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Sequential Design of Computer Experiments for Constrained Optimization

  • Brian J. Williams
  • Thomas J. Santner
  • William I. Notz
  • Jeffrey S. Lehman
Chapter

Abstract

This paper proposes a sequential method of designing computer or physical experiments when the goal is to optimize one integrated signal function subject to constraints on the integral of a second response function. Such problems occur, for example, in industrial problems where the computed responses depend on two types of inputs: manufacturing variables and noise variables. In industrial settings, manufacturing variables are determined by the product designer; noise variables represent field conditions which are modeled by specifying a probability distribution for these variables. The update scheme of the proposed method selects the control portion of the next input site to maximize a posterior expected “improvement” and the environmental portion of this next input is selected to minimize the mean square prediction error of the objective function at the new control site. The method allows for dependence between the objective and constraint functions. The efficacy of the algorithm relative to the single-stage design and relative to a design assuming independent responses is illustrated. Implementation issues for the deterministic and measurement error cases are discussed as are some generalizations of the method.

Keywords

Computer Experiment Constraint Function Sequential Design Spatial Autoregressive Model Control Portion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

Acknowledgments

This work was sponsored, in part, by grants DMS-0406026 and DMS-0806134 (The Ohio State University) from the National Science Foundation. The authors would like to thank Han Gang for computational help.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Brian J. Williams
    • 1
  • Thomas J. Santner
    • 2
  • William I. Notz
    • 2
  • Jeffrey S. Lehman
    • 3
  1. 1.Los Alamos National LaboratoryLos AlamosUSA
  2. 2.Department of StatisticsThe Ohio State UniversityColumbusUSA
  3. 3.JPMorganChaseHome Finance Marketing AnalyticsColumbusUSA

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