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研究生:林謝興
研究生(外文):Lin Shieh-Shing
論文名稱:具非集總步幅之修正式平行區域比例梯度法及具耦合不等式限制之非線性大型網路最佳化問題的解法
論文名稱(外文):Methods for Modified Parallel Block Scaled Gradient with Decentralized Step-size and Nonlinear Large Network Optimization Problem with Coupling Inequality Constraints
指導教授:林心宇
指導教授(外文):Lin Shin-Yeu
學位類別:博士
校院名稱:國立交通大學
系所名稱:電機與控制工程系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:71
中文關鍵詞:熱極限限制式
相關次數:
  • 被引用被引用:0
  • 點閱點閱:168
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  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0
首先,我們提出一種修正式之平行區域比例梯度法(scaled gradient)來解大型分佈系統中區域可加的未受限最佳化問題。相較於典型的平行區域比例梯度法,我們的方法提出兩個重要修正:(1) 我們加入預先處理(pre-processing)步驟以降低計算時間。(2) 我們提出一種非集總(decentralized)阿密歐型式(Armijo-type)步幅(step-size)決定法則,以克服在分散式計算環境下決定步幅的困難。此種方法只使用少量的資料傳輸,就能使我們所提的平行運算法(parallel algorithm)在分佈式電腦網路中執行。我們證明此方法完全收斂,而且經由測試結果,我們所提出的方法,其效率遠高於以稀疏矩陣為基礎的方法。
  再則,應用以上的技巧,我們提出一個平行的對偶型態運算法,並利用此方法來解一種典型的受限制二次式規劃問題;由驗證的結果可知此方法極適合被實現在一個分佈式電腦網路,而且更可作為大型分佈系統的最佳化工具。
  最後我們提出兩種技巧來解具有多數熱極限限制式(thermal-limit constraints)的最佳電力潮流問題(OPF):(1) 我們以圖理論為基礎的分解技巧來將由多數熱極限限制式引起的大型投射問題(projection problem)分解成彼此互相獨立的中型投射問題。(2) 我們提出以主動集合(active-set)策略為基礎的對應型方法(DT method),來使中型投射問題的求解更有效率。經由測試結果,我們以對應型方法為基礎,植入以上的兩個新的技巧後,對於解具有多數熱極限限制式的電力潮流問題是非常有效率。

First of all, we present a modified parallel block scaled gradient method for solving block additive unconstrained optimization problems of large distributed systems. Our method makes two major modifications on the typical parallel block scaled gradient method: (1) we include a pre-processing step which will reduce the computation time; (2) we present a decentralized Armijo-type step-size rule. This rule will circumvent the difficulty of determining a step-size in a distributed computing environment and enable the proposed parallel algorighm to execute in a distributed computer network with limited amount of data transfer. We prove that method is globally convergent and demonstrate its efficiency comparted to a sparse matrix technique based method by several weighted least square problems of power system state estimation.
Secondly, with the decentralized step-size rule technique. We present a parallel dual-type algorithm for solving a class of quadratic programming problem. Our algorithm is suitable for implementation in a distributed computer network and can be used as a basic optimization tool for handling optimization problems of large distributed system.
Finally, we present two new techniques for solving optimal power flow (OPF) problem with large number of thermal-limit constraints. The first one is a graph method based decomposition technique which can decompose the large-dimension projection problem, caused by the large number of thermal-limit constraints, into several independent medium-dimension projection subproblems at the expense of slight increment of the dual problem’s dimension. The second technique is an active-set strategy based DT method, which can solve the medium-dimension projection subproblems efficiently. We have used the DT method embedded with these two new techniques in solving numerous OPFs with large number of thermal-limit constraints. The test results show that the proposed techniques are very efficient and effectively improve the DT method for handling large number of thermal-limit constraints.

英文摘要 i
中文摘要 ii
誌 謝 iii
目 錄 iv
表目錄 vi
圖目錄 vii
註解目錄 viii
第一章 序論 1
1.1 未受限之網路最佳化問題 1
1.2 具限制條件之網路最佳化問題 2
1.3 論文大綱 2
第二章 以修正式平行區域比例梯度法來解大型分佈系統中
區域可加的未受限最佳化問題 3
2.1 簡介 3
2.2 問題描述 4
2.3 具非集總步幅的修正式平行區域比例梯度法 7
2.3.1 平行預先處理步驟 7
2.3.2 具非集總步幅法則的平行區域比例梯度法 7
2.3.2.1 平行區域比例梯度法 7
2.3.2.2 非集總阿密歐型式步幅法則 8
2.3.2.3 平行運算法摘要 10
2.3.3 具非集總阿密歐型式步幅的PBSG方法的收斂 10
2.4 應用 19
2.4.1未受限加權最小平方(WLS)問題 19
2.4.2將所提的方法應用於WLS問題 20
2.5 測試結果 21
2.5.1 測試系統 21
2.5.2 具非集總阿密歐型式步幅的PBSG方法收斂與計算效率 21
第三章 以一個平行的對偶型態運算法來解一種典型的受限制二次式
規劃問題 24
3.1 簡介 24
3.2 平行對偶型態法 26
3.2.1 對偶問題 26
3.2.2 平行對偶型態法 27
3.3 應用 30
3.3.1 受限制加權最小平方(CWLS)問題 30
3.3.2 連續可規劃法及所提運算法的結合 32
3.4 測試結果 33
第四章 一個對應型方法為基礎來解非線性大型網路最佳化問題 35
4.1 簡介 35
4.2 圖理論為基礎的分解技巧 36
4.2.1 轉換熱極限限制式 36
4.2.2 圖形建立與分類 36
4.2.3 圖理論為基礎的分解運算法 39
4.2.4 分解步驟的圖解與例子 40
4.3 中型投射子問題的解法 41
4.3.1 中型投射子問題 41
4.3.2 以主動集合策略為基礎的對應型方法 41
4.4 具有多數熱極限限制式OPF問題的解法 44
4.5 測試結果 50
第五章 結論 55
參考文獻 56
自傳 59
著作目錄 60

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