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

Ehsan Mehdad, J.P.C. Kleijnen

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Efficient Global Optimization (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, EGO uses ordinary Kriging (OK), which is a special case of universal Kriging (UK). In our EGO variant we use intrinsic Kriging (IK), which eliminates the need to estimate the parameters that quantify the trend in UK. In random simulation, EGO uses stochastic Kriging (SK), but we use 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 selection method uses optimal computer budget allocation (OCBA), which allocates the available total number of replications over simulated combinations. We derive 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 differ significantly from EGO with SK combined with the OCBA allocation rule.
Original languageEnglish
Pages (from-to)1725-1737
JournalThe Journal of the Operational Research Society
Volume69
Issue number11
Publication statusPublished - Nov 2018

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Global optimization
Intrinsic
Simulation
Kriging
Black box
Experiments

Keywords

  • global optimization
  • Gaussian process
  • kriging
  • intrinsic Kriging
  • metamodel

Cite this

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title = "Efficient global optimization for black-box simulation via sequential intrinsic Kriging",
abstract = "Efficient Global Optimization (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, EGO uses ordinary Kriging (OK), which is a special case of universal Kriging (UK). In our EGO variant we use intrinsic Kriging (IK), which eliminates the need to estimate the parameters that quantify the trend in UK. In random simulation, EGO uses stochastic Kriging (SK), but we use 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 selection method uses optimal computer budget allocation (OCBA), which allocates the available total number of replications over simulated combinations. We derive 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 differ significantly from EGO with SK combined with the OCBA allocation rule.",
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Efficient global optimization for black-box simulation via sequential intrinsic Kriging. / Mehdad, Ehsan; Kleijnen, J.P.C.

In: The Journal of the Operational Research Society, Vol. 69, No. 11, 11.2018, p. 1725-1737.

Research output: Contribution to journalArticleScientificpeer-review

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