IDEAS home Printed from https://ideas.repec.org/a/taf/tjorxx/v69y2018i11p1725-1737.html
   My bibliography  Save this article

Efficient global optimisation for black-box simulation via sequential intrinsic Kriging

Author

Listed:
  • Ehsan Mehdad
  • Jack P. C. Kleijnen

Abstract

Efficient global optimisation (EGO) is a popular method that searches sequentially for the global optimum of a simulated system. EGO treats the simulation model as a black-box, and balances local and global searches. In deterministic simulation, classic EGO uses ordinary Kriging (OK), which is a special case of universal Kriging (UK). In our EGO variant we use intrinsic Kriging (IK), which does not need to estimate the parameters that quantify the trend in UK. In random simulation, classic EGO uses stochastic Kriging (SK), but we replace SK by stochastic IK (SIK). Moreover, in random simulation, EGO needs to select the number of replications per simulated input combination, accounting for the heteroscedastic variances of the simulation outputs. A popular method uses optimal computer budget allocation (OCBA), which allocates the available total number of replications to simulated combinations. We replace OCBA by a new allocation algorithm. We perform several numerical experiments with deterministic simulations and random simulations. These experiments suggest that (1) in deterministic simulations, EGO with IK outperforms classic EGO; (2) in random simulations, EGO with SIK and our allocation rule does not perform significantly better than EGO with SK and OCBA.

Suggested Citation

  • Ehsan Mehdad & Jack P. C. Kleijnen, 2018. "Efficient global optimisation for black-box simulation via sequential intrinsic Kriging," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 69(11), pages 1725-1737, November.
  • Handle: RePEc:taf:tjorxx:v:69:y:2018:i:11:p:1725-1737
    DOI: 10.1080/01605682.2017.1409154
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01605682.2017.1409154
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/01605682.2017.1409154?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ehsan Mehdad & Jack P.C. Kleijnen, 2018. "Stochastic intrinsic Kriging for simulation metamodeling," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 34(3), pages 322-337, May.
    2. Bruce Ankenman & Barry L. Nelson & Jeremy Staum, 2010. "Stochastic Kriging for Simulation Metamodeling," Operations Research, INFORMS, vol. 58(2), pages 371-382, April.
    3. Jack P.C. Kleijnen, 2015. "Design and Analysis of Simulation Experiments," International Series in Operations Research and Management Science, Springer, edition 2, number 978-3-319-18087-8, December.
    4. D. Huang & T. Allen & W. Notz & N. Zeng, 2006. "Global Optimization of Stochastic Black-Box Systems via Sequential Kriging Meta-Models," Journal of Global Optimization, Springer, vol. 34(3), pages 441-466, March.
    5. Roustant, Olivier & Ginsbourger, David & Deville, Yves, 2012. "DiceKriging, DiceOptim: Two R Packages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i01).
    6. Lihua Sun & L. Jeff Hong & Zhaolin Hu, 2014. "Balancing Exploitation and Exploration in Discrete Optimization via Simulation Through a Gaussian Process-Based Search," Operations Research, INFORMS, vol. 62(6), pages 1416-1438, December.
    7. J. D. Opsomer & D. Ruppert & M. P. Wand & U. Holst & O. Hössjer, 1999. "Kriging with Nonparametric Variance Function Estimation," Biometrics, The International Biometric Society, vol. 55(3), pages 704-710, September.
    8. Ning Quan & Jun Yin & Szu Ng & Loo Lee, 2013. "Simulation optimization via kriging: a sequential search using expected improvement with computing budget constraints," IISE Transactions, Taylor & Francis Journals, vol. 45(7), pages 763-780.
    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. Pedrielli, Giulia & Wang, Songhao & Ng, Szu Hui, 2020. "An extended Two-Stage Sequential Optimization approach: Properties and performance," European Journal of Operational Research, Elsevier, vol. 287(3), pages 929-945.

