Kriging Metamodeling in Simulation: A Review

This article reviews Kriging (also called spatial correlation modeling). It presents the basic Kriging assumptions and formulas contrasting Kriging and classic linear regression metamodels. Furthermore, it extends Kriging to random simulation, and discusses bootstrapping to estimate the variance of the Kriging predictor. Besides classic one-shot statistical designs such as Latin Hypercube Sampling, it reviews sequentialized and customized designs. It ends with topics for future research.

[1]  N. Zheng,et al.  Global Optimization of Stochastic Black-Box Systems via Sequential Kriging Meta-Models , 2006, J. Glob. Optim..

[2]  Gerald T. Mackulak,et al.  D-Optimal Sequential Experiments for Generating a Simulation-Based Cycle Time-Throughput Curve , 2002, Oper. Res..

[3]  Sonja Kuhnt,et al.  Design and analysis of computer experiments , 2010 .

[4]  Jack P. C. Kleijnen,et al.  A methodology for fitting and validating metamodels in simulation , 2000, Eur. J. Oper. Res..

[5]  Jack P. C. Kleijnen,et al.  A methodology for the fitting and validation of metamodels in simulation , 2000 .

[6]  Dick den Hertog,et al.  Kriging Models that are Robust with Respect to Simulation Errors , 2007 .

[7]  Averill M. Law,et al.  Simulation Modeling and Analysis , 1982 .

[8]  John E. Dennis,et al.  Optimization Using Surrogate Objectives on a Helicopter Test Example , 1998 .

[9]  Ruichen Jin,et al.  On Sequential Sampling for Global Metamodeling in Engineering Design , 2002, DAC 2002.

[10]  T. Mexia,et al.  Author ' s personal copy , 2009 .

[11]  Noel A Cressie,et al.  Statistics for Spatial Data, Revised Edition. , 1994 .

[12]  Timothy W. Simpson,et al.  Sampling Strategies for Computer Experiments: Design and Analysis , 2001 .

[13]  David M. Woodcock,et al.  Designing Efficient Computer Experiments for Metamodel Generation , 2000 .

[14]  V. Toropov,et al.  Design Optimization and Stochastic Analysis based on the Moving Least Squares Method , 2005 .

[15]  Farrokh Mistree,et al.  Kriging Models for Global Approximation in Simulation-Based Multidisciplinary Design Optimization , 2001 .

[16]  J. Oakley Estimating percentiles of uncertain computer code outputs , 2004 .

[17]  T. Simpson,et al.  A Monte Carlo Simulation of the Kriging Model , 2004 .

[18]  John E. Renaud,et al.  Update Strategies for Kriging Models for Use in Variable Fidelity Optimization , 2005 .

[19]  Richard J. Balling,et al.  Approximation of Computationally Expensive and Noisy Functions for Constrained Nonlinear Optimization , 1987 .

[20]  T. Simpson,et al.  Use of Kriging Models to Approximate Deterministic Computer Models , 2005 .

[21]  K. Chaloner,et al.  Bayesian Experimental Design: A Review , 1995 .

[22]  Bert Bettonvil,et al.  Statitical Testing of Optimality Conditions in Multiresponse Simulation-Based Optimization , 2005 .

[23]  Robert E. Shannon,et al.  Design and analysis of simulation experiments , 1978, WSC '78.

[24]  T. W. Layne,et al.  A Comparison of Approximation Modeling Techniques: Polynomial Versus Interpolating Models , 1998 .

[25]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[26]  Søren Nymand Lophaven,et al.  DACE - A Matlab Kriging Toolbox , 2002 .

[27]  B. P. Ziegler,et al.  Theory of Modeling and Simulation , 1976 .

[28]  Raphael T. Haftka,et al.  Optimization and Experiments: A Survey , 1998 .

[29]  R JonesDonald,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998 .

[30]  Bernard Grossman,et al.  Noisy Aerodynamic Response and Smooth Approximations in HSCT Design , 1994 .

[31]  M. Kenward,et al.  An Introduction to the Bootstrap , 2007 .

[32]  Timothy W. Simpson,et al.  Sampling Strategies for Computer Experiments , 2001 .

[33]  Jack P. C. Kleijnen,et al.  Kriging metamodeling in constrained simulation optimization: an explorative study , 2007, 2007 Winter Simulation Conference.

[34]  Jay D. Martin,et al.  On Using Kriging Models as Probabilistic Models in Design , 2004 .

[35]  Ren-Jye Yang,et al.  Approximation methods in multidisciplinary analysis and optimization: a panel discussion , 2004 .

[36]  V. B. Melas,et al.  Design and Analysis of Simulation Experiments , 1995 .

[37]  R. A. Miller,et al.  Sequential kriging optimization using multiple-fidelity evaluations , 2006 .

[38]  Pierre Montés,et al.  Smoothing noisy data by kriging with nugget effects , 1994 .

[39]  G. Matheron Principles of geostatistics , 1963 .

[40]  J. Banks,et al.  Discrete-Event System Simulation , 1995 .

[41]  David M. Steinberg,et al.  Comparison of designs for computer experiments , 2006 .

[42]  Robin K. S. Hankin,et al.  Introducing BACCO, an R Bundle for Bayesian Analysis of Computer Code Output , 2005 .

[43]  Søren Nymand Lophaven,et al.  DACE - A Matlab Kriging Toolbox, Version 2.0 , 2002 .

[44]  Michael James Sasena,et al.  Flexibility and efficiency enhancements for constrained global design optimization with kriging approximations. , 2002 .

[45]  Farrokh Mistree,et al.  Sequential Metamodeling in Engineering Design , 2004 .

[46]  Russell R. Barton,et al.  Ch. 7. A review of design and modeling in computer experiments , 2003 .

[47]  Jack P. C. Kleijnen,et al.  Robustness of Kriging when interpolating in random simulation with heterogeneous variances: Some experiments , 2005, Eur. J. Oper. Res..

[48]  Jack P. C. Kleijnen,et al.  Kriging for interpolation in random simulation , 2003, J. Oper. Res. Soc..

[49]  J. Banks,et al.  Handbook of Simulation , 1998 .

[50]  Jack P. C. Kleijnen,et al.  Application-driven sequential designs for simulation experiments: Kriging metamodelling , 2004, J. Oper. Res. Soc..

[51]  Jack P. C. Kleijnen,et al.  The correct Kriging variance estimated by bootstrapping , 2006, J. Oper. Res. Soc..

[52]  Thomas J. Santner,et al.  Sequential design of computer experiments to minimize integrated response functions , 2000 .

[53]  Philip E. Gill,et al.  Practical optimization , 1981 .

[54]  Michael S. Eldred,et al.  OVERVIEW OF MODERN DESIGN OF EXPERIMENTS METHODS FOR COMPUTATIONAL SIMULATIONS , 2003 .

[55]  Ren-Jye Yang,et al.  High Performance Computing and Surrogate Modeling for Rapid Visualization with Multidisciplinary Optimization , 2004 .

[56]  Jack P. C. Kleijnen,et al.  Experimental Design for Sensitivity Analysis, Optimization and Validation of Simulation Models , 1997 .

[57]  Shawn E. Gano,et al.  Update strategies for kriging models used in variable fidelity optimization , 2006 .

[58]  Jack P. C. Kleijnen,et al.  Customized sequential designs for random simulation experiments: Kriging metamodeling and bootstrapping , 2008, Eur. J. Oper. Res..

[59]  P. C. Gehlen,et al.  Computer Experiments , 1996 .