Optimal Order-of-Addition Experiments under a Prior Constraint

The order-of-addition experiments are widely used in many fields, including food and industrial production, but the relative research under prior constraints is limited. The purpose of this paper is to select an optimal sequence under the restriction that component i is added before component j, while it is unachievable to compare all sequences when the number of components m is large. To achieve this, a constrained PWO model is first provided, and then the D-optimal designs for order-of addition experiments with minimal-points via the modified threshold accepting algorithm is established. The effectiveness of the proposed method is demonstrated through a job scheduling problem with a prior constraint for teaching cases.