Kriging interpolation in simulation: a survey

Many simulation experiments require much computer time, so they necessitate interpolation for sensitivity analysis and optimization. The interpolating functions are 'metamodels' (or 'response surfaces') of the underlying simulation models. Classic methods combine low-order polynomial regression analysis with fractional factorial designs. Modern Kriging provides 'exact' interpolation, i.e., predicted output values at inputs already observed equal the simulated output values. Such interpolation is attractive in deterministic simulation, and is often applied in computer aided engineering. In discrete-event simulation, however, Kriging has just started. Methodologically, a Kriging metamodel covers the whole experimental area; i.e., it is global (not local). Kriging often gives better global predictions than regression analysis. Technically, Kriging gives more weight to 'neighboring' observations. To estimate the Kriging metamodel, space filling designs are used; for example, latin hypercube sampling (LHS). This paper also presents novel, customized (application driven) sequential designs based on cross-validation and bootstrapping.