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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 王偉仲 | |
| dc.contributor.author | Yen-Wen Hsu | en |
| dc.contributor.author | 許彥文 | zh_TW |
| dc.date.accessioned | 2021-06-13T06:39:58Z | - |
| dc.date.available | 2012-01-01 | |
| dc.date.copyright | 2011-08-02 | |
| dc.date.issued | 2011 | |
| dc.date.submitted | 2011-07-25 | |
| dc.identifier.citation | [1] FANG Kai-Tai, MA Chang-Xing, and WINKER Peter. Centered l 2 −discrepancy of
random sampling and latin hypercube design, and construction of uniform designs, 2002. Anglais. [2] Kai-Tai Fang, Xuan Lu, and Peter Winker. Lower bounds for centered and wrap- around l2-discrepancies and construction of uniform designs by threshold accepting. Journal of Complexity, 19(5):692--711, 2003. [3] Changxing Ma and Kai-Tai Fang. A new approach to construction of nearly uniform designs. International Journal of Materials and Product Technology, 20:115 -- 126, 2004. [4] Ruichen Jin, Wei Chen, and Agus Sudjianto. An efficient algorithm for construct- ing optimal design of computer experiments. Journal of Statistical Planning and Inference, 134(1):268--287, 2005. [5] M. Liefvendahl and R. Stocki. A study on algorithms for optimization of latin hy- percubes. Journal of Statistical Planning and Inference, 136(9):3231--3247, 2006. [6] E. R. van Dam, B. Husslage, D. den Hertog, and H. Melissen. Maximin latin hyper- cube designs in two dimensions. Operations Research, 55:158--169, 2007. [7] A. Grosso, A. R. M. J. U. Jamali, and M. Locatelli. Finding maximin latin hyper- cube designs by iterated local search heuristics. European Journal of Operational Research, 197(2):541--547, 2009. [8] Peter Z. G. Qian. Nested latin hypercube designs. Biometrika, 2009. [9] P. Z. G. Qian, M. Ai, and C. F. J. Wu. Construction of nested space-filling designs. ArXiv e-prints, September 2009. [10] G. Rennen, B.G.M. Husslage, E.R. van Dam, and D. den Hertog. Nested maximin latin hypercube designs. CentER Discussion Paper Series, 2009-06, 2009. [11] STINSTRA Erwin, DEN HERTOG Dick, STEHOUWER Peter, and VESTJENS Arjen. Constrained maximin designs for computer experiments. 45(4):7, 2003. Anglais. [12] Jian-Hui Ning, Yong-Dao Zhou, and Kai-Tai Fang. Discrepancy for uniform design of experiments with mixtures. Journal of Statistical Planning and Inference, 141(4): 1487--1496, 2011. [13] S. C. Chuang and Y. C. Hung. Uniform design over general input domains with applications to target region estimation in computer experiments. Computational Statistics & Data Analysis, 54(1):219--232, 2010. [14] Ying Hung, Yasuo Amemiya, and Chien-Fu Jeff Wu. Probability-based latin hyper- cube designs for slid-rectangular regions. Biometrika, 97(4):961 -- 968, 2010. [15] Dennis K. J. Lin Kai-Tai Fang. The uniform design: application of number-theoretic methods in experimental design. Acta Mathematical Application Sinica, 3:363--372, 1980. [16] M. E. Johnson, L. M. Moore, and D. Ylvisaker. Minimax and maximin distance designs. Journal of Statistical Planning and Inference, 26(2):131 -- 148, 1990. [17] Kai-Tai Fang, Dennis K. J. Lin, Peter Winker, and Yong Zhang. Uniform design: Theory and application. Technometrics, 42(3):237--248, 2000. [18] Felipe A C Viana, Gerhard Venter, and Vladimir Balabanov. An algorithm for fast optimal latin hypercube design of experiments. International Journal for Numerical Methods in Engineering, 82:135--156, 2010. [19] Gunter Dueck and Tobias Scheuer. Threshold accepting: A general purpose opti- mization algorithm appearing superior to simulated annealing. Journal of Computa- tional Physics, 90(1):161 -- 175, 1990. [20] D. K. J. Lin, C. Sharpe, and P. Winker. Optimized u-type designs on flexible regions. Computational Statistics & Data Analysis, 54(6):1505--1515, 2010. [21] DRAPER N. R. and GUTTMAN I. Responses surface designs in flexible regions, 1986. Anglais. [22] J. Kennedy and R. Eberhart. Particle swarm optimization. In Neural Networks, 1995. Proceedings., IEEE International Conference on, volume 4, pages 1942--1948, Au- gust 2002. [23] Ioan Cristian Trelea. The particle swarm optimization algorithm: convergence analy- sis and parameter selection. Information Processing Letters, 85(6):317 -- 325, 2003. [24] J. Kennedy and R.C. Eberhart. A discrete binary version of the particle swarm al- gorithm. In Systems, Man, and Cybernetics, 1997. 'Computational Cybernetics and Simulation'., 1997 IEEE International Conference on, volume 5, pages 4104 --4108 vol.5, oct 1997. [25] R. R. Schmidt, E. E. Cruz, and M. Iyengar. Challenges of data center thermal man- agement. IBM Journal of Research and Development, 49(4.5):709--723, 2005. [26] Ying Hung. Adaptive Probability-Based Latin Hypercube Designs. Journal of the American Statistical Association, 106(493):213--219, March 2011. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/35062 | - |
