IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v89y2024i1d10.1007_s10589-024-00588-2.html
   My bibliography  Save this article

Handling of constraints in multiobjective blackbox optimization

Author

Listed:
  • Jean Bigeon

    (Nantes Université
    Group for Research in Decision Analysis, GERAD)

  • Sébastien Le Digabel

    (Polytechnique Montréal
    Group for Research in Decision Analysis, GERAD)

  • Ludovic Salomon

    (Polytechnique Montréal
    Group for Research in Decision Analysis, GERAD)

Abstract

This work proposes the integration of two new constraint-handling approaches into the blackbox constrained multiobjective optimization algorithm DMulti-MADS, an extension of the Mesh Adaptive Direct Search (MADS) algorithm for single-objective constrained optimization. The constraints are aggregated into a single constraint violation function which is used either in a two-phase approach, where the search for a feasible point is prioritized if not available before improving the current solution set, or in a progressive barrier approach, where any trial point whose constraint violation function values are above a threshold are rejected. This threshold is progressively decreased along the iterations. As in the single-objective case, it is proved that these two variants generate feasible and/or infeasible sequences which converge either in the feasible case to a set of local Pareto optimal points or in the infeasible case to Clarke stationary points according to the constraint violation function. Computational experiments show that these two approaches are competitive with other state-of-the-art algorithms.

