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.