IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v200y2020ics0951832019301516.html
   My bibliography  Save this article

Robust optimization: A kriging-based multi-objective optimization approach

Author

Listed:
  • Ribaud, Mélina
  • Blanchet-Scalliet, Christophette
  • Helbert, Céline
  • Gillot, Frédéric

Abstract

In the robust shape optimization context, the evaluation cost of numerical models is reduced by the use of a response surface. Multi-objective methodologies for robust optimization that consist in simultaneously minimizing the expectation and variance of a function have already been developed to answer to this question. However, efficient estimation in the framework of time-consuming simulation has not been completely explored. In this paper, a robust optimization procedure based on Taylor expansion, kriging prediction and a genetic NSGA-II algorithm is proposed. The two objectives are the Taylor expansion of expectation and variance. The kriging technique is chosen to surrogate the function and its derivatives. Afterwards, NSGA-II is performed on kriging response surfaces or kriging expected improvements to construct a Pareto front. One point or a batch of points is chosen carefully to enrich the learning set of the model. When the budget is reached the non-dominated points provide designs that make compromises between optimization and robustness. Seven relevant strategies based on this main procedure are detailed and compared in two test functions (2D and 6D). In each case, the results are compared when the derivatives are observed and when they are not. The procedure is also applied to an industrial case study where the objective is to optimize the shape of a motor fan.

