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

[1] K.T. Fang, M.Q. Liu, H. Qin, and Y. Zhou, Theory and Application of Uniform Experimental Designs. Springer and Science Press, Singapore, 2018. Search in Google Scholar

[2] V.Ya. Halchenko, R.V. Trembovetska, V.V. Tychkov, and A.V. Storchak, “The construction of effective multidimensional computer designs of experiments based on a quasi-random additive recursive Rd– sequence,” Applied Computer Systems, vol. 25, no. 1, pp. 70–76, May 2020. https://doi.org/10.2478/acss-2020-0009 Search in Google Scholar

[3] V.Ya. Galchenko, N.D. Koshevoy, and R.V. Trembovetskaya, “Homogeneous plans of multi-factory experiments on quasi-random R-Roberts sequences for surrogate modeling in a vortex style structuroscopy,” Radio Electronics, Computer Science, Control, vol. 3, pp. 22–30, 2022. https://doi.org/10.15588/1607-3274-2022-3-2 Search in Google Scholar

[4] B. Kuznetsov, I. Bovdui, and T. Nikitina, “Multiobjective optimization of electromechanical servo systems,” in 2019 IEEE 20th International Conference on Computational Problems of Electrical Engineering (CPEE), Lviv-Slavske, Ukraine, Sep. 2019, pp. 1–4. https://doi.org/10.1109/CPEE47179.2019.8949122 Search in Google Scholar

[5] N.D. Koshevoy, V.A. Dergachov, A.V. Pavlik, V.P. Siroklyn, I.I. Koshevaya, and O.A. Hrytsai, “Modified Gray codes for the value (time) optimization of a multifactor experiment plans,” in Conference on Integrated Computer Technologies in Mechanical Engineering– Synergetic Engineering, Springer, Oct. 2021, pp. 331–343. https://doi.org/10.1007/978-3-030-94259-5_29 Search in Google Scholar

[6] S. Harase, “Comparison of Sobol’ sequences in financial applications,” Monte Carlo Methods and Applications, vol. 25, no. 1, pp. 61–74, Jan. 2019. https://doi.org/10.1515/mcma-2019-2029 Search in Google Scholar

[7] H. Ping, D.K. Lin, L. Min-Qian, X. Qingsong, and Z. Yongdao, “Theory and application of uniform designs,” SCIENTIA SINICA Mathematica, vol. 50, no. 5, May 2020, Art. no. 561. https://doi.org/10.1360/SSM-2020-0065 Search in Google Scholar

[8] M. Renardy, L.R. Joslyn, J.A. Millar, and D.E. Kirschner, “To Sobol or not to Sobol? The effects of sampling schemes in systems biology applications,” Mathematical Biosciences, vol. 337, Jul. 2021, Art. no. 108593. https://doi.org/10.1016/j.mbs.2021.108593 Search in Google Scholar

[9] Y. Han, M. Curtis, and A. Kelly, “Space-filling designs for modeling & simulation,” Institute for Defense Analyses, IDA Document NS D-21562, Jun. 2021. [Online]. Available: https://www.ida.org/-/media/feature/publications/s/sp/space-filling-designs-for-modeling-and-simulation-validation/d-21562.ashx Search in Google Scholar

[10] Y. Wang, F. Sun, and H. Xu, “On design orthogonality. Maximin distance and projection uniformity for computer experiments,” Journal of the American Statistical Association, vol. 117, no. 537, pp. 375–385, Jul. 2022. https://doi.org/10.1080/01621459.2020.1782221 Search in Google Scholar

[11] R.B. Chen, C.H. Li, Y. Hung, and W. Wang, “Optimal noncollapsing space-filling designs for irregular experimental regions,” Journal of Computational and Graphical Statistics, vol. 28, no. 1, pp. 74–91, Sep. 2019. https://doi.org/10.1080/10618600.2018.1482760 Search in Google Scholar

[12] I.M. Sobol, “Uniformly distributed sequences with additional uniformity properties,” USSR Comput. Math. and Math. Phys., vol. 16, no. 5, pp. 236–242, 1976. https://doi.org/10.1016/0041-5553(76)90154-3 Search in Google Scholar

