Construction of uniform designs for high-dimensional screening <i>via</i> an adjusted multiple quadrupling algorithm

One of the most common strategies to achieve optimum designs for physical and computer high-dimensional experiments with no model pre-specification and limited budget is to uniformly spread the design points over the experimental domain, which are called uniform designs. A uniform design provides good design space coverage (space-filling), resulting in more accurate estimates using fewer points. Algorithmic search is commonly used for finding such designs, but this approach becomes ineffective for large problems. Though the construction of uniform designs theoretically is challenging, intriguing and encouraging findings have recently been accomplished for highly specialized cases. This paper gives a new theoretical construction method for high-dimensional experiments with a mixture of four-level and sixteen-level factors <i>via</i> an adjusted version of the multiple quadrupling algorithm (Elsawah, Communication in Mathematics and Statistics 10:623-652, 2022). The new technique (called AMQA) is simple to use since it only needs small suitable four-level designs, which may be easily generated theoretically or by algorithmic search. The quality of the small designs ensures the quality of the large designs. The effectiveness of the AMQA is investigated both theoretically and computationally. The main findings demonstrate that, compared with other widely used techniques, the AMQA provides more accurate results for high-dimensional screening using a variety of models, including polynomial, spline, and kriging models, as well as variable selection techniques, including AIC, BIC, RIC, SCAD, and LASSO. To further improve performance, a hybrid algorithm that combines the AMQA with the iterative threshold accepting algorithm is proposed.