Dimensionality-reduction frameworks for computationally expensive problems

Real-world design optimization problems are typically computationally-expensive and to address this various model-assisted evolutionary frameworks have been proposed. However, often such problems are also high-dimensional and in such settings models tend to have poor accuracy and thus degrade the optimization search. To address this we propose two complementary dimensionality-reduction frameworks for evolutionary model-assisted optimization: one uses variable-selection to identify an important subset of the original variables while the other uses topological mapping to project the high-dimensional data to a lower-dimension. Performance analysis with both mathematical test functions and a problem of airfoil shape optimization evaluates the efficacy of the frameworks.