Simulation-Optimization via Kriging and Bootstrapping: a Survey

This survey considers the optimization of simulated systems. The simulation may be either deterministic or random. The sur-vey reects the authors extensive experience with simulation-optimization through Kriging (or Gaussian process) metamod-els using a frequentist (non-Bayesian) approach. The analysis of Kriging metamodels may use bootstrapping. The survey dis-cusses both parametric bootstrapping for deterministic simula-tion and distribution-free bootstrapping for random simulation. The survey uses only basic mathematics and statistics; its 51 references enable further study. More speci\u85cally, this article reviews the following recent topics: (1) A popular simulation-optimization heuristic is E ¢ cient Global Optimization (EGO) using Expected Improvement (EI); parametric bootstrapping can estimate the variance of the Kriging predictor, accounting for the randomness resulting from estimating the Kriging parameters. (2) Optimization with constraints for random simulation outputs and deterministic inputs may use mathematical programming applied to Kriging metamodels; validation of these metamodels may use distribution-free bootstrapping. (3) Taguchian robust optimization accounts for an uncertain environment; this opti-mization may use mathematical programming applied to Kriging metamodels, while distribution-free bootstrapping may estimate the variability of the Kriging metamodels and the resulting ro-bust solution. (4) The bootstrap may improve the convexity or monotonicity of the Kriging metamodel, if the input/output func-tion of the underlying simulation model is assumed to have such a characteristic