Reinsch's smoothing spline simulation metamodels

Metamodels have been used frequently by the simulation community. However, not much research has been done with nonparametric metamodels compared with parametric metamodels. In this paper, smoothing splines for performing nonparametric metamodeling are presented. The use of smoothing splines on metamodeling fitting may provide functions that better approximate the behavior of the target simulation model, compared with linear and nonlinear regression metamodels. The smoothing splines tolerance parameter can be used to tune the smoothness of the resulting metamodel. A good experimental design is crucial for obtaining a better smoothing spline metamodel fitting, as illustrated in the examples.

[1]  Tom Dhaene,et al.  Sequential design and rational metamodelling , 2005, Proceedings of the Winter Simulation Conference, 2005..

[2]  M. Isabel Reis dos Santos,et al.  Using subsystem linear regression metamodels in stochastic simulation , 2009, Eur. J. Oper. Res..

[3]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[4]  Edmund Taylor Whittaker.  On a New Method of Graduation , 1922, Proceedings of the Edinburgh Mathematical Society.

[5]  Jack P. C. Kleijnen,et al.  Improved Design of Queueing Simulation Experiments with Highly Heteroscedastic Responses , 1999, Oper. Res..

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

[7]  J. Freidman,et al.  Multivariate adaptive regression splines , 1991 .

[8]  Averill Law,et al.  Simulation Modeling and Analysis (McGraw-Hill Series in Industrial Engineering and Management) , 2006 .

[9]  C. R. Deboor,et al.  A practical guide to splines , 1978 .

[10]  Adedeji B. Badiru,et al.  Neural network as a simulation metamodel in economic analysis of risky projects , 1998, Eur. J. Oper. Res..

[11]  C. Reinsch.  Smoothing by spline functions , 1967 .

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

[13]  Russell R. Barton,et al.  Metamodels for simulation input-output relations , 1992, WSC '92.

[14]  Mark A. Turnquist,et al.  Simulation optimization using response surfaces based on spline approximations , 1978, SIML.

[15]  M. Isabel Reis dos Santos,et al.  Statistical fitting and validation of non-linear simulation metamodels: A case study , 2006, Eur. J. Oper. Res..

[16]  Krzysztof Pawlikowski,et al.  Steady-state simulation of queueing processes: survey of problems and solutions , 1990, CSUR.

[17]  M. Isabel Reis dos Santos,et al.  Sequential experimental designs for nonlinear regression metamodels in simulation , 2008, Simul. Model. Pract. Theory.

[18]  Jack P. C. Kleijnen,et al.  A Comment on Blanning's “Metamodel for Sensitivity Analysis: The Regression Metamodel in Simulation” , 1975 .

[19]  I J Schoenberg,et al.  SPLINE FUNCTIONS AND THE PROBLEM OF GRADUATION. , 1964, Proceedings of the National Academy of Sciences of the United States of America.

[20]  Loren Paul Rees,et al.  A sequential-design metamodeling strategy for simulation optimization , 2004, Comput. Oper. Res..

[21]  G. Wahba.  Spline models for observational data , 1990 .

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

[23]  V.F. Nicola,et al.  Adaptive importance sampling simulation of queueing networks , 2000, 2000 Winter Simulation Conference Proceedings (Cat. No.00CH37165).

[24]  Pieter-Tjerk de Boer,et al.  Techniques for simulating difficutl queueing problems: adaptive importance sampling simulation of queueing networks , 2000, WSC '00.