    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. Mehdad, E. & Kleijnen, Jack P.C., 2014. "Global Optimization for Black-box Simulation via Sequential Intrinsic Kriging," Other publications TiSEM 8fa8d96f-a086-4c4b-88ab-9, Tilburg University, School of Economics and Management.
    2. Kleijnen, J.P.C. & Mehdad, Ehsan, 2015. "Estimating the Variance of the Predictor in Stochastic Kriging," Other publications TiSEM dbbd2fa2-eccf-4f71-be9b-c, Tilburg University, School of Economics and Management.
    3. Kleijnen, Jack P.C., 2013. "Simulation-Optimization via Kriging and Bootstrapping : A Survey (Revision of CentER DP 2011-064)," Discussion Paper 2013-064, Tilburg University, Center for Economic Research.
    4. Mehdad, E., 2015. "Kriging metamodels and global opimization in simulation," Other publications TiSEM 5b5c276a-fe68-4ce9-b8a8-1, Tilburg University, School of Economics and Management.
    5. Jalali, Hamed & Van Nieuwenhuyse, Inneke & Picheny, Victor, 2017. "Comparison of Kriging-based algorithms for simulation optimization with heterogeneous noise," European Journal of Operational Research, Elsevier, vol. 261(1), pages 279-301.
    6. Qun Meng & Songhao Wang & Szu Hui Ng, 2022. "Combined Global and Local Search for Optimization with Gaussian Process Models," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 622-637, January.
    7. Kamiński, Bogumił, 2015. "A method for the updating of stochastic kriging metamodels," European Journal of Operational Research, Elsevier, vol. 247(3), pages 859-866.
    8. Rojas Gonzalez, Sebastian & Jalali, Hamed & Van Nieuwenhuyse, Inneke, 2020. "A multiobjective stochastic simulation optimization algorithm," European Journal of Operational Research, Elsevier, vol. 284(1), pages 212-226.
    9. Songhao Wang & Szu Hui Ng & William Benjamin Haskell, 2022. "A Multilevel Simulation Optimization Approach for Quantile Functions," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 569-585, January.
    10. Xuefei Lu & Alessandro Rudi & Emanuele Borgonovo & Lorenzo Rosasco, 2020. "Faster Kriging: Facing High-Dimensional Simulators," Operations Research, INFORMS, vol. 68(1), pages 233-249, January.
    11. Erickson, Collin B. & Ankenman, Bruce E. & Sanchez, Susan M., 2018. "Comparison of Gaussian process modeling software," European Journal of Operational Research, Elsevier, vol. 266(1), pages 179-192.
    12. Kleijnen, Jack P.C. & Mehdad, E. & van Beers, W.C.M., 2012. "Convex and monotonic bootstrapped kriging," Other publications TiSEM 972e079d-0209-45bf-b25e-a, Tilburg University, School of Economics and Management.
    13. Satyajith Amaran & Nikolaos V. Sahinidis & Bikram Sharda & Scott J. Bury, 2016. "Simulation optimization: a review of algorithms and applications," Annals of Operations Research, Springer, vol. 240(1), pages 351-380, May.
    14. Lihua Sun & L. Jeff Hong & Zhaolin Hu, 2014. "Balancing Exploitation and Exploration in Discrete Optimization via Simulation Through a Gaussian Process-Based Search," Operations Research, INFORMS, vol. 62(6), pages 1416-1438, December.
    15. Michael Ludkovski, 2015. "Kriging Metamodels and Experimental Design for Bermudan Option Pricing," Papers 1509.02179, arXiv.org, revised Oct 2016.
    16. Pedrielli, Giulia & Wang, Songhao & Ng, Szu Hui, 2020. "An extended Two-Stage Sequential Optimization approach: Properties and performance," European Journal of Operational Research, Elsevier, vol. 287(3), pages 929-945.
    17. Jack P. C. Kleijnen, 2017. "Comment on Park et al.’s “Robust Kriging in computer experiments”," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(6), pages 739-740, June.
    18. Kleijnen, Jack P.C., 2009. "Kriging metamodeling in simulation: A review," European Journal of Operational Research, Elsevier, vol. 192(3), pages 707-716, February.
    19. Kleijnen, Jack P.C. & van Beers, W.C.M. & van Nieuwenhuyse, I., 2011. "Expected Improvement in Efficient Global Optimization Through Bootstrapped Kriging - Replaces CentER DP 2010-62," Discussion Paper 2011-015, Tilburg University, Center for Economic Research.
    20. Kleijnen, Jack P.C. & Mehdad, E., 2013. "Conditional simulation for efficient global optimization," Other publications TiSEM 52e4860d-9887-4a63-b19a-7, Tilburg University, School of Economics and Management.

    More about this item

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C9 - Mathematical and Quantitative Methods - - Design of Experiments
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

    Statistics

    Access and download statistics

    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:taf:tjorxx:v:69:y:2018:i:11:p:1725-1737. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/tjor .

    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.