Response surface methodology revisited

Response surface methodology (RSM) searches for the input combination that optimizes the simulation output. RSM treats the simulation model as a black box. Moreover, this paper assumes that simulation requires much computer time. In the first stages of its search, RSM locally fits first-order polynomials. Next, classic RSM uses steepest descent (SD); unfortunately, SD is scale dependent. Therefore, Part 1 of this paper derives scale independent 'adapted' SD (ASD) accounting for covariances between components of the local gradient. Monte Carlo experiments show that ASD indeed gives a better search direction than SD. Part 2 considers multiple outputs, optimizing a stochastic objective function under stochastic and deterministic constraints. This part uses interior point methods and binary search, to derive a scale independent search direction and several step sizes in that direction. Monte Carlo examples demonstrate that a neighborhood of the true optimum can indeed be reached, in a few simulation runs.

[1]  G. Box,et al.  On the Experimental Attainment of Optimum Conditions , 1951 .

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

[3]  Earl R. Barnes,et al.  A variation on Karmarkar’s algorithm for solving linear programming problems , 1986, Math. Program..

[4]  R. John.  Response Surfaces: Designs and Analyses , 1989 .

[5]  Jack P. C. Kleijnen,et al.  Simulation and optimization in production planning: A case study , 1993, Decis. Support Syst..

[6]  Joan M. Donohue,et al.  Simulation Designs and Correlation Induction for Reducing Second-Order Bias in First-Order Response Surfaces , 1993, Oper. Res..

[7]  Douglas C. Montgomery,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[8]  Joan M. Donohue,et al.  Simulation designs for the estimation of quadratic response surface gradients in the presence of model misspecification , 1995 .

[9]  A. I. Khuri.  12 Multiresponse surface methodology , 1996, Design and analysis of experiments.

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

[11]  George E. P. Box,et al.  Statistics as a Catalyst to Learning , 1999 .

[12]  Raymond H. Myers,et al.  Response Surface Methodology--Current Status and Future Directions , 1999 .

[13]  James C. Spall,et al.  Stochastic optimization and the simultaneous perturbation method , 1999, WSC '99.

[14]  George E. P. Box,et al.  Statistics as a catalyst to learning by scientific method , 1999 .

[15]  Paul A. Ruud,et al.  An Introduction to Classical Econometric Theory , 2000 .

[16]  Rommert Dekker,et al.  A framework for Response Surface Methodology for simulation optimization , 2000, 2000 Winter Simulation Conference Proceedings (Cat. No.00CH37165).

[17]  Nicholas I. M. Gould,et al.  Trust Region Methods , 2000, MOS-SIAM Series on Optimization.

[18]  Jaime Trevino,et al.  A flexible simulation tool for manufacturing-cell design, II: response surface analysis and case study , 2001 .

[19]  M. Hossein Safizadeh,et al.  Minimizing the bias and variance of the gradient estimate in RSM simulation studies , 2002, Eur. J. Oper. Res..

[20]  Jack P. C. Kleijnen,et al.  Response surface methodology's steepest ascent and step size revisited , 2004, Eur. J. Oper. Res..