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 mod...

Full description

Saved in:
Bibliographic Details
Published in:AIAA journal 2014-05, Vol.52 (5), p.1010-1023
Main Authors: Viswanath, Asha, Forrester, A. I. J, Keane, A. J
Format: Article
Language:English
Subjects:
Aerospace engineering
Aerospace engines
Air transportation and traffic
Aircraft
Aircraft design
Applied sciences
Compressor rotors
Constraints
Design of experiments
Design optimization
Exact sciences and technology
Ground, air and sea transportation, marine construction
Mathematical analysis
Mathematical models
Optimization
Optimization algorithms
Searching
Topographic mapping
Topography
Wing design
Wings (aircraft)
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0001-1452
1533-385X
DOI:10.2514/1.J052414