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Efficient Global Optimization for Black-Box Simulation via Sequential Intrinsic Kriging

Author

Listed:
  • Mehdad, Ehsan

    (Tilburg University, Center For Economic Research)

  • Kleijnen, J.P.C.

    (Tilburg University, Center For Economic Research)

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.
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Suggested Citation

  • Mehdad, Ehsan & Kleijnen, J.P.C., 2015. "Efficient Global Optimization for Black-Box Simulation via Sequential Intrinsic Kriging," Discussion Paper 2015-042, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:5e785713-146c-4e5b-b671-f7eb4a8b7a41
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    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.
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    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.

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    More about this item

    Keywords

    global optimization; Gaussian process; Kriging; intrinsic Krgigin; metamodel;
    All these keywords.

    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

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