, Didier & Liu, Wei & Waller, S.Travis. & Rey, David, 2024. "Single-leader multi-follower games for the regulation of two-sided mobility-as-a-service markets," European Journal of Operational Research, Elsevier, vol. 317(3), pages 718-736.
    18. Gabriel Lopez Zenarosa & Oleg A. Prokopyev & Eduardo L. Pasiliao, 2021. "On exact solution approaches for bilevel quadratic 0–1 knapsack problem," Annals of Operations Research, Springer, vol. 298(1), pages 555-572, March.
    19. Acuna, Jorge A. & Zayas-Castro, Jose L. & Feijoo, Felipe, 2022. "A bilevel Nash-in-Nash model for hospital mergers: A key to affordable care," Socio-Economic Planning Sciences, Elsevier, vol. 83(C).
    20. Jacquet, Quentin & van Ackooij, Wim & Alasseur, Clémence & Gaubert, Stéphane, 2024. "Quadratic regularization of bilevel pricing problems and application to electricity retail markets," European Journal of Operational Research, Elsevier, vol. 313(3), pages 841-857.

    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:inm:orijoc:v:36:y:2024:i:2:p:327-335. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.