Suggested Citation

  • Jean Bigeon & Sébastien Le Digabel & Ludovic Salomon, 2024. "Handling of constraints in multiobjective blackbox optimization," Computational Optimization and Applications, Springer, vol. 89(1), pages 69-113, September.
    • Handle: RePEc:spr:coopap:v:89:y:2024:i:1:d:10.1007_s10589-024-00588-2
    DOI: 10.1007/s10589-024-00588-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-024-00588-2
    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/s10589-024-00588-2?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. Paul Feliot & Julien Bect & Emmanuel Vazquez, 2017. "A Bayesian approach to constrained single- and multi-objective optimization," Journal of Global Optimization, Springer, vol. 67(1), pages 97-133, January.
    2. Stamatios-Aggelos N. Alexandropoulos & Christos K. Aridas & Sotiris B. Kotsiantis & Michael N. Vrahatis, 2019. "Multi-Objective Evolutionary Optimization Algorithms for Machine Learning: A Recent Survey," Springer Optimization and Its Applications, in: Ioannis C. Demetriou & Panos M. Pardalos (ed.), Approximation and Optimization, pages 35-55, Springer.
    3. Charles Audet & Andrew R. Conn & Sébastien Le Digabel & Mathilde Peyrega, 2018. "A progressive barrier derivative-free trust-region algorithm for constrained optimization," Computational Optimization and Applications, Springer, vol. 71(2), pages 307-329, November.
    4. Audet, Charles & Savard, Gilles & Zghal, Walid, 2010. "A mesh adaptive direct search algorithm for multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 204(3), pages 545-556, August.
    5. Jean Bigeon & Sébastien Le Digabel & Ludovic Salomon, 2021. "DMulti-MADS: mesh adaptive direct multisearch for bound-constrained blackbox multiobjective optimization," Computational Optimization and Applications, Springer, vol. 79(2), pages 301-338, June.
    6. Charles Audet & J. Dennis & Sébastien Digabel, 2010. "Globalization strategies for Mesh Adaptive Direct Search," Computational Optimization and Applications, Springer, vol. 46(2), pages 193-215, June.
    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. Audet, Charles & Bigeon, Jean & Cartier, Dominique & Le Digabel, Sébastien & Salomon, Ludovic, 2021. "Performance indicators in multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 292(2), pages 397-422.
    2. Tommaso Giovannelli & Giampaolo Liuzzi & Stefano Lucidi & Francesco Rinaldi, 2022. "Derivative-free methods for mixed-integer nonsmooth constrained optimization," Computational Optimization and Applications, Springer, vol. 82(2), pages 293-327, June.
    3. Srikanth Reddy, K. & Panwar, Lokesh & Panigrahi, B.K. & Kumar, Rajesh, 2018. "Modeling and analysis of profit based self scheduling of GENCO in electricity markets with renewable energy penetration and emission constraints," Renewable Energy, Elsevier, vol. 116(PA), pages 48-63.
    4. Jean Bigeon & Sébastien Le Digabel & Ludovic Salomon, 2021. "DMulti-MADS: mesh adaptive direct multisearch for bound-constrained blackbox multiobjective optimization," Computational Optimization and Applications, Springer, vol. 79(2), pages 301-338, June.
    5. Suyun Liu & Luis Nunes Vicente, 2022. "Accuracy and fairness trade-offs in machine learning: a stochastic multi-objective approach," Computational Management Science, Springer, vol. 19(3), pages 513-537, July.
    6. J. Martínez & F. Sobral, 2013. "Constrained derivative-free optimization on thin domains," Journal of Global Optimization, Springer, vol. 56(3), pages 1217-1232, July.
    7. Dawei Zhan & Huanlai Xing, 2020. "Expected improvement for expensive optimization: a review," Journal of Global Optimization, Springer, vol. 78(3), pages 507-544, November.
    8. Jiyuan Zhang & Bin Zhang & Shiqian Xu & Qihong Feng & Xianmin Zhang & Derek Elsworth, 2021. "Interpretation of Gas/Water Relative Permeability of Coal Using the Hybrid Bayesian-Assisted History Matching: New Insights," Energies, MDPI, vol. 14(3), pages 1-19, January.
    9. Mariacrocetta Sambito & Stefania Piazza & Gabriele Freni, 2021. "Stochastic Approach for Optimal Positioning of Pumps As Turbines (PATs)," Sustainability, MDPI, vol. 13(21), pages 1-12, November.
    10. Wang, Honggang, 2017. "Multi-objective retrospective optimization using stochastic zigzag search," European Journal of Operational Research, Elsevier, vol. 263(3), pages 946-960.
    11. Cédric Durantin & Julien Marzat & Mathieu Balesdent, 2016. "Analysis of multi-objective Kriging-based methods for constrained global optimization," Computational Optimization and Applications, Springer, vol. 63(3), pages 903-926, April.
    12. Moody Chu & Matthew Lin & Liqi Wang, 2014. "A study of singular spectrum analysis with global optimization techniques," Journal of Global Optimization, Springer, vol. 60(3), pages 551-574, November.
    13. A. L. Custódio & J. F. A. Madeira, 2018. "MultiGLODS: global and local multiobjective optimization using direct search," Journal of Global Optimization, Springer, vol. 72(2), pages 323-345, October.
    14. Amaioua, Nadir & Audet, Charles & Conn, Andrew R. & Le Digabel, Sébastien, 2018. "Efficient solution of quadratically constrained quadratic subproblems within the mesh adaptive direct search algorithm," European Journal of Operational Research, Elsevier, vol. 268(1), pages 13-24.
    15. Pouya Aghaei pour & Jussi Hakanen & Kaisa Miettinen, 2024. "A surrogate-assisted a priori multiobjective evolutionary algorithm for constrained multiobjective optimization problems," Journal of Global Optimization, Springer, vol. 90(2), pages 459-485, October.
    16. Charles Audet & Andrew R. Conn & Sébastien Le Digabel & Mathilde Peyrega, 2018. "A progressive barrier derivative-free trust-region algorithm for constrained optimization," Computational Optimization and Applications, Springer, vol. 71(2), pages 307-329, November.
    17. W. L. Hare & Y. Lucet, 2014. "Derivative-Free Optimization Via Proximal Point Methods," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 204-220, January.
    18. Koziel, Slawomir & Pietrenko-Dabrowska, Anna, 2022. "Constrained multi-objective optimization of compact microwave circuits by design triangulation and pareto front interpolation," European Journal of Operational Research, Elsevier, vol. 299(1), pages 302-312.
    19. Svenson, Joshua & Santner, Thomas, 2016. "Multiobjective optimization of expensive-to-evaluate deterministic computer simulator models," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 250-264.
    20. Duro, João A. & Ozturk, Umud Esat & Oara, Daniel C. & Salomon, Shaul & Lygoe, Robert J. & Burke, Richard & Purshouse, Robin C., 2023. "Methods for constrained optimization of expensive mixed-integer multi-objective problems, with application to an internal combustion engine design problem," European Journal of Operational Research, Elsevier, vol. 307(1), pages 421-446.

    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:coopap:v:89:y:2024:i:1:d:10.1007_s10589-024-00588-2. 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.