Optimization and Engineering

, Volume 9, Issue 4, pp 375–391

Quality assessment of coarse models and surrogates for space mapping optimization


DOI: 10.1007/s11081-007-9032-0

Cite this article as:
Koziel, S., Bandler, J.W. & Madsen, K. Optim Eng (2008) 9: 375. doi:10.1007/s11081-007-9032-0


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.


Space mapping Surrogate modeling Space mapping optimization Engineering design optimization Convergence conditions Coarse model quality 

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Simulation Optimization Systems Research Laboratory, Department of Electrical and Computer EngineeringMcMaster UniversityHamiltonCanada
  2. 2.Bandler CorporationDundasCanada
  3. 3.Informatics and Mathematical ModellingTechnical University of DenmarkLyngbyDenmark

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