| dc.description.abstract | 在實驗設計中，時常會觀察到有不規則形狀的實驗區域。在以 Central Composite Discrepancy 為實驗均勻性的衡量指標之下，我們提
出 Discrete Particle Swarm Optimization (DPSO) 最佳化演算法在一般性的實驗區域上找尋最佳化實驗設計。實驗數據顯示此演算法能比現有文獻中的最佳化演算法更有效率地找尋最佳實驗設計。為處理高維度的 Central Composite Discrepancy 龐大計算量，我們利用圖形處理器做運算上的加速而能夠在合理的時間內尋找的不錯的均勻實驗設計。 | zh_TW |
| dc.description.abstract | In experiment designs, irregular shapes of experimental regions are often observed. Using a recently proposed discrepancy measurement Central Composite Discrepancy as uniformity criterion, we propose a Discrete Particle Swarm Optimization algorithm for optimizing experimental designs on the general input domains. Numerical results show evidences that the new proposed algorithm is superior to other optimization algorithm in established literature. For the high computation cost of computing Central Composite Discrepancy on higher dimensions, using Graphic Processing Unit for acceleration enable us to find uniform design on higher dimensions in reasonable time. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T06:39:58Z (GMT). No. of bitstreams: 1 ntu-100-R98221031-1.pdf: 13932279 bytes, checksum: 95d745b18fc3d4f202f4143f34bae6be (MD5) Previous issue date: 2011 | en |
| dc.description.tableofcontents | Table of Contents i
List of Algorithms iv List of Tables v List of Figures vii 摘要 viii Abstract ix 1 Introduction 1 2 Problem Formulation 3 2.1 Uniform Design . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Uniformity Criterion on General Input Domain . . . . . . . 3 2.2.1 Central Composite Discrepancy . . . . . . . . . . . 3 2.2.2 Criterion Properties . . . . . . . . . . . . . . . . . 4 2.2.3 Approximation . . . . . . . . . . . . . . . . . . . 9 2.2.4 Optimization Goal . . . . . . . . . . . . . . . . . . 12 3 Review of Optimization Algorithms 13 i3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.2 Threshold Accepting . . . . . . . . . . . . . . . . . . . . . 13 3.3 Particle Swarm Optimization . . . . . . . . . . . . . . . . 15 4 Proposed New Optimization Algorithm 20 4.1 Discrete Particle Swarm Optimization . . . . . . . . . . . . 20 4.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 23 5 Acceleration of CCD Function Evaluation by Paralleling Com- puting via Graphic Processing Unit 25 5.1 Introduction to Graphic Processing Unit . . . . . . . . . . . 25 5.2 Parallel Acceleration Scheme for Computing CCD . . . . . 26 5.3 Other Code Optimizations for Graphic Processing Unit . . . 27 5.4 Time Comparison . . . . . . . . . . . . . . . . . . . . . . 28 6 Numerical Result 30 6.1 Flexible Region . . . . . . . . . . . . . . . . . . . . . . . 30 6.2 Comparison of Threshold Accepting and Discrete Particle Swarm Optimization Algorithm on Flexible Regions of Di- mension 2 and 3 . . . . . . . . . . . . . . . . . . . . . . . 32 6.3 Uniform Design on Flexible Regions of Dimension 4 and 5 generated by Discrete Particle Swarm Optimization Algorithm 36 7 Real Application 38 8 Conclusion 41 Appendix 42Computation Detail of CCD p . . . . . . . . . . . . . . . . . . . 42 Bibliography 44 | |
| dc.language.iso | en | |
| dc.subject | 平行計算 | zh_TW |
| dc.subject | 均勻實驗設計 | zh_TW |
| dc.subject | 離散粒子群優化演算法 | zh_TW |
| dc.subject | 最佳化問題 | zh_TW |
| dc.subject | 圖形顯示器 | zh_TW |
| dc.subject | Paral- lel Computing | en |
| dc.subject | Uniform Experiment Design | en |
| dc.subject | Discrete Particle Swarm Optimization | en |
| dc.subject | Optimization Problem | en |
| dc.subject | Graphic Processing Unit | en |
| dc.title | 高維度不規則區域最佳均勻實驗設計的快速算法 | zh_TW |
| dc.title | Efficient Optimization Algorithm of Uniform Experiment
Design on High Dimension Irregular Region | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 99-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.coadvisor | 陳瑞彬 | |
| dc.contributor.oralexamcommittee | 洪英超 | |
| dc.subject.keyword | 均勻實驗設計,離散粒子群優化演算法,最佳化問題,圖形顯示器,平行計算, | zh_TW |
| dc.subject.keyword | Uniform Experiment Design,Discrete Particle Swarm Optimization,Optimization Problem,Graphic Processing Unit,Paral- lel Computing, | en |
| dc.relation.page | 47 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2011-07-25 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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