IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v63y2016i3p903-926.html
   My bibliography  Save this article

Analysis of multi-objective Kriging-based methods for constrained global optimization

Author

Listed:
  • Cédric Durantin
  • Julien Marzat
  • Mathieu Balesdent

Abstract

Metamodeling, i.e., building surrogate models to expensive black-box functions, is an interesting way to reduce the computational burden for optimization purpose. Kriging is a popular metamodel based on Gaussian process theory, whose statistical properties have been exploited to build efficient global optimization algorithms. Single and multi-objective extensions have been proposed to deal with constrained optimization when the constraints are also evaluated numerically. This paper first compares these methods on a representative analytical benchmark. A new multi-objective approach is then proposed to also take into account the prediction accuracy of the constraints. A numerical evaluation is provided on the same analytical benchmark and a realistic aerospace case study. Copyright Springer Science+Business Media New York 2016

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:63:y:2016:i:3:p:903-926
    DOI: 10.1007/s10589-015-9789-6
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-015-9789-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10589-015-9789-6?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. Kleijnen, Jack P.C., 2009. "Kriging metamodeling in simulation: A review," European Journal of Operational Research, Elsevier, vol. 192(3), pages 707-716, February.
    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.
    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. Kleijnen, Jack & van Nieuwenhuyse, I. & van Beers, W.C.M., 2022. "Constrained Optimization in Simulation : Efficient Global Optimization and Karush-Kuhn-Tucker Conditions (revision of 2021-031)," Discussion Paper 2022-015, Tilburg University, Center for Economic Research.
    2. Dawei Zhan & Huanlai Xing, 2020. "Expected improvement for expensive optimization: a review," Journal of Global Optimization, Springer, vol. 78(3), pages 507-544, November.
    3. Angelina Roche, 2018. "Local optimization of black-box functions with high or infinite-dimensional inputs: application to nuclear safety," Computational Statistics, Springer, vol. 33(1), pages 467-485, March.
    4. Shengguan Xu & Hongquan Chen, 2018. "Nash game based efficient global optimization for large-scale design problems," Journal of Global Optimization, Springer, vol. 71(2), pages 361-381, June.
    5. Yaohui Li & Jingfang Shen & Ziliang Cai & Yizhong Wu & Shuting Wang, 2021. "A Kriging-Assisted Multi-Objective Constrained Global Optimization Method for Expensive Black-Box Functions," Mathematics, MDPI, vol. 9(2), pages 1-20, January.
    6. Julien Pelamatti & Loïc Brevault & Mathieu Balesdent & El-Ghazali Talbi & Yannick Guerin, 2019. "Efficient global optimization of constrained mixed variable problems," Journal of Global Optimization, Springer, vol. 73(3), pages 583-613, March.
    7. Lei, Fei & Gu, Ke & Du, Bin & Xie, Xiaoping, 2017. "Comprehensive global optimization of an implicit constrained multi-physics system for electric vehicles with in-wheel motors," Energy, Elsevier, vol. 139(C), pages 523-534.

    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. Tian, Wei & Song, Jitian & Li, Zhanyong & de Wilde, Pieter, 2014. "Bootstrap techniques for sensitivity analysis and model selection in building thermal performance analysis," Applied Energy, Elsevier, vol. 135(C), pages 320-328.
    2. Wang, Zequn & Wang, Pingfeng, 2015. "A double-loop adaptive sampling approach for sensitivity-free dynamic reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 346-356.
    3. Puppo, L. & Pedroni, N. & Maio, F. Di & Bersano, A. & Bertani, C. & Zio, E., 2021. "A Framework based on Finite Mixture Models and Adaptive Kriging for Characterizing Non-Smooth and Multimodal Failure Regions in a Nuclear Passive Safety System," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    4. Zio, E., 2018. "The future of risk assessment," Reliability Engineering and System Safety, Elsevier, vol. 177(C), pages 176-190.
    5. Wen, Zhixun & Pei, Haiqing & Liu, Hai & Yue, Zhufeng, 2016. "A Sequential Kriging reliability analysis method with characteristics of adaptive sampling regions and parallelizability," Reliability Engineering and System Safety, Elsevier, vol. 153(C), pages 170-179.
    6. Gaspar, B. & Teixeira, A.P. & Guedes Soares, C., 2017. "Adaptive surrogate model with active refinement combining Kriging and a trust region method," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 277-291.
    7. Palar, Pramudita Satria & Zuhal, Lavi Rizki & Shimoyama, Koji, 2023. "Enhancing the explainability of regression-based polynomial chaos expansion by Shapley additive explanations," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    8. Turati, Pietro & Pedroni, Nicola & Zio, Enrico, 2017. "Simulation-based exploration of high-dimensional system models for identifying unexpected events," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 317-330.
    9. Xuan Li & Xiaoping Zhou & Jingming Hou & Yuan Liu & Shuhong Xue & Huan Ma & Bowen Su, 2024. "A Hydrodynamic Model and Data-Driven Evolutionary Multi-Objective Optimization Algorithm Based Optimal Operation Method for Multi-barrage Flood Control," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 38(11), pages 4323-4341, September.
    10. 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.
    11. Wu, Zeping & Wang, Donghui & Okolo N, Patrick & Hu, Fan & Zhang, Weihua, 2016. "Global sensitivity analysis using a Gaussian Radial Basis Function metamodel," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 171-179.
    12. Liang Pei & Chunhui Wang & Liying Sun & Lili Wang, 2022. "Temporal and Spatial Variation (2001–2020) Characteristics of Wind Speed in the Water Erosion Area of the Typical Black Soil Region, Northeast China," IJERPH, MDPI, vol. 19(17), pages 1-17, August.
    13. 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.
    14. Strang, Kenneth David, 2012. "Importance of verifying queue model assumptions before planning with simulation software," European Journal of Operational Research, Elsevier, vol. 218(2), pages 493-504.
    15. Jesús Martínez-Frutos & David Herrero-Pérez, 2016. "Kriging-based infill sampling criterion for constraint handling in multi-objective optimization," Journal of Global Optimization, Springer, vol. 64(1), pages 97-115, January.
    16. Fu, Quanlu & Wu, Jiyan & Wu, Xuemian & Sun, Jian & Tian, Ye, 2024. "Managing network congestion with link-based incentives: A surrogate-based optimization approach," Transportation Research Part A: Policy and Practice, Elsevier, vol. 182(C).
    17. Wu, Xu & Kozlowski, Tomasz & Meidani, Hadi, 2018. "Kriging-based inverse uncertainty quantification of nuclear fuel performance code BISON fission gas release model using time series measurement data," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 422-436.
    18. Dawei Zhan & Huanlai Xing, 2020. "Expected improvement for expensive optimization: a review," Journal of Global Optimization, Springer, vol. 78(3), pages 507-544, November.
    19. Mert Edali & Gönenç Yücel, 2020. "Analysis of an individual‐based influenza epidemic model using random forest metamodels and adaptive sequential sampling," Systems Research and Behavioral Science, Wiley Blackwell, vol. 37(6), pages 936-958, November.
    20. Wang, Honggang, 2017. "Multi-objective retrospective optimization using stochastic zigzag search," European Journal of Operational Research, Elsevier, vol. 263(3), pages 946-960.

    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:63:y:2016:i:3:p:903-926. 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.