A toolbox for optimal design
Abstract
In the past few years we have developed some expertise in solving optimization
problems that involve large scale simulations in various areas of Computational
Geophysics and Engineering. We will discuss some of those applications here,
namely: inversion of seismic data, characterization of piezoelectrical crystals
material properties, optimal design of piezoelectrical transducers and
opto-electronic devices, and the optimal design of steel structures.
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A common theme among these different applications is that the goal functional
is very expensive to evaluate, often, no derivatives are readily available, and
some times the dimensionality can be large.
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Thus parallelism is a need, and when no derivatives are present, search type
methods have to be used for the optimization part. Additional difficulties can
be ill-conditioning and non-convexity, that leads to issues of global
optimization. Another area that has not been extensively explored in numerical
optimization and that is important in real applications is that of
multiobjective optimization.
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As a result of these varied experiences we are currently designing a toolbox
to facilitate the rapid deployment of these techniques to other areas of
application with a minimum of retooling.