Exact designs for order-of-addition experiments under a transition-effect model

In the chemical, pharmaceutical, and food industries, sometimes the order of adding a set of components has an impact on the final product. These are instances of the Order-of-Addition (OofA) problem, which aims to find the optimal sequence of the components. Extensive research on this topic has been conducted, but almost all designs are found by optimizing the D−optimality criterion. However, when prediction of the response is important, there is still a need for I−optimal designs. Furthermore, designs are needed for experiments where some orders are infeasible due to constraints. A new model for OofA experiments is presented that uses transition effects to model the effect of order on the response. Three algorithms are proposed to find D− and I−efficient exact designs under this new model: Simulated Annealing, a metaheuristic algorithm, Bubble Sorting, a greedy local optimization algorithm, and the Greedy Randomized Adaptive Search Procedure (GRASP), another metaheuristic algorithm. These three algorithms are generalized to handle block constraints, where components are grouped into blocks with a fixed order. Finally, two examples are shown to illustrate the effectiveness of the proposed designs and models, even under block constraints.