Construction of Quasi-DOE on Sobol’s Sequences with Better Uniformity 2D Projections

Abstract

In order to establish the projection properties of computer uniform designs of experiments on Sobol’s sequences, an empirical comparative statistical analysis of the homogeneity of 2D projections of the best known improved designs of experiments was carried out using the novel objective indicators of discrepancies. These designs show an incomplete solution to the problem of clustering points in low-dimensional projections graphically and numerically, which requires further research for new Sobol’s sequences without the drawback mentioned above. In the article, using the example of the first 20 improved Sobol’s sequences, a methodology for creating refined designs is proposed, which is based on the unconventional use of these already found sequences. It involves the creation of the next dimensional design based on the best homogeneity and projection properties of the previous one. The selection of sequences for creating an initial design is based on the analysis of numerical indicators of the weighted symmetrized centered discrepancy for two-dimensional projections. According to the algorithm, the combination of sequences is fixed for the found variant and a complete search of the added one-dimensional sequences is performed until the best one is detected. According to the proposed methodology, as an example, a search for more perfect variants of designs for factor spaces from two to nine dimensions was carried out. New combinations of Sobol’s sequences with better projection properties than those already known are given. Their effectiveness is confirmed by statistical calculations and graphically demonstrated box plots and histograms of the projection indicators distribution of the weighted symmetrized centred discrepancy. In addition, the numerical results of calculating the volumetric indicators of discrepancies for the created designs with different number of points are given.