Variable reduction for surrogate-based optimization

Real-world problems such as computational fluid dynamics simulations and finite element analyses are computationally expensive. A standard approach to mitigating the high computational expense is Surrogate-Based Optimization (SBO). Yet, due to the high-dimensionality of many simulation problems, SBO is not directly applicable or not efficient. Reducing the dimensionality of the search space is one method to overcome this limitation. In addition to the applicability of SBO, dimensionality reduction enables easier data handling and improved data and model interpretability. Regularization is considered as one state-of-the-art technique for dimensionality reduction. We propose a hybridization approach called Regularized-Surrogate-Optimization (RSO) aimed at overcoming difficulties related to high-dimensionality. It couples standard Kriging-based SBO with regularization techniques. The employed regularization methods are based on three adaptations of the least absolute shrinkage and selection operator (LASSO). In addition, tree-based methods are analyzed as an alternative variable selection method. An extensive study is performed on a set of artificial test functions and two real-world applications: the electrostatic precipitator problem and a multilayered composite design problem. Experiments reveal that RSO requires significantly less time than standard SBO to obtain comparable results. The pros and cons of the RSO approach are discussed, and recommendations for practitioners are presented.