Optimal designs for order-of-addition screening factorial experiments

Order-of-addition (OofA) experiments are widely used in various fields to investigate how sequences of adding components influence system behavior. In many real-world OofA experiments, the responses are influenced by both the addition sequence and the level combinations of factors. This paper studies the design and modeling of OofA experiments in scenarios where the number of components exceeds the available positions, and the response is further affected by the factorial effects of factors. Designing such experiments is complex due to the vast number of possible combinations of components, sequences, and factor levels. We present a new model that combines OofA experiments with factorial experiments, enabling the identification of optimal sequences from a large set of components and the best level combinations for factors. We show the D-optimality of the full design under this model and offer two algebraic methods for constructing optimal fractional designs with economic run sizes. The effectiveness of the proposed designs is validated through two simulation studies: one on the single machine scheduling problem and another on the traveling salesman problem, as well as a real-world pplication in mobile game strategy optimization.