Suggested Citation

  • Ribaud, Mélina & Blanchet-Scalliet, Christophette & Helbert, Céline & Gillot, Frédéric, 2020. "Robust optimization: A kriging-based multi-objective optimization approach," Reliability Engineering and System Safety, Elsevier, vol. 200(C).
  • Handle: RePEc:eee:reensy:v:200:y:2020:i:c:s0951832019301516
    DOI: 10.1016/j.ress.2020.106913
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832019301516
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ress.2020.106913?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. Dupuy, Delphine & Helbert, Céline & Franco, Jessica, 2015. "DiceDesign and DiceEval: Two R Packages for Design and Analysis of Computer Experiments," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 65(i11).
    2. Julien Marzat & Eric Walter & Hélène Piet-Lahanier, 2013. "Worst-case global optimization of black-box functions through Kriging and relaxation," Journal of Global Optimization, Springer, vol. 55(4), pages 707-727, April.
    3. Janis Janusevskis & Rodolphe Le Riche, 2013. "Simultaneous kriging-based estimation and optimization of mean response," Journal of Global Optimization, Springer, vol. 55(2), pages 313-336, February.
    4. 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.
    5. 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.
    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. Li, Xiaoke & Zhu, Heng & Chen, Zhenzhong & Ming, Wuyi & Cao, Yang & He, Wenbin & Ma, Jun, 2022. "Limit state Kriging modeling for reliability-based design optimization through classification uncertainty quantification," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
    2. You, Geonhwa, 2024. "A comprehensive approach for calibrating anthropogenic effects on atmosphere degradation," Renewable and Sustainable Energy Reviews, Elsevier, vol. 191(C).
    3. Xiaodong Song & Mingyang Li & Zhitao Li & Fang Liu, 2021. "Global Optimization Algorithm Based on Kriging Using Multi-Point Infill Sampling Criterion and Its Application in Transportation System," Sustainability, MDPI, vol. 13(19), pages 1-17, September.
    4. Marrel, Amandine & Iooss, Bertrand, 2024. "Probabilistic surrogate modeling by Gaussian process: A new estimation algorithm for more robust prediction," Reliability Engineering and System Safety, Elsevier, vol. 247(C).
    5. Teixeira, Rui & Martinez-Pastor, Beatriz & Nogal, Maria & O’Connor, Alan, 2021. "Reliability analysis using a multi-metamodel complement-basis approach," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    6. Marrel, Amandine & Iooss, Bertrand, 2024. "Probabilistic surrogate modeling by Gaussian process: A review on recent insights in estimation and validation," Reliability Engineering and System Safety, Elsevier, vol. 247(C).
    7. Nan, Hang & Liang, Hao & Di, Haoyuan & Li, Hongshuang, 2024. "A gradient-assisted learning strategy of Kriging model for robust design optimization," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    8. Rivier, M. & Congedo, P.M., 2022. "Surrogate-Assisted Bounding-Box approach applied to constrained multi-objective optimisation under uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 217(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. Lauvernet, Claire & Helbert, Céline, 2020. "Metamodeling methods that incorporate qualitative variables for improved design of vegetative filter strips," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    2. 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.
    3. Sarhadi, Hassan & Naoum-Sawaya, Joe & Verma, Manish, 2020. "A robust optimization approach to locating and stockpiling marine oil-spill response facilities," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 141(C).
    4. Jeong, Jaehee & Premsankar, Gopika & Ghaddar, Bissan & Tarkoma, Sasu, 2024. "A robust optimization approach for placement of applications in edge computing considering latency uncertainty," Omega, Elsevier, vol. 126(C).
    5. Baker, Erin & Bosetti, Valentina & Salo, Ahti, 2016. "Finding Common Ground when Experts Disagree: Belief Dominance over Portfolios of Alternatives," MITP: Mitigation, Innovation and Transformation Pathways 243147, Fondazione Eni Enrico Mattei (FEEM).
    6. Qiu, Ruozhen & Sun, Minghe & Lim, Yun Fong, 2017. "Optimizing (s, S) policies for multi-period inventory models with demand distribution uncertainty: Robust dynamic programing approaches," European Journal of Operational Research, Elsevier, vol. 261(3), pages 880-892.
    7. Chassein, André & Goerigk, Marc, 2018. "Compromise solutions for robust combinatorial optimization with variable-sized uncertainty," European Journal of Operational Research, Elsevier, vol. 269(2), pages 544-555.
    8. Maillet, Bertrand & Tokpavi, Sessi & Vaucher, Benoit, 2015. "Global minimum variance portfolio optimisation under some model risk: A robust regression-based approach," European Journal of Operational Research, Elsevier, vol. 244(1), pages 289-299.
    9. Morteza Davari & Erik Demeulemeester, 2019. "The proactive and reactive resource-constrained project scheduling problem," Journal of Scheduling, Springer, vol. 22(2), pages 211-237, April.
    10. Zhang, Wei & (Ato) Xu, Wangtu, 2017. "Simulation-based robust optimization for the schedule of single-direction bus transit route: The design of experiment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 106(C), pages 203-230.
    11. Antonio G. Martín & Manuel Díaz-Madroñero & Josefa Mula, 2020. "Master production schedule using robust optimization approaches in an automobile second-tier supplier," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(1), pages 143-166, March.
    12. Chassein, André & Goerigk, Marc & Kurtz, Jannis & Poss, Michael, 2019. "Faster algorithms for min-max-min robustness for combinatorial problems with budgeted uncertainty," European Journal of Operational Research, Elsevier, vol. 279(2), pages 308-319.
    13. Jiang, Sheng-Long & Wang, Meihong & Bogle, I. David L., 2023. "Plant-wide byproduct gas distribution under uncertainty in iron and steel industry via quantile forecasting and robust optimization," Applied Energy, Elsevier, vol. 350(C).
    14. Shunichi Ohmori, 2021. "A Predictive Prescription Using Minimum Volume k -Nearest Neighbor Enclosing Ellipsoid and Robust Optimization," Mathematics, MDPI, vol. 9(2), pages 1-16, January.
    15. Lamas, Patricio & Goycoolea, Marcos & Pagnoncelli, Bernardo & Newman, Alexandra, 2024. "A target-time-windows technique for project scheduling under uncertainty," European Journal of Operational Research, Elsevier, vol. 314(2), pages 792-806.
    16. Metzker Soares, Paula & Thevenin, Simon & Adulyasak, Yossiri & Dolgui, Alexandre, 2024. "Adaptive robust optimization for lot-sizing under yield uncertainty," European Journal of Operational Research, Elsevier, vol. 313(2), pages 513-526.
    17. Walid Ben-Ameur & Adam Ouorou & Guanglei Wang & Mateusz Żotkiewicz, 2018. "Multipolar robust optimization," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(4), pages 395-434, December.
    18. Boge, Sven & Goerigk, Marc & Knust, Sigrid, 2020. "Robust optimization for premarshalling with uncertain priority classes," European Journal of Operational Research, Elsevier, vol. 287(1), pages 191-210.
    19. Hanks, Robert W. & Weir, Jeffery D. & Lunday, Brian J., 2017. "Robust goal programming using different robustness echelons via norm-based and ellipsoidal uncertainty sets," European Journal of Operational Research, Elsevier, vol. 262(2), pages 636-646.
    20. Postek, Krzysztof & den Hertog, Dick & Kind, J. & Pustjens, Chris, 2016. "Adjustable Robust Strategies for Flood Protection," Discussion Paper 2016-038, Tilburg University, Center for Economic Research.

    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:reensy:v:200:y:2020:i:c:s0951832019301516. 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/reliability-engineering-and-system-safety .

    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.