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研究生：	蔡承濂 Tsai, Cheng-Lien
論文名稱：	以更有效率之方式結合控制變量於完全連續選擇程序 More Efficient Fully Sequential Selection Procedures with Control Variates
指導教授：	蔡青志 Tsai, Shing-Chih
學位類別：	碩士 Master
系所名稱：	管理學院 - 工業與資訊管理學系 Department of Industrial and Information Management
論文出版年：	2017
畢業學年度：	105
語文別：	中文
論文頁數：	73
中文關鍵詞：	排序與選擇程序、控制變量、變異減免技術
外文關鍵詞：	Ranking & Selection, Control Variates, Variance Reduction
相關次數：	點閱：101 下載：0
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現實生活中存在許多複雜且具隨機性的問題，當問題難以使用數學模式分析時，均可以使用系統模擬產生樣本觀察值並用以幫助決策。而決策者在面對模擬問題時，若問題全部的候選解個數不多，則可使用排序與選擇程序來選擇最佳系統，其中完全連續選擇程序被廣泛用以解決這些候選解個數不多之模擬問題；但由於完全連續選擇程序之效率受模擬系統變異程度影響，若系統之績效表現值之變異程度過大，將使得抽樣成本及運算時間提高。模擬領域中發展之變異減免技術則用以改善此問題，其將原本樣本平均數估計量用新的估計量取代，則新的樣本變異數較原本樣本變異數小，使得完全連續選擇程序更加有效率。本研究分析變異減免技術中之控制變量 (Control Variate; CV)，探討其結合於完全連續選擇程序中造成的影響，並提出更有效率之完全連續選擇程序。
在過往文獻中，合併控制變量之完全連續選擇程序為了使程序具有統計保證性，使得樣本數有浪費之情況發生，在本研究中提出兩種程序FSP-A與FSP-B，其藉由同時更新CV 模型之線性參數 β̂(r) 與樣本變異數以提升程序之效率，針對兩種程序對於樣本數與統計保證性之影響進行探討，並同時驗證其為更有效率之程序且正確選擇機率滿足統計保證性。另外使用Biased Control Variate (BCV) 與 Control Variate using Estimated Mean (CVEM) 於新程序中，並藉由兩種不同之線性參數提升程序之效率與可用性。
本研究所提出之FSP-A 與FSP-B其抽樣數皆較過往文獻之程序少，並且同時滿足信心水準；在CV模型之線性參數收斂速度較慢之情境下，FSP-B之表現則優於FSP-A。而控制值期望值未知之程序，由於可供選擇之控制值增加，若是其估計控制值期望值之額外抽樣數夠多，而且控制值與輸出值之間相關性夠大，則可在滿足信心水準之條件下，其效率較控制值期望值已知之程序高。

In past studies, the Fully Sequential Selection Procedure (FSP) algorithm combined with Control Variates (CV) required an initial stage to estimate the linear parameter (β̂) without updating the linear parameter and variance when taking more samples in the screening stage. We propose two FSP algorithms with CV that update the linear parameter and sample variance when we take more samples. The first algorithm uses the new β̂ between the next sample and the next updating point when updating β̂; the second algorithm uses the newest β̂ for all samples when updating β̂. Since the second algorithm uses the best β̂ in all samples, the variance reduction will be more significant. These two algorithms perform better than past procedures with CV. By continuing to update β̂ and the variance, the variance reduction effectiveness is close to that of the scenario for actual linear parameters. One limitation of CV is the expectation of CV has to be known. In real practice, there are more effective CV which their expectations are unknown. If we introduce the unknown mean CV into a fully sequential procedure, the estimator will be a biased estimator. We propose a method which uses the β̂ to minimize the mean square error of estimators and continue updating β̂ to reduce the bias of estimators. The numerical experiments indicate that the probability of correct selection is higher than that of the procedure using original β̂ to minimize the variance of estimators.

中文摘要............................................................................................i
英文延伸摘要.....................................................................................ii
誌謝...................................................................................................vii
目錄...................................................................................................viii
表目錄...............................................................................................x
圖目錄...............................................................................................xi
第一章  緒論.......................................................................................1
1.1 研究背景與動機...........................................................................1
1.2 研究目的......................................................................................4
1.3 研究流程......................................................................................5
第二章 文獻回顧................................................................................6
2.1 排序與選擇程序...........................................................................6
2.2 控制變量......................................................................................9
2.3 偏誤控制變量..............................................................................12
2.4 合併 CV 之排序與選擇程序.........................................................15
2.5 小結.............................................................................................16
第三章 研究方法................................................................................17
3.1 更新 β̂ 帶來的影響.......................................................................17
3.1.1 β̂ 之收斂特性............................................................................17
3.1.2 更新 β̂ 對樣本之間獨立性的影響...............................................21
3.1.3 移除初始階段 m0 用以估計 β̂ 之樣本........................................23
3.2 完全連續選擇程序........................................................................26
3.2.1 FSP-CV with β̂ Updating (各個更新區段使用不同之 β̂).............29
3.2.2 FSP-CV with β̂ Updating (全部之樣本使用同樣更新後之 β̂)......30
3.3 使用 BCV 或 CVEM 之完全連續選擇程序....................................32
第四章 實驗設計與分析......................................................................39
4.1 實驗評估.......................................................................................39
4.2 實驗結果.......................................................................................40
4.2.1 FSP-A 與 FSP-B 實驗結果比較.................................................40
4.2.2 BCV 與 CVEM 實驗結果比較....................................................48
4.2.3 實例驗證....................................................................................53
第五章 結論........................................................................................59
5.1 研究結論與建議............................................................................59
5.1.1 FSP-A 與 FSP-B.......................................................................59
5.1.2 使用 BCV 或 CVEM 之完全連續選擇程序.................................60
5.2 未來研究方向................................................................................61
參考文獻.............................................................................................62
A Appendix.........................................................................................66
A.1 Proof of  Theorem 3.1...................................................................66
A.1.1 The Construction of Brownian Motion Process.........................66
A.1.2 Proof of the PCS guarantee......................................................72
                                    

宋奇檠, 2016。合併變異數縮減技術於完全連續選擇程序。國立成功大學工業與資訊管理學系碩士論文
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校內：2022-07-01公開
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