Dimensionality Reduction in Expensive Optimization Problems

Computer simulations are being used in engineering in science as a partial replacement for laboratory experiments. Such simulations are often computationally expensive hence metamodels are used to approximate them and to yield output values more economically. While this setup works well in low-dimensional settings it often struggles in high-dimensional ones due to poor metamodel prediction accuracy. As such this study explores frameworks which add a dimensionality-reduction component so that the modelling and optimization are performed on reduced-dimensionality problems thereby improving the metamodel accuracy and the obtained solutions. An extensive performance analysis with both mathematical test functions and an engineering application shows the effectiveness of the proposed frameworks.