UCLA

This dissertation explores advanced optimization techniques, focusing on hyperparameter tuning, design strategy selection, and novel optimization methods. First, we investigate a modified Differential Evolution (DE) algorithm for generating uniform projection designs, emphasizing the importance of hyperparameter configuration. We analyze the surface structure of these hyperparameters and provide guidelines for optimizing settings under various conditions. Next, we examine the role of initial design choices in prediction and sequential optimization using Efficient Global Optimization (EGO), demonstrating that uniform projection designs outperform traditional strategies such as maximin distance designs, particularly in high-dimensional spaces. Finally, we introduce a Kriging-based sequential region shrinking method that integrates EGO to efficiently reduce the search space by targeting promising data points. Comparative results show that this method not only requires fewer computational resources than conventional tuning techniques like grid and random search but also outperforms other Bayesian optimization methods such as TREGO. These findings offer significant contributions to the optimization field, enhancing both theoretical understanding and practical applications.