### Simulation optimization via bootstrapped Kriging: survey

Kleijnen, JPC *(Universiteit van Tilburg)*

Wednesday 07 September 2011, 12:00-12:30

Seminar Room 1, Newton Institute

#### Abstract

This presentation surveys simulation optimization via Kriging (also called Gaussian Process or spatial correlation) metamodels. These metamodels may be analyzed through bootstrapping, which is a versatile statistical method but must be adapted to the specific problem being analyzed. More precisely, a random or discrete- event simulation may be run several times for the same scenario (combination of simulation input values); the resulting replicated responses may be resampled with replacement, which is called ìdistribution-free bootstrappingî. In engineering, however, deterministic simulation is often applied; such a simulation is run only once for the same scenario, so "parametric bootstrapping" is used. This bootstrapping assumes a multivariate Gaussian distribution, which is sampled after its parameters are estimated from the simulation input/output data. More specifically, this talk covers the following recent approaches: (1) Efficient Global Optimiz ation (EGO) via Expected Improvement (EI) using parametric bootstrapping to obtain an estimator of the Kriging predictor's variance accounting for the randomness resulting from estimating the Kriging parameters. (2) Constrained optimization via Mathematical Programming applied to Kriging metamodels using distribution-free bootstrapping to validate these metamodels. (3) Robust optimization accounting for an environment that is not exactly known (so it is uncertain); this optimization may use Mathematical Programming and Kriging with distribution-free bootstrapping to estimate the Pareto frontier. (4) Bootstrapped Kriging may preserve a characteristic such as monotonicity of the outputs as a function of the inputs.

#### Presentation

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