Design space reduction in optimization using generative topographic mapping

Description/Abstract

Dimension reduction in design optimization is an extensively researched area. The need arises in design
problems dealing with very high dimensions, which increase the computational burden of the design process because the sample space required for the design search varies exponentially with the dimensions.
This work describes the application of a latent variable method called Generative Topographic Mapping (GTM) in dimension reduction of a data set by transformation into a low-dimensional latent space. The
attraction it presents is that the variables are not removed, but only transformed and hence there is
no risk of missing out on information relating to all the variables. The method has been tested on the
Branin test function initially and then on an aircraft wing weight problem. Ongoing work involves finding
a suitable update strategy for adding inll points to the trained GTM in order to converge to the global optimum effectively. Three update methods tested on GTM so far are discussed.