結合變異數縮減技術於隨機網路

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：16

、訪客IP：3.14.253.106

姓名

陳品頤(Pin-Yi Chen) 查詢紙本館藏

畢業系所

工業管理研究所

論文名稱

結合變異數縮減技術於隨機網路
(Combination of Variance Reduction Technique on Stochastic Edge Networks)

相關論文

★ 應用失效模式效應分析於產品研發時程之改善	★ 服務品質因子與客戶滿意度關係研究-以汽車保修廠服務為例
★ 家庭購車決策與行銷策略之研究	★ 計程車車隊派遣作業之研究
★ 電業服務品質與服務失誤之探討-以台電桃園區營業處為例	★ 應用資料探勘探討筆記型電腦異常零件-以A公司為例
★ 車用配件開發及車主購買意願探討(以C公司汽車配件業務為實例)	★ 應用田口式實驗法於先進高強度鋼板阻抗熔接條件最佳化研究
★ 以層級分析法探討評選第三方物流服務要素之研究-以日系在台廠商為例	★ 變動良率下的最佳化批量研究
★ 供應商庫存管理架構下運用層級分析法探討供應商評選之研究-以某電子代工廠為例	★ 台灣地區快速流通消費產品銷售預測模型分析研究–以聯華食品可樂果為例
★ 競爭優勢與顧客滿意度分析以中華汽車為例	★ 綠色採購導入對電子代工廠的影響-以A公司為例
★ 以德菲法及層級分析法探討軌道運輸業之供應商評選研究–以T公司為例	★ 應用模擬系統改善存貨管理制度與服務水準之研究-以電線電纜製造業為例

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

由於基本的蒙特卡羅方法（Monte Carlo Method）存在明顯的缺點包括抽樣效率相對較弱、需要大量樣本，因此有了變異數縮減技術(Variance Reduction Technique)，來改善上述缺點，而抽樣方法會影響到抽出樣本是否精準，所以抽樣方法也算是變異數縮減技術的一環；變異數縮減法包含了對偶變量(Antithetic Random Variables)、控制變量技術(Control variates)、分層抽樣(Stratification)、重要性抽樣(Importance Sampling)、拉丁超立方抽樣(Latin Hypercube Sampling)以及隨機亂數法(Common random numbers )。
交叉熵(Cross-entropy)策略是一種通用方法應用於組結合多極值優化以及罕見事件模擬(rare event )。在本文中，交叉熵策略被應用於在重要性抽樣中尋找最佳的重要性機率密度函數（IPDF），然後通過拉丁超立方抽樣（LHS）對獲得的IPDF進行抽樣。最後，使用對偶變量法（ARV）技術可以再進一步降低測試函數的變異數。本篇使用的例子進行模擬結果說明，基於本篇交叉熵策略的新型組合抽樣方法（CSMCES）能夠在一定的精確度下有效地減小樣本量，提高效率。

摘要(英)

Due to the apparent drawbacks of Monte Carlo method including comparatively lower sampling efficiency, requiring a large number of samples. Variance Reduction Technique used to improve those drawbacks. The method of sampling will affect the precision, so sampling methods also a part of variance reduction technique. Variance Reduction Technique includes Antithetic random variables(ARV), Control variates technique(CV), Stratification, Importance sampling(IS), Latin hypercube sampling (LHS)and Common random numbers(CRN).
Cross-entropy(CE) strategy provides a general, simple and efficient method for solving such problems like the quadratic assignment problem and the rare event-simulation. Before we are sampling, CE strategy is use to choose an importance probability density function(IPDF). And then use LHS to sampling the IPDF we got. After that, used ARV technique can be further to reduce the variance of test function. The simulation results of stochastic edge networks examples show that this combined sampling method with CE strategy (CSMCES) can enhance efficiency under certain level of precision and effectively reduce sample size.

關鍵字(中)

★ 蒙地卡羅模擬
★ 變異數縮減技術
★ 重要性抽樣
★ 交叉熵法
★ 拉丁超立方抽樣
★ 對偶變量法

關鍵字(英)

論文目次

中文摘要 i
Abstract ii
目錄 iii
圖目錄 v
表目錄 vi
一、緒論 1
1-1 研究背景 1
1-2 研究動機與目的 2
1-3 研究架構 3
二、文獻探討 4
2-1 抽樣方法 4
2-1-1 拉丁超立方體抽樣(Latin Hypercube Sampling) 4
2-1-2 重要性抽樣(Importance Sampling) 5
2-1-3 逆變換抽樣(Inverse transform sampling) 9
2-2 變異數縮減法 10
2-2-1 對偶變量(Antithetic Random Variables) 10
2-2-2 控制變量技術(Control variates) 11
2-2-3 隨機亂數法(Common random numbers ) 12
2-3 結合變異數縮減技術 14
三、研究方法 15
3-1 精確度 15
3-2 結合抽樣方法與交叉熵法 16
四、實驗結果 19
4-1 例子與實驗結果 19
4-1-1 以隨機網路圖形1為例 21
4-1-2 以隨機網路圖形2為例 26
4-1-3 以隨機網路圖形3為例 31
五、結論與未來展望 36
5-1 結論 36
5-2 未來展望 38
參考文獻 39

