The Construction of Effective Multi-Dimensional Computer Designs of Experiments Based on a Quasi-Random Additive Recursive Rd-sequence

Abstract

Uniform multi-dimensional designs of experiments for effective research in computer modelling are highly demanded. The combinations of several one-dimensional quasi-random sequences with a uniform distribution are used to create designs with high homogeneity, but their optimal choice is a separate problem, the solution of which is not trivial. It is believed that now the best results are achieved using Sobol’s LPτ-sequences, but this is not observed in all cases of their combinations. The authors proposed the creation of effective uniform designs with guaranteed acceptably low discrepancy using recursive Rd-sequences and not requiring additional research to find successful combinations of vectors set distributed in a single hypercube. The authors performed a comparative analysis of both approaches using indicators of centred and wrap-around discrepancies, graphical visualization based on Voronoi diagrams. The conclusion was drawn on the practical use of the proposed approach in cases where the requirements for the designs allowed restricting to its not ideal but close to it variant with low discrepancy, which was obtained automatically without additional research.

Keywords

• computer designs of the experiment
• generalized discrepancy
• lp-sequence
• parameterless additive recursive rd-sequences
• quasi-random expanding sequences
• uniformity of distribution
• voronoi diagrams