Abstract
This article uses a sequentialized experimental design to select simulation input combinations for global optimization, based on Kriging (also called Gaussian process or spatial correlation modeling); this Kriging is used to analyze the input/output data of the simulation model (computer code). This design and analysis adapt the classic expected improvement (EI) in efficient global optimization (EGO) through the introduction of an unbiased estimator of the Kriging predictor variance; this estimator uses parametric bootstrapping. Classic EI and bootstrapped EI are compared through various test functions, including the six-hump camel-back and several Hartmann functions. These empirical results demonstrate that in some applications bootstrapped EI finds the global optimum faster than classic EI does; in general, however, the classic EI may be considered to be a robust global optimizer.
Highlights
Simulation is often used to estimate the global optimum of the real system being simulated
The classic Kriging literature, software, and practice replace the optimal weights λ in (2) by the estimated optimal weights λ0 which result from replacing the unknown covariances Σi;i and σi;n+1 in (3) by their estimators Σi;i and σi;n+1 that result from the Maximum Likelihood Estimators (MLEs) σ2 and θj
We study the expected improvement” (EI) criterion in the efficient global optimization” (EGO) approach to global optimization
Summary
Simulation is often used to estimate the global optimum of the real system being simulated (like many researchers in this area do, we use the terms ”optimum” and ”optimization” even if there are no constraints so the problem concerns minimization or maximization). We show that the effectiveness of EGO may be improved through the use of a bootstrapped estimator We quantify this effectiveness through the number of simulation observations needed to reach the global optimum. We assume expensive simulation; i.e., simulating a single point requires relatively much computer time compared with the computer time needed for fitting and analyzing a Kriging metamodel. It took 36 to 160 hours of computer time for a single run of a car-crash simulation model at Ford; see [22].
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