IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v69y2017i2d10.1007_s10898-017-0529-6.html
   My bibliography  Save this article

A certified Branch & Bound approach for reliability-based optimization problems

Author

Listed:
  • Benjamin Martin

    (Universidade Nova de Lisboa
    École Polytechnique)

  • Marco Correia

    (Universidade Nova de Lisboa)

  • Jorge Cruz

    (Universidade Nova de Lisboa)

Abstract

Reliability-based optimization problems are optimization problems considering a constraint that measures reliability of the modelled system: the probability of a safety event with respect to controllable decision variables and uncertain random variables. Most solving approaches use approximate techniques for evaluating this reliability constraint. As a consequence, the reliability of the computed optimal decision is not guaranteed. In this paper, we investigate an interval-based Branch & Bound for solving globally reliability-based optimization problems with numerical guarantee. It combines an interval Branch & Bound framework with a certified reliability analysis technique. This technique considers the reliability constraint and induced safety region modelled within Probabilistic Continuous Constraint Programming paradigm. The certified reliability analysis is numerically handled by an interval quadrature algorithm. In addition, a new interval quadrature function for two random variables, based on linear models of the safety region is described. Two implementations of the Branch & Bound, which differ on how the certified reliability analysis is handled throughout the optimization process, are presented. A numerical study of these two variants shows the relevance of the interval linear model-based quadrature function.

Suggested Citation

  • Benjamin Martin & Marco Correia & Jorge Cruz, 2017. "A certified Branch & Bound approach for reliability-based optimization problems," Journal of Global Optimization, Springer, vol. 69(2), pages 461-484, October.
    • Handle: RePEc:spr:jglopt:v:69:y:2017:i:2:d:10.1007_s10898-017-0529-6
    DOI: 10.1007/s10898-017-0529-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-017-0529-6
    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/s10898-017-0529-6?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. Norbert Kuschel & Rüdiger Rackwitz, 1997. "Two basic problems in reliability-based structural optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(3), pages 309-333, October.
    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. Kwok Tai Chui & Wadee Alhalabi & Sally Shuk Han Pang & Patricia Ordóñez de Pablos & Ryan Wen Liu & Mingbo Zhao, 2017. "Disease Diagnosis in Smart Healthcare: Innovation, Technologies and Applications," Sustainability, MDPI, vol. 9(12), pages 1-23, December.

    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. Rocchetta, Roberto & Crespo, Luis G., 2021. "A scenario optimization approach to reliability-based and risk-based design: Soft-constrained modulation of failure probability bounds," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    2. Li, Junxiang & Chen, Jianqiao, 2019. "Solving time-variant reliability-based design optimization by PSO-t-IRS: A methodology incorporating a particle swarm optimization algorithm and an enhanced instantaneous response surface," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    3. Okoro, Aghatise & Khan, Faisal & Ahmed, Salim, 2023. "Dependency effect on the reliability-based design optimization of complex offshore structure," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    4. Yuan, Xiukai & Lu, Zhenzhou, 2014. "Efficient approach for reliability-based optimization based on weighted importance sampling approach," Reliability Engineering and System Safety, Elsevier, vol. 132(C), pages 107-114.
    5. Jensen, H.A. & Muñoz, A. & Papadimitriou, C. & Millas, E., 2016. "Model-reduction techniques for reliability-based design problems of complex structural systems," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 204-217.
    6. Rocchetta, Roberto & Crespo, Luis G. & Kenny, Sean P., 2020. "A scenario optimization approach to reliability-based design," Reliability Engineering and System Safety, Elsevier, vol. 196(C).
    7. Zhang, Xiaobo & Lu, Zhenzhou & Cheng, Kai, 2021. "Reliability index function approximation based on adaptive double-loop Kriging for reliability-based design optimization," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    8. Karadeniz, Halil & ToÄŸan, Vedat & Vrouwenvelder, Ton, 2009. "An integrated reliability-based design optimization of offshore towers," Reliability Engineering and System Safety, Elsevier, vol. 94(10), pages 1510-1516.
    9. ToÄŸan, Vedat & Karadeniz, Halil & DaloÄŸlu, AyÅŸe T., 2010. "An integrated framework including distinct algorithms for optimization of offshore towers under uncertainties," Reliability Engineering and System Safety, Elsevier, vol. 95(8), pages 847-858.
    10. Zhang, Zheng & Wang, Pan & Hu, Huanhuan & Li, Lei & Li, Haihe & Yue, Zhufeng, 2022. "Efficient reliability-based design optimization for hydraulic pipeline with adaptive sampling region," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    11. Ahmed, Hussam & Chateauneuf, Alaa, 2014. "Optimal number of tests to achieve and validate product reliability," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 242-250.
    12. Eldred, M.S. & Swiler, L.P. & Tang, G., 2011. "Mixed aleatory-epistemic uncertainty quantification with stochastic expansions and optimization-based interval estimation," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1092-1113.
    13. Chaudhuri, Anirban & Kramer, Boris & Willcox, Karen E., 2020. "Information Reuse for Importance Sampling in Reliability-Based Design Optimization," Reliability Engineering and System Safety, Elsevier, vol. 201(C).

    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:jglopt:v:69:y:2017:i:2:d:10.1007_s10898-017-0529-6. 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.