[13] S.S. Garud, I.A. Karimi, and M. Kraft, “Design of computer experiments: A review,” Computers & Chemical Engineering, vol. 106, pp. 71–95, Nov. 2017. https://doi.org/10.1016/j.compchemeng.2017.05.010 Search in Google Scholar

[14] A. Singhee and R.A. Rutenbar, Novel Algorithms for Fast Statistical Analysis of Scaled Circuits. Springer Science & Business Media, 2009. https://doi.org/10.1007/978-90-481-3100-6 Search in Google Scholar

[15] S. Joe and F.Y. Kuo, “Constructing Sobol sequences with better two-dimensional projections,” SIAM Journal on Scientific Computing, vol. 30, no. 5, pp. 2635–2654, 2008. https://doi.org/10.1137/070709359 Search in Google Scholar

[16] M. Bayousef and M. Mascagni, “A computational investigation of the optimal Halton sequence in QMC applications,” Monte Carlo Methods and Applications, vol. 25, no. 3, pp. 187–207, Aug. 2019. https://doi.org/10.1515/mcma-2019-2041 Search in Google Scholar

[17] I.M. Sobol’, D. Asotsky, A. Kreinin, and S. Kucherenko, “Construction and comparison of high-dimensional Sobol’ generators,” Wilmott, vol. 2011, no. 56, pp. 64–79, Nov. 2011. https://doi.org/10.1002/wilm.10056 Search in Google Scholar

[18] E. Atanassov, “Deterministic algorithm for optimising the direction numbers of the Sobol’ sequence,” Mathematics and Education in Mathematics, vol. 50, pp. 83–94, 2021. https://smb.math.bas.bg/mem/index.php/memjournal/article/view/9 Search in Google Scholar

[19] E. Atanassov, S. Ivanovska, and A. Karaivanova, “Optimization of the direction numbers of the Sobol sequences,” in International Conference on Variability of the Sun and Sun-like Stars: from Asteroseismology to Space Weather, Springer, Cham, Sep. 2019, pp. 145–154. https://doi.org/10.1007/978-3-030-55347-0_13 Search in Google Scholar

[20] E. Atanassov and S. Ivanovska, “On the use of Sobol’ sequence for high dimensional simulation,” in International Conference on Computational Science, Springer, Cham, 2022, pp. 646–652. https://doi.org/10.1007/978-3-031-08760-8_53 Search in Google Scholar

[21] D. Panagiotopoulos, Z. Mourelatos, and D. Papadimitriou, “A group-based space-filling design of experiments algorithm,” SAE International Journal of Materials and Manufacturing, vol. 11, no. 4, pp. 441–452, Apr. 2018. https://doi.org/10.4271/2018-01-1102 Search in Google Scholar

[22] BRODA, “High dimensional Sobol’ sequences,” 2021. [Online]. Available: https://www.broda.co.uk/software.html Search in Google Scholar

[23] X. Ke, R. Zhang, and H.J. Ye, “Two-and three-level lower bounds for mixture L2-discrepancy and construction of uniform designs by threshold accepting,” Journal of Complexity, vol. 31, no. 5, pp. 741–753, Oct. 2015. https://doi.org/10.1016/j.jco.2015.01.002 Search in Google Scholar

[24] L. He, H. Qin, and J. Ning, “Weighted symmetrized centered discrepancy for uniform design,” Communications in Statistics-Simulation and Computation, vol. 51, no. 8, pp. 4509–4519, Mar. 2020. https://doi.org/10.1080/03610918.2020.1744063 Search in Google Scholar

[25] “Sobol sequence generator.” [Online]. Available: https://web.maths.unsw.edu.au/~fkuo/sobol/. Accessed 15 Feb 2022. Search in Google Scholar

[26] I.M. Sobol’ and R.B. Statnikov, The Choice of Optimum Parameters in Tasks with Many Criteria, 2^nd ed. Drofa, Moscow, 2006. Search in Google Scholar