Optimization methods
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Date |
15/09/2006 |
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Author |
T.
V. Tran, S. Brisset, P. Brochet |
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Affiliation |
L2EP
– EC Lille – France |
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Email |
tran.tuan-vu@ec-lille.fr, stephane.brisset@ec-lille.fr, pascal.brochet@ec-lille.fr |
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Method |
Aggressive
Space Mapping |
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References |
[1] J. W.
Bandler, R. M. Biernacki, S. H. Chen, P. A. Grobelny and R. H. Hemmers,
“Space Mapping Technique for Electromagnetic Optimization” IEEE Transactions on Microwave theory and
techniques, vol. 42, no. 12, pp. 2536-2544, 1994. [2] J. W.
Bandler, R. M. Biernacki, S. H. Chen, R. H. Hemmers, and K. Madsen,
“Electromagnetic Optimization Exploiting Aggressive Space Mapping.” IEEE Transactions on Microwave theory and
techniques, vol. 43, no. 12, pp. 2874-2882, 1995. [3] H. Choi, D.
Kim, I. Park, and S. Hahn. “A new design technique of magnetic systems using
space mapping algorithm.” IEEE
Transactions on Magnetics, vol. 37, no 5, pp. 3627-3630, 2001. [4] D. Echeverria, “Optimisation in
Electromagnetic with the Space-Mapping Technique”, COMPEL, Vol. 24, No. 3, 2005, pp. 952-966. [5] L. Encica, D. Echeverría, E. Lomonova, A. J.
A. Vandenput, P. W. Hemker, and D. Lahaye, “Efficient optimal design of
electromagnetic actuators using space-mapping,” presented at the 6th World
Congr. Structural and Multidisciplinary Optimization, 2005. [6] J. Sondergaard, Non-linear Optimization Using Space
Mapping, Tech. Rep. IMM-EKS-1999-23, |
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Description of the method |
The
technique Space Mapping technique is aim to align one “coarse” model and one
“fine” model in order to speed up the process of the numerical optimization. The coarse model is the analytical model, c(z)
and the fine model is the 3D FE model, f(x). The parameter extraction and the
computation of xi+1 and zopt are made with the sequential
quadratic programming (SQP). The
algorithm Aggressive Space Mapping (ASM) starts with the optimization of the
analytical model to obtain zopt. Then 3D FE with the geometric (zopt)
is modeled to validate the constraints. The key of SM technique is the
parameter extraction. In fact, for this problem with constraints, the process
parameter extraction is a research of the minimum between responses of both
models while satisfying the constraints equality. The solution (xi+1)
is solved by the optimization SQP with the constraints inequality from the
linear approximation around the current point xi. A trust region
methodology ( |
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Publication of the method |
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