模擬最佳化方法能藉由電腦進行模擬實驗來解決實務中無法以解析技巧求解的問題，在現實生活中應用甚廣，已為目前很常見的技術之一。而若要針對大型問題進行最佳化，仍所費不貲，因此在進行最佳化前常引入篩選因子機制以減少所需的模擬成本。然而典型的模擬最佳化方法是以期望值做為系統的績效指標，在許多問題上期望值並不適合作為績效指標，而分量就是良好的選擇，相較於期望值，分量較有彈性，且能提供更多的資訊，現在卻少有針對分量式最佳化問題的研究。本研究提出針對分量式最佳化問題的演算法，依CSB與STRONG為基礎架構進行修改，使演算法能自動化及有收斂性的保證，篩選因子也能透過統計檢定的方式確保結果的正確性以利最佳化進行，並探討分量估計與線性分量迴歸以建構更準確的模型，以不同的實驗設計方法與擴增方式使演算法能以較少的模擬觀測數達到收斂效果。此外，本研究提出之演算法亦使用變異數縮減技巧提高演算法的求解效率，也能使演算法更穩定的收斂至最佳解。

Simulation optimization is a widely-used technique which can adopt in many practical situations, because when the analytical form of a problem was not available, it can still conduct experiments to simulate the real system. However, classic simulation optimization focused on expectation, seldom research focused on quantile. Quantile is an important alternative to expectation in some problems which enables risk control. When it comes to large-scaled problems, it is important to conduct screening experiments to eliminate unimportant factors. In this research, a framework for quantile-based simulation optimization has been proposed. Due to the limitation of resources and computation abilities, it is significant to enhance the efficiency and reduce the number of observations of algorithm. To achieve our goals, we proposed an improved framework based on CSB and STRONG by using efficient experimental scheme that consists of efficient designs and checking the strong consistency of quantile regression. The screening procedure can control the Type I error to ensure the result and make the optimization procedure more efficient. In addition, a sequential design framework and an assignment strategy for random number streams are also involved to obtain computation gains, which are able to reduce the number of observations.

摘要 II
Abstract III
目錄 IV
圖目錄 VI
表目錄 VII
第一章 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 3
1.3 論文架構 3
第二章 文獻探討 5
2.1 分量估計 5
2.2 篩選因子方法 7
2.3 實驗設計方法 9
2.4 模擬最佳化 11
第三章 問題定義 14
第四章 演算法架構 16
4.1 篩選因子架構 17
4.2 STRONG架構 23
4.3 中心點分量估計 27
4.4 建構分量迴歸模型 27
4.5 Stage Ι 29
4.6 Stage ΙΙ 33
4.7 Inner Loop 35
4.8 變異數縮減 41
第五章 數值實驗 43
5.1 測試函數 43
5.2 績效指標 46
5.3 數值結果 46
第六章 實證問題 50
第七章 結論與未來研究 54
參考文獻 55

