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Quality assessment of coarse models and surrogates for space mapping optimization

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Abstract

One of the central issues in space mapping optimization is the quality of the underlying coarse models and surrogates. Whether a coarse model is sufficiently similar to the fine model may be critical to the performance of the space mapping optimization algorithm and a poor coarse model may result in lack of convergence. Although similarity requirements can be expressed with proper analytical conditions, it is difficult to verify such conditions beforehand for real-world engineering optimization problems. In this paper, we provide methods of assessing the quality of coarse/surrogate models. These methods can be used to predict whether a given model might be successfully used in space mapping optimization, to compare the quality of different coarse models, or to choose the proper type of space mapping which would be suitable to a given engineering design problem. Our quality estimation methods are derived from convergence results for space mapping algorithms. We provide illustrations and several practical application examples.

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Authors and Affiliations

  1. Simulation Optimization Systems Research Laboratory, Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON, L8S 4K1, Canada

    Slawomir Koziel

  2. Bandler Corporation, Dundas, ON, L9H 5E7, Canada

    John W. Bandler

  3. Informatics and Mathematical Modelling, Technical University of Denmark, DK-2800, Lyngby, Denmark

    Kaj Madsen

Authors
  1. Slawomir Koziel
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  2. John W. Bandler
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  3. Kaj Madsen
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Corresponding author

Correspondence to Slawomir Koziel.

Additional information

This work was supported in part by the Natural Sciences and Engineering Research Council of Canada under Grants RGPIN7239-06 and STPGP336760-06.

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Koziel, S., Bandler, J.W. & Madsen, K. Quality assessment of coarse models and surrogates for space mapping optimization. Optim Eng 9, 375–391 (2008). https://doi.org/10.1007/s11081-007-9032-0

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  • DOI: https://doi.org/10.1007/s11081-007-9032-0

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