Machine Learning Based Prediction of Alphabetic Optimality Criteria in Central Composite Designs

Abstract

This study analyses the effectiveness of machine learning approaches in predicting optimality criteria of Central Composite Designs (CCDs). The study focuses on three types of CCD: Rotatable Central Composite Design (RCCD), Spherical Central Composite Design (SCCD), and Face-Centered Central Composite Design (FCCD) for dimensions varying from k = 3 to k = 10. The purpose is to find out if geometric and structural features of CCD can be used as predictors of design efficiency. Geometric variables such as the number of factors, type of CCD, axial distance, and total number of experimental trials were utilised to forecast A-efficiency, D-efficiency, and G-efficiency. Linear Regression, Random Forest, XGBoost, Support Vector Regression (SVR), k-Nearest Neighbours (KNN), and Decision Tree. Six machine learning methods were used and evaluated by the value of $R^2$ and RMSE. It was found that machine learning nonlinear algorithms significantly outperformed the linear regression algorithm on both low- and high-dimensional datasets. The best results were obtained with SVR and XGBoost where the prediction of D-efficiency approached almost deterministic (R² \approx 0.99). Additionally, the total number of runs turned out to be the most important predictor of all three criteria.