Simulation-optimization via Kriging and bootstrapping: a survey

Abstract

This article surveys optimization of simulated systems. The simulation may be either deterministic or random. The survey reflects the author's extensive experience with simulationoptimization through Kriging (or Gaussian process) metamodels. The analysis of these metamodels may use parametric bootstrapping for deterministic simulation or distribution-free bootstrapping (or resampling) for random simulation. The survey covers: (1) Simulationoptimization through "efficient global optimization" (EGO) using "expected improvement" (EI); this EI uses the Kriging predictor variance, which can be estimated through parametric bootstrapping accounting for 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 distribution-free bootstrapping. (3) Taguchian robust optimization for uncertain environments, using mathematical programming - applied to Kriging metamodels - and distribution free 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.