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

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  • 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
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    References listed on IDEAS

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    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.
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    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.
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    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

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