Optimal Designs – Theory, Algorithms and Applications

Design of Experiments plays an important role in modern science and engineering applications. It is one of the core fields in statistics area, and it is also a powerful tool in investigating new or existing processes to gain further insights. Optimal designs of experiments, which optimize the performances of different processes or target on maximizing the information gained from the limited data, are widely desired and used. Depending on the physical constraints and experimental requirements, various types of optimal designs are implemented, including D-optimal designs, space-filling designs, orthogonal designs and order-of-addition designs. It is often very challenging to construct optimal designs with flexible sizes, and theoretical results only exist for certain design sizes.

This dissertation focuses on optimal designs of experiments. More specifically, optimal space-filling designs, orthogonal designs, and order-of-addition designs in experiments with discrete elements, as well as D-optimal and G-optimal designs in experiments with continuous elements. For each type of the optimal designs, corresponding theories, related algorithms, applications, and my contributions to this area will be discussed.