Simulation-optimization via Kriging and bootstrapping: a survey

This article surveys optimization of simulated systems. The simulation may be either deterministic or random. The survey reflects the author’s extensive experience with simulation‐optimization through Kriging (or Gaussian process) metamodels, analysed through parametric bootstrapping for deterministic and random simulation and distribution‐free bootstrapping (or resampling) for random simulation. The survey covers: (1) simulation‐optimization through ‘efficient global optimization’ using ‘expected improvement’ (EI); this EI uses the Kriging predictor variance, which can be estimated through bootstrapping accounting for the estimation of the Kriging parameters; (2) optimization with constraints for multiple random simulation outputs and deterministic inputs through mathematical programming applied to Kriging metamodels validated through bootstrapping; (3) Taguchian robust optimization for uncertain environments, using mathematical programming–applied to Kriging metamodels–and bootstrapping to estimate the variability of the Kriging metamodels and the resulting robust solution; (4) bootstrapping for improving convexity or preserving monotonicity of the Kriging metamodel.