A novel hybrid algorithm for designing mixed three- and nine-level experiments without modeling assumptions

Abstract

In classical design theory, the majority of selection criteria for optimal designs depend on a model that is presumptively true to the experimenters. The model used to choose the design can be substantially misspecified when the true model is unknown or ambiguous. As a result, the selected design will be ineffective in fitting the true model. Space-filling designs (SFDs) can be utilized to solve this issue and spare the experimenters from having to specify the models. Uniform designs (UDs) are a desirable type of SFDs for industrial experiments without modeling assumptions and computer experiments with limited computational budgets. UDs are commonly generated using algorithmic search, but large experiments render this approach ineffective. Theoretical construction of UDs is challenging even for especial cases. This paper gives an easy-to-use non-iterative technique for constructing UDs for large experiments with a mixture of three- and nine-level factors. To investigate the efficiency and robustness of the new designs, their modeling performance is investigated using computer experiments with a variety of true models. The results reveal that they have good performance even with few experimental runs compared with the existing recommended designs. Theoretical justifications for some conditions that can improve the space-filling behavior of the new designs are investigated. Furthermore, a hybrid algorithm is provided to further enhance the performance of the new designs by combining our new non-iterative method with the iterative threshold accepting algorithm.