跳到主要內容

臺灣博碩士論文加值系統

(18.97.9.169) 您好!臺灣時間:2025/02/16 07:28
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

我願授權國圖
: 
twitterline
研究生:羅華文
研究生(外文):Hua-Wen Luo
論文名稱:代理輔助最佳化的動態精度控制法
論文名稱(外文):Dynamic Precision Control in Surrogate Assisted Optimization
指導教授:王偉仲
口試委員:陳瑞彬黃聰明
口試日期:2011-01-11
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2011
畢業學年度:99
語文別:英文
論文頁數:50
中文關鍵詞:動態精度控制最佳化問題代理曲面均勻設計收斂分析
外文關鍵詞:dynamic precision controloptimizationsurrogateresponse surfacesuniform design
相關次數:
  • 被引用被引用:0
  • 點閱點閱:348
  • 評分評分:
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:1
In many optimization problems, the number of function evaluations is severely limited by time or cost. These problems pose a special challenge to the field of global optimization, since existing methods often require more function evaluations than can be comfortably afforded. One way to address this challenge is to t response surfaces or surrogate surface to data collected
by evaluating the objective and constraint functions at a few points. These surfaces can then be used for visualization, trade o analysis, and optimization. We then show how these approximating functions can be used to construct an efficient global optimization algorithm with a credible stopping rule. The key to using response surfaces for global optimization lies in balancing the need to exploit the approximating surface (by sampling where it is minimized) with the need to improve the approximation (by sampling where prediction error may be high). Striking this balance requires solving certain auxiliary problems which have previously been considered intractable, but we show how these computational obstacles can be overcome.

1 Introduction. 7
2 Method. 9
2.1 Mani Components of Algorithm. . . . . . . . . . . . . . . . . . . . . . 11
2.2 Theoretical Algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3 Convergence analysis 25
4 Numerical Experiments. 30
4.1 Shift-invert problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.2 Lyapunov exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2.1 Numerical Results for Solving LE 1. . . . . . . . . . . . . . . . 37
4.2.2 Numerical Results for Solving LE 2. . . . . . . . . . . . . . . . 41

[1] G.E.P. Box and KB Wilson. On the experimental attainment of optimum conditions. Journal of the Royal Statistical Society. Series B (Methodological), 13(1):1-45, 1951.
[2] W.C. Davidon. Variable metric method for minimization. SIAM Journal on Optimization, 1:1, 1991.
[3] R. Hooke and TA Jeeves. Direct search solution of numerical and statistical problems. Journal of the ACM (JACM), 8(2):212-229, 1961.
[4] M. C. Kennedy and A. O''Hagan. Predicting the output from a complex computer code when fast approximations are available. Biometrika, 87(1):1-13, 2000.
[5] Z. Qian, C.C. Seepersad, V.R. Joseph, J.K. Allen, and C.F.J. Wu. Building surrogate models based on detailed and approximate simulations. Journal of Mechanical Design, 128:668, 2006.
[6] Peter Z. G. Qian and C. F. Je Wu. Bayesian hierarchical modeling for integrating low-accuracy and high-accuracy experiments. Technometrics, 50(2):192-204, 2008.
[7] Neil W. Bresslo Alex Ander I J. Forrester and Andy J. Keane. Optimization using surrogate models and partially converged computational fluid dynamics simulations. Proc. R. Soc. A, 462:2177-2204, 2006.
[8] Alexander I. J. Forrester, András Sóbester, and Andy J. Keane. Multi-fidelity optimization via surrogate modelling. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 463(2088):3251-3269, 2007.
[9] L. C. Lai. Adaptive search regions in derivative free optimization problems. Master’s thesis, 2008.
[10] Weichung Wang, Ray-Bing Chen, and Chia-Lung Hsu. A surrogate-assisted method using adaptive multi-accurate function evaluations. 2008.
[11] http://en.wikipedia.org/wiki/kriging.
[12] http://www.math.hkbu.edu.hk/uniformdesign.
[13] R. Barrett. Templates for the solution of linear systems: building blocks for iterative methods. Society for Industrial Mathematics, 1994.

QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top