Banks, J. (Ed.). (1998). Handbook of simulation: principles, methodology, advances, applications, and practice. John Wiley & Sons.
Bassett, G. W., & Koenker, R. W. (1986). Strong consistency of regression quantiles and related empirical processes. Econometric Theory, 2(2), 191-201.
Batur, D., & Choobineh, F. (2010). A quantile-based approach to system selection. European Journal of Operational Research, 202(3), 764-772.
Bettonvil, B., & Kleijnen, J. P. (1997). Searching for important factors in simulation models with many factors: Sequential bifurcation. European Journal of Operational Research, 96(1), 180-194.
Borror, C. M., Montgomery, D. C., & Myers, R. H. (2002). Evaluation of statistical designs for experiments involving noise variables. Journal of Quality Technology, 34(1), 54-70.
Box, G. E., & Behnken, D. W. (1960). Some new three level designs for the study of quantitative variables. Technometrics, 2(4), 455-475.
Box, G. E., & Draper, N. R. (1959). A basis for the selection of a response surface design. Journal of the American Statistical Association, 54(287), 622-654.
Box, G. E., & Draper, N. R. (1963). The choice of a second order rotatable design. Biometrika, 335-352.
Brodin, E. (2007). Extreme value statistics and quantile estimation with applications in finance and insurance. Chalmers University of Technology.
Chang, K. H. (2015). Improving the efficiency and efficacy of stochastic trust-region response-surface method for simulation optimization. IEEE Transactions on Automatic Control, 60(5), 1235-1243.
Chang, K. H., Hong, L. J., & Wan, H. (2013). Stochastic trust-region response-surface method (STRONG)—A new response-surface framework for simulation optimization. INFORMS Journal on Computing, 25(2), 230-243.
Cheng, R. C. (1997, December). Searching for important factors: Sequential bifurcation under uncertainty. In Proceedings of the 29th conference on Winter simulation (pp. 275-280). IEEE Computer Society.
Conn, A. R., Gould, N. I., & Philippe, L. (2000). Toint. Trust-region methods, Society for Industrial and Applied Mathematics, Philadelphia, PA.
Dette, H., & Trampisch, M. (2012). Optimal designs for quantile regression models. Journal of the American Statistical Association, 107(499), 1140-1151.
Dielman, T., Lowry, C., & Pfaffenberger, R. (1994). A comparison of quantile estimators. Communications in Statistics-Simulation and Computation, 23(2), 355-371.
Fu, M. C. (2006). Gradient estimation. Handbooks in operations research and management science, 13, 575-616.
Fu, M. C. (2002). Optimization for simulation: Theory vs. practice. INFORMS Journal on Computing, 14(3), 192-215.
Fu, M. C., & HILL, S. D. (1997). Optimization of discrete event systems via simultaneous perturbation stochastic approximation. IIE transactions, 29(3), 233-243.
Gunst, R. F. (1996). Response surface methodology: process and product optimization using designed experiments.
Harrell, F. E., & Davis, C. E. (1982). A new distribution-free quantile estimator. Biometrika, 69(3), 635-640.
Hoke, A. T. (1974). Economical second-order designs based on irregular fractions of the 3 n factorial. Technometrics, 16(3), 375-384.
Kleijnen, J. P. (2008). Design and analysis of simulation experiments. International series in operations research and management science.
Kleijnen, J. P., Bettonvil, B., & Persson, F. (2003). Finding the important factors in large discrete-event simulation: sequential bifurcation and its applications.
Kleijnen, J. P., Pierreval, H., & Zhang, J. (2011). Methodology for determining the acceptability of system designs in uncertain environments. European Journal of Operational Research, 209(2), 176-183.
Kirkpatrick, S. (1984). Optimization by simulated annealing: Quantitative studies. Journal of statistical physics, 34(5-6), 975-986.
Koenker, R., & Hallock, K. F. (2001). Quantile regression. Journal of economic perspectives, 15(4), 143-156.
L'Ecuyer, P. (1994, December). Efficiency improvement and variance reduction. In Proceedings of the 26th conference on Winter simulation (pp. 122-132). Society for Computer Simulation International.
Montgomery, D. C. (2017). Design and analysis of experiments. John wiley & sons.
Moré, J. J., Garbow, B. S., & Hillstrom, K. E. (1981). Testing unconstrained optimization software. ACM Transactions on Mathematical Software (TOMS), 7(1), 17-41.
Neddermeijer, H. G., Van Oortmarssen, G. J., Piersma, N., & Dekker, R. (2000, December). A framework for response surface methodology for simulation optimization. In Proceedings of the 32nd conference on Winter simulation (pp. 129-136). Society for Computer Simulation International.
Nicolai, R. P., Dekker, R., Piersma, N., & van Oortmarssen, G. J. (2004, December). Automated response surface methodology for stochastic optimization models with unknown variance. In Proceedings of the 36th conference on Winter simulation (pp. 491-499). Winter Simulation Conference.
Robbins, H., & Monro, S. (1985). A stochastic approximation method. In Herbert Robbins Selected Papers (pp. 102-109). Springer, New York, NY.
Roquemore, K. G. (1976). Hybrid designs for quadratic response surfaces. Technometrics, 18(4), 419-423.
Staudte, R. G., & Sheather, S. J. (2011). Robust estimation and testing (Vol. 918). John Wiley & Sons.
Shapiro, A., Dentcheva, D., & Ruszczyński, A. (2009). Lectures on stochastic programming: modeling and theory. Society for Industrial and Applied Mathematics.
Tekin, E., & Sabuncuoglu, I. (2004). Simulation optimization: A comprehensive review on theory and applications. IIE transactions, 36(11), 1067-1081.
Wan, H., Ankenman, B. E., & Nelson, B. L. (2006). Controlled sequential bifurcation: A new factor-screening method for discrete-event simulation. Operations Research, 54(4), 743-755.
Wilcox, R. R., Erceg-Hurn, D. M., Clark, F., & Carlson, M. (2014). Comparing two independent groups via the lower and upper quantiles. Journal of Statistical Computation and Simulation, 84(7), 1543-1551.
Zhang, T. F., Yang, J. F., & Lin, D. K. (2011). Small Box–Behnken design. Statistics & Probability Letters, 81(8), 1027-1033.
莊承霖. "分量最佳化之梯度搜尋架構." 清華大學工業工程與工程管理學系學位論文 (2014): 1-43.
呂盈暄. "運用有效篩選因子方法求解分量式模擬最佳化." 清華大學工業工程與工程管理學系學位論文 (2017): 1-57.