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Erschienen in: Structural and Multidisciplinary Optimization 1/2018

05.07.2017 | RESEARCH PAPER

Ensemble of metamodels: extensions of the least squares approach to efficient global optimization

verfasst von: Wallace G. Ferreira, Alberto L. Serpa

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 1/2018

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Abstract

In this work we present LSEGO, an approach to drive efficient global optimization (EGO), based on LS (least squares) ensemble of metamodels. By means of LS ensemble of metamodels it is possible to estimate the uncertainty of the prediction with any kind of model (not only kriging) and provide an estimate for the expected improvement function. For the problems studied, the proposed LSEGO algorithm has shown to be able to find the global optimum with less number of optimization cycles than required by the classical EGO approach. As more infill points are added per cycle, the faster is the convergence to the global optimum (exploitation) and also the quality improvement of the metamodel in the design space (exploration), specially as the number of variables increases, when the standard single point EGO can be quite slow to reach the optimum. LSEGO has shown to be a feasible option to drive EGO with ensemble of metamodels as well as for constrained problems, and it is not restricted to kriging and to a single infill point per optimization cycle.

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Fußnoten
1
For instance, even with high end computers clusters used nowadays in automotive industry, one single full vehicle analysis of high fidelity safety crash FEM model takes up to 15 processing hours with 48 CPU in parallel. With respect to CFD analysis one single complete car aerodynamics model for drag calculation, by using 96 CPU, should take up 30 hours to finish. An interesting essay regarding this “never-ending” need of computer resources in structural optimization can be found in Venkatararaman and Haftka (2004).
 
2
Only for notational convenience, without loss of generality, we will assume that all equality constraints h(x) can be properly transformed into inequality constraints g(x).
 
3
Matlab is a well known and widely used numerical programing platform and it is developed and distributed by The Mathworks Inc., see www.​mathworks.​com.
 
4
Boxplot is a common statistical graph used for visual comparison of the distribution of different variables in a same plane. The box is defined by lines at the lower quartile (25%), median (50%) and upper quartile (75%) of the data. The lines extending above and upper each box (named as whiskers) indicate the spread for the rest of the data out of the quartiles definition. If existent, outliers are represented by plus signs “ + ”, above/below the whiskers. We used the Matlab function boxplot (with default parameters) to create the plots.
 
5
For further details and recent updates on SURROGATES Toolbox refer to the website: https://​sites.​google.​com/​site/​srgtstoolbox/​.
 
6
As a common practice for metamodel based optimization purposes, the number of points in initial DOE is often in the range 5n v to 10n v .
 
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Metadaten
Titel
Ensemble of metamodels: extensions of the least squares approach to efficient global optimization
verfasst von
Wallace G. Ferreira
Alberto L. Serpa
Publikationsdatum
05.07.2017
Verlag
Springer Berlin Heidelberg
Erschienen in
Structural and Multidisciplinary Optimization / Ausgabe 1/2018
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-017-1745-x

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