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


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.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] T. J. Santner, B. J. Williams and W. I. Notz, The Design and Analysis of Computer Experiments. New York: Springer (Springer series in statistics), 2018.

  • [2] S. Koziel and X.-S. Yang, Computational Optimization, Methods and Algorithms. Berlin Heidelberg: Springer-Verlag (Studies in Comp. Intelligence), 2016.

  • [3] J. Ping, Z. Qi and S. Xinyu, Surrogate Model-Based Engineering Design and Optimization. Springer (Springer Tracts in Mechanical Engineering), 2020.

  • [4] T. El-Ghazali, Metaheuristics From Design To Implementation. Wiley: (Wiley Series on Parallel and Distributed Computing), 2009.

  • [5] W. D. Kelton and A. M. Law, Simulation Modeling and Analysis. 3rd ed. New York: McGraw-Hill, Mathematics @ Analysis, 2004.

  • [6] N. D. Koshevoy, E. M. Kostenko, A. V. Pavlyk, I. I. Koshevaja and T. G. Rozhnova, “Research of multiple plans in multi-factor experiments with a minimum number of transitions of levels of factors,” Radio Electronics, Computer Science, Control, vol. 49, issue 2, pp. 53–59, 2019.

  • [7] L. Kuipers and H. Niederreiter, Uniform distribution of sequences. Moscow: Nauka, 1985.

  • [8] P. Jäckel, Monte Carlo Methods in Finance. Wiley, 2002.

  • [9] S. G. Radchenko, Methodology of regression analysis: monograph. Kyiv: Korniychuk, 2011. (in Russian)

  • [10] P. Hellekalek, G. Larcher, (Eds). Random and Quasi-Random Point Sets. 1st ed. Springer: Lecture notes in statistics 138, 1998.

  • [11] M. Roberts, May 2018. The unreasonable effectiveness of quasirandom sequences. [Online]. Available:

  • [12] M. Elsawah, Constructing Uniform Experimental Designs: In View of Centered and Wrap-around Discrepancy. 1st ed. LAP LAMBERT Academic Publishing, 2014.

  • [13] I. M. Sobol and R.B. Statnikov, The choice of optimal parameters in problems with many criteria. Moskow: Drofa, 2006. (in Russian)


Journal + Issues