IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v79y2021i2d10.1007_s10589-021-00272-9.html
   My bibliography  Save this article

DMulti-MADS: mesh adaptive direct multisearch for bound-constrained blackbox multiobjective optimization

Author

Listed:
  • Jean Bigeon

    (GERAD and Département de mathématiques et génie industriel
    CNRS, LS2N)

  • Sébastien Le Digabel

    (GERAD and Département de mathématiques et génie industriel)

  • Ludovic Salomon

    (GERAD and Département de mathématiques et génie industriel)

Abstract

The context of this research is multiobjective optimization where conflicting objectives are present. In this work, these objectives are only available as the outputs of a blackbox for which no derivative information is available. This work proposes a new extension of the mesh adaptive direct search (MADS) algorithm to multiobjective derivative-free optimization with bound constraints. This method does not aggregate objectives and keeps a list of non dominated points which converges to a (local) Pareto set as long as the algorithm unfolds. As in the single-objective optimization MADS algorithm, this method is built around a search step and a poll step. Under classical direct search assumptions, it is proved that the so-called DMulti-MADS algorithm generates multiple subsequences of iterates which converge to a set of local Pareto stationary points. Finally, computational experiments suggest that this approach is competitive compared to the state-of-the-art algorithms for multiobjective blackbox optimization.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:79:y:2021:i:2:d:10.1007_s10589-021-00272-9
    DOI: 10.1007/s10589-021-00272-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-021-00272-9
    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/s10589-021-00272-9?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. G. Cocchi & G. Liuzzi & A. Papini & M. Sciandrone, 2018. "An implicit filtering algorithm for derivative-free multiobjective optimization with box constraints," Computational Optimization and Applications, Springer, vol. 69(2), pages 267-296, March.
    2. 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.
    3. Sergeyev, Yaroslav D. & Kvasov, Dmitri E. & Mukhametzhanov, Marat S., 2017. "Operational zones for comparing metaheuristic and deterministic one-dimensional global optimization algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 141(C), pages 96-109.
    4. 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.
    5. 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.
    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. Wenyu Wang & Taimoor Akhtar & Christine A. Shoemaker, 2022. "Integrating $$\varepsilon $$ ε -dominance and RBF surrogate optimization for solving computationally expensive many-objective optimization problems," Journal of Global Optimization, Springer, vol. 82(4), pages 965-992, April.
    2. C. P. Brás & A. L. Custódio, 2020. "On the use of polynomial models in multiobjective directional direct search," Computational Optimization and Applications, Springer, vol. 77(3), pages 897-918, December.
    3. Alberto Lovison & Kaisa Miettinen, 2021. "On the Extension of the DIRECT Algorithm to Multiple Objectives," Journal of Global Optimization, Springer, vol. 79(2), pages 387-412, February.
    4. Zandieh, Fatemeh & Ghannadpour, Seyed Farid, 2023. "A comprehensive risk assessment view on interval type-2 fuzzy controller for a time-dependent HazMat routing problem," European Journal of Operational Research, Elsevier, vol. 305(2), pages 685-707.
    5. Dalila B. M. M. Fontes & S. Mahdi Homayouni, 2023. "A bi-objective multi-population biased random key genetic algorithm for joint scheduling quay cranes and speed adjustable vehicles in container terminals," Flexible Services and Manufacturing Journal, Springer, vol. 35(1), pages 241-268, March.
    6. Mesquita-Cunha, Mariana & Figueira, José Rui & Barbosa-Póvoa, Ana Paula, 2023. "New ϵ−constraint methods for multi-objective integer linear programming: A Pareto front representation approach," European Journal of Operational Research, Elsevier, vol. 306(1), pages 286-307.
    7. Gaggero, Mauro & Paolucci, Massimo & Ronco, Roberto, 2023. "Exact and heuristic solution approaches for energy-efficient identical parallel machine scheduling with time-of-use costs," European Journal of Operational Research, Elsevier, vol. 311(3), pages 845-866.
    8. Ducardo L. Molina & Juan Ricardo Vidal Medina & Alexis Sagastume Gutiérrez & Juan J. Cabello Eras & Jesús A. Lopez & Simón Hincapie & Enrique C. Quispe, 2023. "Multiobjective Optimization of the Energy Efficiency and the Steam Flow in a Bagasse Boiler," Sustainability, MDPI, vol. 15(14), pages 1-17, July.
    9. 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.
    10. Francisco Jonatas Siqueira Coelho & Allan Rivalles Souza Feitosa & André Luís Michels Alcântara & Kaifeng Li & Ronaldo Ferreira Lima & Victor Rios Silva & Abel Guilhermino da Silva-Filho, 2023. "HyMOTree: Automatic Hyperparameters Tuning for Non-Technical Loss Detection Based on Multi-Objective and Tree-Based Algorithms," Energies, MDPI, vol. 16(13), pages 1-22, June.
    11. Gholamreza Shojatalab & Seyed Hadi Nasseri & Iraj Mahdavi, 2023. "New multi-objective optimization model for tourism systems with fuzzy data and new approach developed epsilon constraint method," OPSEARCH, Springer;Operational Research Society of India, vol. 60(3), pages 1360-1385, September.
    12. Wang, Honggang, 2017. "Multi-objective retrospective optimization using stochastic zigzag search," European Journal of Operational Research, Elsevier, vol. 263(3), pages 946-960.
    13. 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.
    14. Yong Wang & Kunzhao Wang & Gaige Wang, 2022. "Neural Network Algorithm with Dropout Using Elite Selection," Mathematics, MDPI, vol. 10(11), pages 1-17, May.
    15. Matteo Lapucci & Pierluigi Mansueto, 2023. "A limited memory Quasi-Newton approach for multi-objective optimization," Computational Optimization and Applications, Springer, vol. 85(1), pages 33-73, May.
    16. 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.
    17. Wang Chen & Xinmin Yang & Yong Zhao, 2023. "Conditional gradient method for vector optimization," Computational Optimization and Applications, Springer, vol. 85(3), pages 857-896, July.
    18. 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.
    19. Raka Jovanovic & Antonio P. Sanfilippo & Stefan Voß, 2022. "Fixed set search applied to the multi-objective minimum weighted vertex cover problem," Journal of Heuristics, Springer, vol. 28(4), pages 481-508, August.
    20. G. Cocchi & G. Liuzzi & S. Lucidi & M. Sciandrone, 2020. "On the convergence of steepest descent methods for multiobjective optimization," Computational Optimization and Applications, Springer, vol. 77(1), pages 1-27, 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:coopap:v:79:y:2021:i:2:d:10.1007_s10589-021-00272-9. 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.