A sequential optimal Latin hypercube design method using an efficient recursive permutation evolution algorithm

References

• Ataie-Ashtiani, Behzad, M. Mahdi Rajabi, and Hans Janssen. 2015. “Efficiency Enhancement of Optimized Latin Hypercube Sampling Strategies: Application to Monte Carlo Uncertainty Analysis and Meta-modeling.” Advances in Water Resources 76: 127–139.
   Web of Science ®Google Scholar
• Ba, S. 2015. “SLHD: Maximin-Distance (Sliced) Latin Hypercube Designs.”
   Google Scholar
• Bates, Stuart J., Johann Sienz, and Vassili V. Toropov. 2004. “Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures.” Structural Dynamics and Materials Conference, Vol. 7, Palm Springs, California, pp. 5217–5223.
   Google Scholar
• Chen, Jiajie, Peter Z. G. Qian, and Jin Xu. 2015. “Sequentially Refined Latin Hypercube Designs: Reusing Every Point.” JASA Journal of the American Statistical Association 110 (512): 1696–1706.
   Web of Science ®Google Scholar
• Gharian, D., F. M. M. Ghaini, M. H. Heydari, and Z. Avazzadeh. 2020. “A Meshless Solution for the Variable-Order Time Fractional Nonlinear Klein–Gordon Equation.” International Journal of Applied and Computational Mathematics 6 (5): 130.
   Google Scholar
• Jin, Ruichen, Wei Chen, and Agus Sudjianto. 2005. “An Efficient Algorithm for Constructing Optimal Design of Computer Experiments.” Journal of Statistical Planning and Inference 134 (1): 268–287. doi:10.1016/j.jspi.2004.02.014.
   Web of Science ®Google Scholar
• Johnson, M. E., L. M. Moore, and D. Ylvisaker. 1990. “Minimax and Maximin Distance Designs.” Journal of Statistical Planning & Inference 26 (2): 131–148.
   Web of Science ®Google Scholar
• Li, William W., and C. F. Jeff Wu. 1997. “Columnwise-Pairwise Algorithms with Applications to the Construction of Supersaturated Designs.” Technometrics 39 (2): 171–179. doi:10.1080/00401706.1997.10485082.
   Web of Science ®Google Scholar
• Long, Teng, Di Wu, Xin Chen, Xiaosong Guo, and Li Liu. 2016. “A Deterministic Sequential Maximin Latin Hypercube Design Method Using Successive Local Enumeration for Metamodel-Based Optimization.” Engineering Optimization 48 (6): 1019–1036.
   Web of Science ®Google Scholar
• Mckay, M. D., R. J. Beckmanw, and J. Conover. 1979. “A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code.” Technometrics 21 (2): 239–245.
   Web of Science ®Google Scholar
• Morris, M. D., and T. J. Mitchell. 1995. “Exploratory Designs for Computational Experiments.” Journal of Statistical Planning and Inference 43 (3): 381–402.
   Web of Science ®Google Scholar
• Pho, Kim-Hung, M. H. Heydari, Bui Anh Tuan, and Mohammad Reza Mahmoudi. 2020. “Numerical Study of Nonlinear 2D Optimal Control Problems with Multi-term Variable-Order Fractional Derivatives in the Atangana-Baleanu-Caputo Sense.” Chaos, Solitons & Fractals 134: 109695.
   Web of Science ®Google Scholar
• Rennen, G., B. Husslage, E. Van Dam, and D. Den Hertog. 2010. “Nested Maximin Latin Hypercube Designs.” Structural & Multidisciplinary Optimization 41 (3): 371–395.
   Web of Science ®Google Scholar
• Shan, Songqing, and G. Gary Wang. 2010. “Survey of Modeling and Optimization Strategies to Solve High-Dimensional Design Problems with Computationally-Expensive Black-Box Functions.” Structural & Multidisciplinary Optimization 41 (2): 219–241.
   Web of Science ®Google Scholar
• Shang, Xiaobing, Tao Chao, Ping Ma, and Ming Yang. 2020. “An Efficient Local Search-Based Genetic Algorithm for Constructing Optimal Latin Hypercube Design.” Engineering Optimization 52 (2): 271–287.
   Web of Science ®Google Scholar
• Shewry, M. C., and H. P. Wynn. 1987. “Maximum Entropy Sampling.” Journal of Applied Statistics 14 (2): 165–170.
   Google Scholar
• Shi, Renhe, Teng Long, Nianhui Ye, Yufei Wu, Zhao Wei, and Zhenyu Liu. 2021. “Metamodel-Based Multidisciplinary Design Optimization Methods for Aerospace System.” Astrodynamics 5 (3): 185–215. doi:10.1007/s42064-021-0109-x.
   Google Scholar
• Simpson, T. W., A. J. Booker, D. Ghosh, A. A. Giunta, P. N. Koch, and R. J. Yang. 2004. “Approximation Methods in Multidisciplinary Analysis and Optimization: A Panel Discussion.” Structural & Multidisciplinary Optimization 27 (5): 302–313.
   Web of Science ®Google Scholar
• Simpson, T. W., J. D. Poplinski, P. N. Koch, and J. K. Allen. 2001. “Metamodels for Computer-Based Engineering Design: Survey and Recommendations.” Engineering with Computers 17 (2): 129–150.
   Web of Science ®Google Scholar
• Sun, Yibo, Xiuyun Meng, Teng Long, and Yufei Wu. 2019. “A Fast Optimal Latin Hypercube Design Method Using an Improved Translational Propagation Algorithm.” Engineering Optimization 3: 1–17.
   Google Scholar
• Tang, Chengmei, Yongquan Zhou, Qifang Luo, and Zhonghua Tang. 2022. “An Enhanced Pathfinder Algorithm for Engineering Optimization Problems.” Engineering with Computers 38 (Suppl. 2): 1481–1503. doi:10.1007/s00366-021-01286-x.
   Web of Science ®Google Scholar
• Viana, F. A. C. 2016. “A Tutorial on Latin Hypercube Design of Experiments.” Quality and Reliability Engineering International 32 (5): 1975–1985. doi:10.1002/qre.1924.
   Web of Science ®Google Scholar
• Viana, Fac, G. Venter, and V. Balabanov. 2010. “An Algorithm for Fast Optimal Latin Hypercube Design of Experiments.” International Journal for Numerical Methods in Engineering 82 (2): 135–156.
   Web of Science ®Google Scholar
• Wu, Z., D. Wang, P. N. Okolo, K. Zhao, and W. Zhang. 2017. “Efficient Space-Filling and Near-Orthogonality Sequential Latin Hypercube for Computer Experiments.” Computer Methods in Applied Mechanics & Engineering 324: 348–365.
   Web of Science ®Google Scholar
• Yang, J. W., Z. P. Wu, W. J. Wang, W. H. Zhang, H. L. Zhao, and J. B. Sun. 2022. “A Surrogate-Based Optimization Method for Mixed-Variable Aircraft Design.” Engineering Optimization 54 (1): 113–133. doi:10.1080/0305215x.2020.1855156.
   Web of Science ®Google Scholar
• Zhu, H. G., L. Liu, T. Long, and L. Peng. 2012. “A Novel Algorithm of Maximin Latin Hypercube Design Using Successive Local Enumeration.” Engineering Optimization 44 (5): 551–564. doi:10.1080/0305215x.2011.591790.
   Web of Science ®Google Scholar