Generative Topographic Mapping for Dimension Reduction in Engineering Design

Abstract

Multi-variate design optimization is plagued by the problem of a design space which increases exponentially with number of variables. The computational burden caused by this ‘curse of dimensionality’ can be avoided by reducing the dimension of the problem. This work describes a dimension reduction method called generative topographic mapping. Unlike the earlier practice of removing irrelevant design variables for dimension reduction, this method transforms the high dimensional data space to a low dimensional one. Hence there is no risk of missing out on information relating to any variables during the dimension reduction. The method is demonstrated using the two dimensional Branin function and applied to a problem in wing design.