IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v412y2022ics0096300321006615.html
   My bibliography  Save this article

Pseudo-feasible solutions in evolutionary bilevel optimization: Test problems and performance assessment

Author

Listed:
  • Mejía-de-Dios, Jesús-Adolfo
  • Mezura-Montes, Efrén
  • Toledo-Hernández, Porfirio

Abstract

This work presents a study about a special class of infeasible solutions called here as pseudo-feasible solutions in bilevel optimization. This work is focused on determining how such solutions can affect the performance of an evolutionary algorithm. After its formal definition, and based on theoretical results, two conditions to detect and deal with them are proposed. Moreover, a novel and scalable set of test problems with characterized pseudo-feasible solutions is introduced. Furthermore, an algorithm designed to solve bilevel optimization problems (BOP) is adapted with the above mentioned conditions and tested in already known test problems and also in the new testbed so as to analyze its performance when compared with state-of-the-art evolutionary approaches for BOPs. The obtained results suggest that the presence of pseudo-feasible solutions can be considered as a source of difficulty in this type of optimization problems, since their presence may lead to incorrect comparisons among algorithms.

Suggested Citation

  • Mejía-de-Dios, Jesús-Adolfo & Mezura-Montes, Efrén & Toledo-Hernández, Porfirio, 2022. "Pseudo-feasible solutions in evolutionary bilevel optimization: Test problems and performance assessment," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    • Handle: RePEc:eee:apmaco:v:412:y:2022:i:c:s0096300321006615
    DOI: 10.1016/j.amc.2021.126577
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300321006615
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2021.126577?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. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    2. Michel Gendreau & Jean-Yves Potvin, 2005. "Metaheuristics in Combinatorial Optimization," Annals of Operations Research, Springer, vol. 140(1), pages 189-213, November.
    3. Fuchang Gao & Lixing Han, 2012. "Implementing the Nelder-Mead simplex algorithm with adaptive parameters," Computational Optimization and Applications, Springer, vol. 51(1), pages 259-277, January.
    4. Jerome Bracken & James T. McGill, 1973. "Mathematical Programs with Optimization Problems in the Constraints," Operations Research, INFORMS, vol. 21(1), pages 37-44, February.
    5. 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.
    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. Xiang Li & Tiesong Hu & Xin Wang & Ali Mahmoud & Xiang Zeng, 2023. "The New Solution Concept to Ill-Posed Bilevel Programming: Non-Antagonistic Pessimistic Solution," Mathematics, MDPI, vol. 11(6), pages 1-13, March.

    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. R. Paulavičius & C. S. Adjiman, 2020. "New bounding schemes and algorithmic options for the Branch-and-Sandwich algorithm," Journal of Global Optimization, Springer, vol. 77(2), pages 197-225, June.
    2. Lei Fang & Hecheng Li, 2013. "Lower bound of cost efficiency measure in DEA with incomplete price information," Journal of Productivity Analysis, Springer, vol. 40(2), pages 219-226, October.
    3. Rebeca Ramirez Acosta & Chathura Wanigasekara & Emilie Frost & Tobias Brandt & Sebastian Lehnhoff & Christof Büskens, 2023. "Integration of Intelligent Neighbourhood Grids to the German Distribution Grid: A Perspective," Energies, MDPI, vol. 16(11), pages 1-16, May.
    4. Bo Zeng, 2020. "A Practical Scheme to Compute the Pessimistic Bilevel Optimization Problem," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 1128-1142, October.
    5. 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.
    6. Carlos Henggeler Antunes & Maria João Alves & Billur Ecer, 2020. "Bilevel optimization to deal with demand response in power grids: models, methods and challenges," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 814-842, October.
    7. 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.
    8. Ashenafi Woldemariam & Semu Kassa, 2015. "Systematic evolutionary algorithm for general multilevel Stackelberg problems with bounded decision variables (SEAMSP)," Annals of Operations Research, Springer, vol. 229(1), pages 771-790, June.
    9. Massol, Olivier & Tchung-Ming, Stéphane & Banal-Estañol, Albert, 2015. "Joining the CCS club! The economics of CO2 pipeline projects," European Journal of Operational Research, Elsevier, vol. 247(1), pages 259-275.
    10. Tamás Kis & András Kovács & Csaba Mészáros, 2021. "On Optimistic and Pessimistic Bilevel Optimization Models for Demand Response Management," Energies, MDPI, vol. 14(8), pages 1-22, April.
    11. Mofidi, Seyed Shahab & Pazour, Jennifer A., 2019. "When is it beneficial to provide freelance suppliers with choice? A hierarchical approach for peer-to-peer logistics platforms," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 1-23.
    12. Christine Tawfik & Sabine Limbourg, 2018. "Pricing Problems in Intermodal Freight Transport: Research Overview and Prospects," Sustainability, MDPI, vol. 10(9), pages 1-22, September.
    13. Casorrán, Carlos & Fortz, Bernard & Labbé, Martine & Ordóñez, Fernando, 2019. "A study of general and security Stackelberg game formulations," European Journal of Operational Research, Elsevier, vol. 278(3), pages 855-868.
    14. Martine Labbé & Alessia Violin, 2016. "Bilevel programming and price setting problems," Annals of Operations Research, Springer, vol. 240(1), pages 141-169, May.
    15. Gang Du & Yi Xia & Roger J. Jiao & Xiaojie Liu, 2019. "Leader-follower joint optimization problems in product family design," Journal of Intelligent Manufacturing, Springer, vol. 30(3), pages 1387-1405, March.
    16. Carvalho, Margarida & Lodi, Andrea, 2023. "A theoretical and computational equilibria analysis of a multi-player kidney exchange program," European Journal of Operational Research, Elsevier, vol. 305(1), pages 373-385.
    17. Andreas Lanz & Gregor Reich & Ole Wilms, 2022. "Adaptive grids for the estimation of dynamic models," Quantitative Marketing and Economics (QME), Springer, vol. 20(2), pages 179-238, June.
    18. Shi, Yi & Deng, Yawen & Wang, Guoan & Xu, Jiuping, 2020. "Stackelberg equilibrium-based eco-economic approach for sustainable development of kitchen waste disposal with subsidy policy: A case study from China," Energy, Elsevier, vol. 196(C).
    19. Lucio Bianco & Massimiliano Caramia & Stefano Giordani & Veronica Piccialli, 2016. "A Game-Theoretic Approach for Regulating Hazmat Transportation," Transportation Science, INFORMS, vol. 50(2), pages 424-438, May.
    20. 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.

    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:eee:apmaco:v:412:y:2022:i:c:s0096300321006615. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.