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Constrained design optimization using generative topographic mapping

Constrained design optimization using generative topographic mapping
Constrained design optimization using generative topographic mapping
High-dimensional design-optimization problems involving complex and time-consuming solvers present computational challenges and are expensive to execute. Even though surrogate models can replace these expensive problems with simpler models, the initial design of experiment for constructing these models effectively is still exponential to the dimension of the problem. Traditional screening methods in optimization reduce the dimension of the problem by discarding variables, which is undesirable. In this paper, a latent variable model called generative topographic mapping is proposed to reduce the dimension of the problem so as to facilitate an optimization search in a low-dimensional space without removing any variables from the design problem. The method works by transforming high-dimensional data to be embedded on a low dimensional manifold. It is demonstrated on a two-dimensional Branin function subjected to nonlinear constraints and then applied to real engineering constrained optimization problems of an aircraft wing design and an aircraft compressor rotor. The model developed in this work proved to be more effective in dealing with constrained optimization problems by effectively learning the constraint boundary, hence finding feasible best designs when compared to other surrogate models like kriging.
0001-1452
1010-1023
Viswanath, Asha
385f876f-ce34-4973-be3a-e6a0339fb48f
Forrester, A.I.J.
176bf191-3fc2-46b4-80e0-9d9a0cd7a572
Keane, A.J.
26d7fa33-5415-4910-89d8-fb3620413def
Viswanath, Asha
385f876f-ce34-4973-be3a-e6a0339fb48f
Forrester, A.I.J.
176bf191-3fc2-46b4-80e0-9d9a0cd7a572
Keane, A.J.
26d7fa33-5415-4910-89d8-fb3620413def

Viswanath, Asha, Forrester, A.I.J. and Keane, A.J. (2014) Constrained design optimization using generative topographic mapping. AIAA Journal, 52 (5), 1010-1023. (doi:10.2514/1.J052414).

Record type: Article

Abstract

High-dimensional design-optimization problems involving complex and time-consuming solvers present computational challenges and are expensive to execute. Even though surrogate models can replace these expensive problems with simpler models, the initial design of experiment for constructing these models effectively is still exponential to the dimension of the problem. Traditional screening methods in optimization reduce the dimension of the problem by discarding variables, which is undesirable. In this paper, a latent variable model called generative topographic mapping is proposed to reduce the dimension of the problem so as to facilitate an optimization search in a low-dimensional space without removing any variables from the design problem. The method works by transforming high-dimensional data to be embedded on a low dimensional manifold. It is demonstrated on a two-dimensional Branin function subjected to nonlinear constraints and then applied to real engineering constrained optimization problems of an aircraft wing design and an aircraft compressor rotor. The model developed in this work proved to be more effective in dealing with constrained optimization problems by effectively learning the constraint boundary, hence finding feasible best designs when compared to other surrogate models like kriging.

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Accepted/In Press date: 20 September 2013
e-pub ahead of print date: 28 February 2014
Published date: May 2014
Organisations: Computational Engineering & Design Group

Identifiers

Local EPrints ID: 374201
URI: http://eprints.soton.ac.uk/id/eprint/374201
ISSN: 0001-1452
PURE UUID: cf57e3d9-ddb6-481e-8503-1cb312c5c9d4

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Date deposited: 10 Feb 2015 10:20
Last modified: 28 Aug 2019 18:44

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