序贯最大最小距离设计的空间填充性

doi:10.7523/j.issn.2095-6134.2018.06.003

中国科学院大学学报 ›› 2018, Vol. 35 ›› Issue (6): 731-734.DOI: 10.7523/j.issn.2095-6134.2018.06.003

序贯最大最小距离设计的空间填充性

滕一阳¹, 武赟², 熊世峰², 杨建奎¹

1 北京邮电大学理学院, 北京 100876;
2 中国科学院数学与系统科学研究院, 北京 100190

收稿日期:2017-09-29 修回日期:2017-11-16 发布日期:2018-11-15
通讯作者: 熊世峰
基金资助:
国家自然科学基金（11471172，11671386）资助

A space-filling property of sequential maximin distance designs

TENG Yiyang¹, WU Yun², XIONG Shifeng², YANG Jiankui¹

1 School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China;
2 Academy of Mathmetics and Systems Science, Chinese Academy of Science Beijng 100190, China

Received:2017-09-29 Revised:2017-11-16 Published:2018-11-15

摘要/Abstract

摘要： 最大最小距离设计是计算机试验中常用的一种空间填充设计。讨论序贯最大最小距离设计的空间填充性质，证明在样本量趋于无穷时，这种序贯设计中的点在试验区域内达到稠密.

关键词: 序贯设计, 空间填充设计, 计算机试验

Abstract: Maximin distance designs, as a class of space-filling designs, are commonly used in computer experiments. In this paper we discuss the space-filling properties of sequential maximin distance design. We prove that the points in such a sequential design become dense in the experimental region as the sample size goes to infinity.

Key words: sequential design, space-filling design, computer experiment

中图分类号:

O212.6

滕一阳, 武赟, 熊世峰, 杨建奎. 序贯最大最小距离设计的空间填充性[J]. 中国科学院大学学报, 2018, 35(6): 731-734.

TENG Yiyang, WU Yun, XIONG Shifeng, YANG Jiankui. A space-filling property of sequential maximin distance designs[J]. , 2018, 35(6): 731-734.

参考文献

[1] Morris M D, Mitchell T J, Ylvisaker D. Bayesian design and analysis of computer experiments:use of derivatives in surface prediction[J]. Technometrics, 1993, 35(3):243-255.
[2] Morris M D. A class of three-level experimental designs for response surface modeling[J]. Technometrics, 2000, 42(2):111-121.
[3] Moore L M, Mckay M D, Campbell K S. Combined array experiment design[J]. Reliability Engineering and System Safety, 2006, 91(10/11):1281-1289.
[4] Lehman J S, Santner T J, Notz W I. Designing computer experiments to determine robust control variables[J]. Statistica Sinica, 2004, 14(2):571-590.
[5] Mu W Y, Xiong S F. On algorithmic construction of maxmin distance designs[J].Communications in Statistics-Simulation and Computation, 2016, 11(1):1-14.
[6] Santner T J, Williams B J, Notz W I. The design and analysis of computer experiments[M]. New York:Springer, 2003:138.
[7] Tang B X. A theorem for selecting oa-based latin hypercubes using a distance criterion[J]. Communication in Statistics-Theory and Methods, 2007, 23(7):2047-2058.
[8] Crombecq K, Dheane T. Generating sequential space-filling designs using genetic algorithms and Monte Carlo methods[C]//International Conference on Simulated Evolution and Learning, 2010, 6457:80-84.
[9] Dobriban E, Fortney K. Space-filling properties of good lattice point sets[J]. Biometrika, 2015, 124(4):959-966.
[10] Zhou Y D, Xu H. Space-filling fractional factorial designs[J]. Journel of the American Statistical Association, 2014, 109(507):1134-1144.
[11] Wahl F, Mercadier C, Helbert C. A standardized distance-based index to assess the quality of space-filling designs[J]. Statistics & Computing, 2017, 27(2):319-329.
[12] Johnson M, Moore L, Ylvisaker D. Minimax and maximin distance design[J]. Journal of Statistical Planning and Inference. 1990, 24(2):131-148.
[13] Li Z, Nakayama S. Maximin distance-lattice hypercube design for computer experiment based on genetic algorithm[C]//International Conferences on Info-tech and Info-net, 2001, 2:814-819.
[14] Marengo E, Todeschini R. A new algorithm for optimal, distance-based experimental design[J]. Chemometrics and Intelligent Laboratory Systems, 1992, 16(1):37-44.
[15] Coetzer R L J, Roseouw R F, Le Roux N J. Efficient maximin distance designs for experiments in mixtures[J]. Journal of Applied Statistics, 2012, 39(9):1939-1951.
[16] Xia Y, Cai T, Cai T T. Maximum Projection Designs for computer experiments[J]. Biometrika, 2015, 102(2):371-380.
[17] Li K, Jiang B, Ai M. Sliced space-filling designs with different levels of two-dimensional uniformity[J]. Journal of Statistical Planning & Inference, 2015, 157-158:90-99.
[18] Long T, Wu D, Guo X, et al. A deterministic sequential maximin Latin hypercube design method using successive local enumeration for metamodel-based optimization[J]. Engineering Optimization, 2016, 48(6):1019-1036.
[19] Duan W, Ankenman B E, Sanchez S M, et al. Sliced full factorial-based latin hypercube designs as a framework for a batch sequential design algorithm[J]. Technometrics, 2017, 59(1):1-39.

序贯最大最小距离设计的空间填充性

A space-filling property of sequential maximin distance designs

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