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作者(中文):連福詩
作者(外文):Lian, Fu Shi
論文名稱(中文):改進SNM演算法計算效率以求解實務問題
論文名稱(外文):Improving the Efficiency of Stochastic Nelder-Mead Simplex Method For Simulation Optimization
指導教授(中文):張國浩
指導教授(外文):Chang, Kuo Hao
口試委員(中文):吳建偉
侯建良
口試委員(外文):Wu, Chien Wei
Hou, Jiang Liang
學位類別:碩士
校院名稱:國立清華大學
系所名稱:工業工程與工程管理學系
學號:103034472
出版年(民國):104
畢業學年度:103
語文別:中文
論文頁數:42
中文關鍵詞:模擬最佳化SNM演算法OCBA方法
外文關鍵詞:Simulation OptimizationSNM methodOCBA method
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Stochastic Nelder-Mead simplex method (SNM)演算法是一種直接搜索的模擬最佳化算法,它可以處理一些梯度不存在或者不平滑的問題,與Nelder-Mead simplex method (NM)演算法相比,它採用了有效的樣本量確定方法以及有效的局部搜索和全局搜索的架構,從而解決了NM演算法在決定樣本量上的問題和最優解質量無法判定的缺點。但是,SNM決定樣本量的方法在每一循環中對各個變數所分配實驗次數皆相同,導致了運算效率的降低。本文通過使用OCBA (Optimal Computing Budget Allocation) 等方法確定各個變數被分配的實驗次數,從而提高SNM演算法的有效性。同時,本文對於搜索架構提出了針對反射步驟的修正從而降低實施收縮步驟的概率。改進後的方法本文將其記為Improved SNM,簡稱I-SNM方法。實驗證明,本文提出的I-SNM方法能夠有效的提高SNM演算法的效率。
Stochastic Nelder-Mead simplex method (SNM) is a direct search algorithm in simulation optimization, which can deal with some problems which are unsmooth or whose gradient does not exist. Comparing with the Nelder-Mead simplex algorithm (NM), SNM used an effective method for determining the sample size, and effective local search and global search architecture. It solved two problems of the NM algorithm: (1) lacking of sample size scheduling, (2) the optimal quality cannot be determined. However, the sample size assigned for each variable in each iteration are the same in SNM method, leading to lower operational efficiency. This article determines the number of experiments assigned to each variable in each iteration by using OCBA (Optimal Computing Budget Allocation) method to improve the efficiency of the algorithm of SNM. Meanwhile, this paper proposes a modification for the reflection step to reduce the probability of contraction. Experimental results show that the proposed I-SNM algorithm can effectively improve efficiency.
第一章 緒論 1
1.1研究背景與動機 1
1.2研究目的 2
1.3論文構架 3
第二章 文獻綜述 5
2.1模擬最佳化 5
2.1.1 隨機近似法 6
2.1.2 反應曲面法 7
2.1.3 直接搜尋法 7
2.2 元啟發式方法(Metaheuristics) 7
2.2.1元啟發式方定義與分類 7
2.2.2 幾種常見元啟發式方法 8
2.3 SNM演算法 9
2.4 樣本量估計計劃 10
第三章 SNM演算法的有效性改進方法 12
3.1 問題定義 12
3.2 SNM演算法 13
3.2.1 基本框架 13
3.2.2 搜尋架構 14
3.2.3 Adaptive Random Search (ARS) 17
3.3 OCBA方法 17
3.3.1 選擇最優解 17
3.3.2 OCBA方法程序 19
3.4 I-SNM方法 20
3.4.1 基本步驟 20
3.4.2 搜尋架構修正 (Modification) 21
第四章 實證分析 23
4.1 測試函數 23
4.2 評價指標 25
4.3 結果分析 26
4.3.1 I-SNM方法效果評估 26
4.3.2 詳細數值結果 27
第五章 個案研究 33
第六章 結論與展望 36
參考文獻 37
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