Date of Award
5-2024
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematical Sciences
Committee Chair/Advisor
Qiong Zhang
Committee Member
Christopher McMahan
Committee Member
Patrick Gerard
Committee Member
Deborah Kunkel
Abstract
This dissertation is comprised of three parts. The first proposes a sequential approach to determine the experimental setting with the minimum variance (Kerfonta et al., 2024). Two acquisition functions are developed to assist developing the approach. Theoretical results along with a case study using data from crystallization experiments is conducted to show the ability of the proposed method to correctly select the experiment with the minimum variance. The second and third parts propose adaptations to the Bayesian optimization algorithm using transformed additive Gaussian processes (TAG) as the surrogate model. The goal of using the TAG framework is to decompose the optimization problem into multiple one-dimensional optimization problems. The second part of this dissertation proposes a Bayesian optimization algorithm for single objective optimization using TAG as the surrogate model and a modified expected improvement acquisition function. To demonstrate the advantages of the proposed method, it will be compared to Bayesian optimization with a Gaussian process surrogate model using the expected improvement acquisition function. The final part of this dissertation proposes a bi-objective Bayesian optimization algorithm that uses TAG as the surrogate model and a modified expected hypervolume improvement acquisition function. This approach is compared to classical bi-objective Bayesian optimization using a Gaussian process surrogate model. Functions from existing bi-objective optimization literature are used to demonstrate the advantages of the proposed method.
Recommended Citation
Kerfonta, Caroline, "Selected Topics on Sequential Designs for Decision Making" (2024). All Dissertations. 3616.
https://open.clemson.edu/all_dissertations/3616