Details of Research Outputs

The majority of classical optimization criteria for designing experiments rely on prior assumptions on the used models that are presumptively correct to guide experimenters before conducting their experiments. These criteria are unlikely to be useful for experiments with unknown models, and the resulting designs are not going be effective at fitting the actual models. Space-filling designs (SFDs), which release the experimenters from having to specify the models, can be utilized to address this problem. Uniform designs (UDs) are a preferred class of SFDs for physical and computer experiments with constrained resources and without prior assumptions. In order to construct UDs, algorithmic search, especially the threshold accepting (TA) algorithm, is extensively used. However, large-scale experiments reveal that algorithmic search is costly, laborious and inefficient. The demand for theoretical constructing algorithms for UDs, which are difficult to come up with even in special cases, is therefore considerable. A novel theoretical construction algorithm for large UDs with a mixture of two-, three-, and nine-level factors is given in this paper. The new algorithm combines enhanced versions of the multiple doubling (MD) algorithm (Elsawah in Stat Pap 62(6):2923–2967, 2021) with the multiple tripling (MT) algorithm (Elsawah in J Comput Appl Math 384:113164, 2021) using a new coding scheme map. The performance of the new proposed MD-MT hybrid algorithm is investigated based on the modeling ability of its resulting designs that show a good performance even for a small number of experimental points and without prior assumptions on the used models. In addition, the effectiveness of the new designs is studied in terms of several optimality criteria for both full- and low-dimensional investigations. The iterative TA algorithm is merged with the new proposed theoretical MD-MT hybrid algorithm to produce the new MD-MT-TA hybrid algorithm, which enhances the performance even more. Furthermore, some conditions for generating non-isomorphic space-filling designs are looked at.