電腦實驗(computer experiment)是探索複雜系統輸出反應值和輸入參數之間關係的重要工具，其重要特性是每一次的實驗非常耗費時間及運算的成本。一般在電腦實驗中，研究者較常關心的多是反應曲面的配適和輸出反應值的最佳化等問題(如極大或極小值)。借由一真實平行分散處理系統的啟發，本文所關心的是如何找出系統反應值的局部目標區域。此目標區域有一個非常重要的特性，即區域內外的輸出值所呈現的反應曲面並不連續，因此一般傳統的反應曲面法(response surface methodology)無法適用。本文提出一個新的、可估計不同類型電腦實驗目標區域的有效方法，其中包含了逐步均勻設計和建立分類模型的概
念，電腦模擬的結果也證明了所提方法準確又有效率。

Computer experiment has been an important tool for exploring the relationships between the input factors and the output responses. It’s important feature is that conducting an experiment is usually time consuming and computationally expensive. In general, researchers are more interested in finding an adequate model for the response surface and the related output optimization problems over the entire input space. Motivated by a real-life parallel and distributed system, here we focus on finding a localized “target region” for the computer experiment. The experiment here has an important characteristic - the response surface is not continuous over the target region of interest. Thus, the traditional response surface methodology (RSM) cannot be directly applied. In this thesis, a novel and efficient methodology for estimating this type of target regions of computer experiment is proposed. The method incorporates the concept of sequential uniform design (UD) and the development of classification techniques based on support vector machines (SVM). Computer simulation shows that the proposed method can efficiently and precisely estimate the target region of
computer experiment with different shapes.

Box, G.E.P., Drapper, D.R., (1987), “Empirical Model Building and Response Surfaces,”
John Wiley & Sons, New York.
Chen, R.B., Hsu, Y.W., Hung, Y., Wang, W. (2012), “Central Composite Discrepany-
Based Uniform Designs for Irregular Experimental Regions,” Computational Statistics & Data Analysis.
Cheng, C.S., Li, K.C., (1995), “A study of the method of principal Hessian direction
for analysis of data from design experiments,” Statistica Sinica 5, 617-639.
Chuang, S.C., Hung, Y.C. (2010), “Uniform design over general input domains with
applications to target region estimation in computer experiments,” Computational Statistics & Data Analysis, 54, 219-232.
Fang, K.T., Lin, D.J., Winker, P., and Zhang, Y. (2000), “Uniform Design: Theory and
Applications,“ Technometrics, 42, 237-248.
Hickernell, F.J., (1999), “Goodness-of-fit statistics, discrepancies and robust designs,”
Statistics & Probability Letters 44, 73-78.
Huang, C.M., Lee, Y.J., Lin, D.K.J., Huang, S.Y., (2007), “Model selection for support vector machines via uniform design,” Computational Statistics & Data Analysis 52,
335-346.
Hung, Y.C., Chang, C.C., (2008), “Dynamic scheduling for switched processing systems with substantial service-mode switching times,” Queneing Systems: Theory
and Applications 60, 87-109.
Johnson, M.E., Moore, L.M., and Ylvisaker, D. (1990), “Minimax and Maximin
Distance Designs,” Journal of Statistical Planning and Inference. 26. 131-148.
Keerthi, S.S., Lin, C.J., (2003), “Asymptotic behaviors of support vector machines
with Gaussian kernel,” Neural Computation 15, 1667-1689.
McKay, M.D., Beckman, R.J., and Conover, W.J. (1979), “A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a
Computer Code,” Technometrics, 21, 239-245.
Owen, A.B. (1992), “Orthogonal Arrays for Computer Experiments, Integration and
Visualization,” Statistica Sinica, 2, 439-452.
Ranjan, P., Bingham, D., and Michailidis, G. (2008), “Sequential Experimental Design for Contour Estimation From Complex Computer Codes,” Technometrics, 50, 527-
541.
Sacks, J., Welch, W.J., Mitchell, T.J., Wynn, H.P., (1989). “Design and Analysis of
Computer Experiments,” Statistical Science, 4, 409-423.
Tang, B. (1993), “Orthogonal Array-Based Latin Hypercubes,” Journal of the American
Statistical Association, 88, 1392-1397.
Vapnik, V.N., (1998), “Statistical Learning Theory,” Wiley, New York.
Wang, D., Zhang, X., Fan, M. and Ye, X., (2015), “An Efficient Classifier Based on Hierarchical Mixing Linear Support Vector Machines,” IJCAI, AAAI Press, 3897-
3903.
Wu, C.F.J., Hamada, M., (2000), “Experiments: Planning, Analysis, and Parameter
Design,” Wiley, New York