Simulation Optimization via Bootstrapped Kriging: Tutorial (Replaced by CentER DP 2013-064)

Kriging (or Gaussian Process) metamodels may be analyzed through bootstrapping, which is a versatile statistical method but must be adapted to the speci c problem being analyzed. More precisely, a random or discrete-event simulation may be run several times for the same scenario (combination of simulation inputs); the resulting replicated responses may be resampled with replacement, which is called "distribution-free bootstrapping". 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's input/output data. More specifically, this tutorial covers the following recent approaches: (1) E¢ cient Global Optimization (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) Assuming a characteristic like monotonicity for the outputs as a function of the inputs, bootstrapped Kriging may preserve this characteristic