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Robust optimization using computer experiments

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  • Stinstra, Erwin
  • den Hertog, Dick

Abstract

During metamodel-based optimization three types of implicit errors are typically made. The first error is the simulation-model error, which is defined by the difference between reality and the computer model. The second error is the metamodel error, which is defined by the difference between the computer model and the metamodel. The third is the implementation error. This paper presents new ideas on how to cope with these errors during optimization, in such a way that the final solution is robust with respect to these errors. We apply the robust counterpart theory of Ben-Tal and Nemirovsky to the most frequently used metamodels: linear regression and Kriging models. The methods proposed are applied to the design of two parts of the TV tube. The simulation-model errors receive little attention in the literature, while in practice these errors may have a significant impact due to propagation of such errors.

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Bibliographic Info

Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 191 (2008)
Issue (Month): 3 (December)
Pages: 816-837

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Handle: RePEc:eee:ejores:v:191:y:2008:i:3:p:816-837

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References

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  1. Sturm, J.F., 2002. "Implementation of Interior Point Methods for Mixed Semidefinite and Second Order Cone Optimization Problems," Discussion Paper, Tilburg University, Center for Economic Research 2002-73, Tilburg University, Center for Economic Research.
  2. den Hertog, Dick & Stehouwer, Peter, 2002. "Optimizing color picture tubes by high-cost nonlinear programming," European Journal of Operational Research, Elsevier, Elsevier, vol. 140(2), pages 197-211, July.
  3. Hertog, D. den & Klerk, E. de & Roos, C., 2002. "On convex quadratic approximation," Open Access publications from Tilburg University urn:nbn:nl:ui:12-226110, Tilburg University.
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Cited by:
  1. Ben-Tal, A. & Hertog, D. den, 2011. "Immunizing Conic Quadratic Optimization Problems Against Implementation Errors," Discussion Paper, Tilburg University, Center for Economic Research 2011-060, Tilburg University, Center for Economic Research.
  2. Siem, A.Y.D. & Hertog, D. den, 2007. "Kriging Models That Are Robust With Respect to Simulation Errors," Discussion Paper, Tilburg University, Center for Economic Research 2007-68, Tilburg University, Center for Economic Research.
  3. He, Zhen & Zhu, Peng-Fei & Park, Sung-Hyun, 2012. "A robust desirability function method for multi-response surface optimization considering model uncertainty," European Journal of Operational Research, Elsevier, Elsevier, vol. 221(1), pages 241-247.

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