近年來可靠度最佳化的問題普遍受到重視，其領域中一個重要的問題為冗餘配置問題(Redundancy Allocation Problem, RAP)，在文獻中此類問題大多考慮在一個串並聯的系統中(series-parallel system)，串並聯系統即為每一個子系統內的備品採取並聯，而每一個子系統之間再進行串聯的一個系統，然而這樣的系統與模型因無法反映現實中的情況，如：通訊系統，其子系統之間存在複雜的連接情況，所以在應用上會受到限制。在這篇論文中，本研究提出了一個以模擬最佳化為基礎的方法論，稱為NPRO (Nested Partitions for Reliability Optimization)，使得本研究得以求解一個複雜網路系統之冗餘配置問題，NPRO以巢狀分割法(Nested Partitions Method, NP)為基礎，並加入了本研究所提出之決策變數轉換、重要性抽樣(Importance Sampling, IS)與拉丁超立方體抽樣(Latin Hypercube Sampling, LHS)，使得NPRO在求解時能夠以有效率的方式進行最佳解之搜尋。在本研究的數值研究中也顯示在有限的電腦資源下，NPRO能夠找出最佳解與近似最佳解，其效果與效率比起兩種現有的演算法來得更佳。

Redundancy allocation problem (RAP) has been an active research area for the past decades. Generalized redundancy allocation problem (GRAP) extends it to a more realistic situation where the system can have a complex network structure, for example, its components are connected with each other neither in series nor in parallel but in some logical relationship. Because of that, solving GRAP has presented major challenges in practice. In this paper, we propose a simulation optimization method, called Nested Partitions for Reliability Optimization (NPRO), to solve GRAP efficiently. Due to a newly-developed partitioning strategy, NPRO can locate the optimal solution in an efficient manner. The incorporation of many useful techniques, including the proposed encoding approach, importance sampling (IS) and Latin hypercube sampling (LHS), further enables NPRO to reduce the number of simulation observations needed in the optimization process, facilitating quick generation of the optimal solution. An extensive numerical experiment is conducted to verify the efficacy and efficiency of NPRO. Results show that NPRO can find the optimal or nearly optimal solution of GRAP within limited computational budget and moreover, it significantly outperforms the other two existing algorithms.

圖目錄 V
表目錄 VI
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 論文架構 3
第二章 文獻回顧 5
2.1 冗餘配置問題 5
2.2 模擬最佳化 8
第三章 數學模型 11
3.1 問題定義 11
3.2 符號定義 12
3.3 冗餘配置問題模型 12
第四章 求解方法 14
4.1 可靠度衡量 14
4.2_NPRO (Nested Partitions Method for Reliability Optimization) 15
4.2.1 轉換方法(Encoding Approach) 19
4.2.2 有效分割方法(Partitioning Approach) 20
4.2.3 拉丁超立方體抽樣(Latin Hypercube Sampling) 22
4.2.4 重要性抽樣(Importance Sampling) 24
第五章 數值結果 26
5.1 簡單網路 26
5.1.1 簡單網路-參數設定 27
5.1.2 簡單網路-演算法參數設定 27
5.1.3 簡單網路-數值結果 28
5.2 複雜網路 37
5.2.1 複雜網路-參數設定 38
5.2.2 複雜網路-演算法參數設定 39
5.2.3 複雜網路-數值結果 40
第六章 結論與未來研究 42
6.1 結論 42
6.2 未來研究 42
參考文獻 43

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