參考文獻

Aionuevo, R. and B. L. Nelson., “Automated estimation and variance reduction via control variates for infinite-horizon simulations.”, Computers & Operations Research. 15, 447-456, 1988.
Bauer, K. W., “Control Variate Selection for Multiresponse Simulation.”, Ph.D. Dissertation. School of Industrial Engineering, Purdue University, W. Lafayette, Ind, 1987.
De Boer, Pieter-Tjerk, Kroese, Dirk P., Mannor, Shie, Rubinstein, Reuven Y., “A tutorial on the Cross-Entropy method.”, Annals of Operations Research . 134 (1). pp. 19–67, 2003.
Eglajs, V., Audze P., “New approach to the design of multifactor experiments.”, Problems of Dynamics and Strengths. 35 (Riga: Zinatne Publishing House). 104–107, 1977.
Glynn P. W. and D. L. Iglehart., “Importance sampling for stochastic simulations.”, Management Science., vol. 35, pp. 1367–1392, 1989.
Glynn, P. W. and W. Whitt. , “Indirect estimation via L = λW.”, Operations Research. 37, 82-103, 1989.
Hao Z.J, X.X Hu., “Error compensation method and rapid accuracy analysis for missile based on latin hypercube sampling.”, Ordnance Industry Automation, Vol.6, 23-25, 2009.
Kahn, H. “Random sampling (Monte Carlo) techniques in neutron attenuation problems—I,” Nucleonics, pp. 27–37, May 1950.
Kahn, H and A. W. Marshall, “Methods of reducing sample size in Monte Carlo computations” , J. Operations Research., pp. 263–278, 1953.
Kahn, H, “Use of different Monte Carlo sampling techniques.”, in Symposium. Monte Carlo Methods, H. A. Meyer, Ed. New York: Wiley, 1956.
Kroese, D.P., T. Taimre, Z.I. Botev., “Handbook of Monte Carlo Methods.”, John Wiley & Sons, 2011.
Lavenberg, S. S., T. L. Moller and C. H. Sauer., “Concomitant control variables applied to the regenerative simulation of queueing systems.”, Operations Research. 27, 134-160, 1979.
Lavenberg, S. S., and P. D. Welch., “A perspective on the use of control variables to increase the efficiency of Monte Carlo simulations.”, Management Science. 27, 322-335, 1981.
McKay, M.D., Beckman, R.J., Conover, W.J., “A comparison of three methods for selecting values of input variables in the analysis of output from a computer code.”, Technometrics . 21 (2): 239–245, May 1979.
Nelson, B. L. and B. W. Schmeiser., “Decomposition of some well-known reduction techniques,” J. Statistical Computation Simulation, vol. 23, pp. 183–209, 1986.
Nelson, B. L., “A perspective on variance reduction in dynamic simulation experiments. Common. Statist. B16, 385-426, 1987a.
Nelson, B. L., “On control variate estimators.”, Computers & Operations Research. 14, 218-225, 1987b.
Nelson, B. L. “Batch size effects on the efficiency of control variates in simulation.”, Eur. J. Operations Research. 43, 184-196, 1989.
Nozari, A., S. F. Arnold and C. D. Pegden., “Control variates for multipopulation simulation experiments.”, HIE Trans. 16, 159-169, 1984.
Glasserman, P., & Yao, D. D. "Some guidelines and guarantees for common random numbers.", Management Science. 38.6: 884-908, 1992.
Porta Nova., A. M. O., and J. R. Wilson., “Using control variates to estimate multiresponse simulation metamodels.”, Winter Simulation Conference Proceedings, 326-334, 1986.
Rubinstein, R. Y., “Optimization of computer simulation models with rare events.”, European Journal of Operations Research, 99, 89-112, 1997.
Rubinstein, R. Y., “The simulated entropy method for combinatorial and continuous optimization.”, Methodology and Computing in Applied Probability, 2, 127-190, 1999.
Rubinstein, R. Y., and R. Markus., “Efficiency of multivariate control variates in Monte Carlo simulation.”, Operations Research. 33, 661-677, 1985.
Saliby, Eduardo., “Descriptive sampling: an improvement over Latin hypercube sampling.”, Proceedings of the 29th conference on Winter simulation, IEEE Computer Society, 1997.
Smith, P. J., Shafi, M., & Gao, H. “Quick simulation: A review of importance sampling techniques in communications systems.”, IEEE Journal on Selected Areas in Communications, 15(4), 597-613,1997.
Tew, J. D., and J. R. Wilson., “Estimating simulation metamodels using integrated variance reduction techniques.”, Technical Report SMS 89-16, School of Industrial Engineering, Purdue University, West Lafayette, Ind, 1989.
Venkatraman, S., and J. R. Wilson., “The efficiency of control variates in multiresponse simulation.”, Operations Research. Lett. 5, 37-42, 1986.
Wang B.C, Y.H Wei, Y.H Sun., “A comparison of different importance sampling methods in controlling variance.”, Statistics and Decision, Vol.9, 78-81, 2015.
Wilson J. R., “Variance reduction techniques for digital simulation.”, Am. J. Math. Manage. Sci., vol. 4, no. 3, 4, pp. 277–312, 1984.
Wilson, J. R., and A. A. B. Pritsker., “Variance reduction in queueing simulation using generalized concomitant variables.”, J. Statistical Computation and Simulation,19, 129-153, 1984a
Wilson, J. R., and A. A. B. Pritsker., “Experimental evaluation of variance reduction techniques for queueing simulation using generalized concomitant variables.”, Management Science. 30, 1459-1472, 1984b.
Xie, X., Li, W., Lu, L., & Yang, M. “A new combined sampling method based on variance minimization strategy.”, In Control and Decision Conference (CCDC), Chinese ,pp. 1841-1844, IEEE, 2016.
Zhang W.F, Y.B Che, Y.S Liu., “Improved Latin hypercube sampling method for reliability evaluation of power systems.”, Automation of Electric Power Systems, Vol.4, 52-57, 2015.

指導教授

葉英傑

審核日期

2018-7-18

推文