近年來，可靠度最佳化問題普遍受到重視，而冗餘配置問題(Redundancy Allocation Problem, RAP)便是其中一個熱門的研究領域。冗餘配置問題主要應用在大型且複雜的系統，像是電力系統、通訊系統或是製造系統，探討如何在滿足資源的限制之下，透過在每一個子系統(subsystem)中配置冗餘的備品，最大化整個系統的可靠度。在本論文中，主要分為兩個面向討論。第一，在現今的工業系統之下，單純的串並聯系統無法滿足實務上的應用，因此我們考慮一個一般化的拓樸結構系統。第二，此問題在資源的限制上採用了機率約束限制式，本研究並不嚴格限制資源的消耗，允許有少數情況超出資源限制，只要大多數的狀況下符合限制即可，而機率限制式本身為一相當複雜的問題，加上此問題隨機變數眾多，且網路可靠度僅可透過模擬方式取得，求解相當困難。本論文提出一個以模擬最佳化為基礎的演算法，使得我們能夠在考慮一般化拓樸結構的系統中求解，並在數值實驗中證明本論文之方法能夠更有效率的求解，且優於現存的求解方法。

The redundancy allocation problem (RAP) is an important reliability optimization problem and has been an active area for the past decades. In literature, most of these system reliability problems are considered in complex system such as electronic systems, power systems, telecommunication systems and manufacturing systems where the reliability of each components is considered as a precise value. In this paper, we extend RAP to a more generalized situation. First, the network topology is generalized, the components in the system can be series-parallel or any logical relationship. Second, this paper uses the chance constraint on the resource limitation. We do not strictly limit the consumption of resources. In some cases, exceeding the resource limit can be allowed, as long as the limitation is met in most cases. The chance constraint is a complicated problem. In addition, this problem has many variables, and the system reliability can only be obtained by simulation. We propose an efficient simulation optimization method. A numerical study shows that the proposed method can locate the optimal solution more efficiently compared to the existing methods.

中文摘要..........................................................I
Abstract.........................................................II
目錄............................................................III
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............................................9
2.3 Nelder-Mead單形法(Nelder-Mead Simplex Method).......13
第三章 數學模型...................................................15
3.1 問題定義.............................................15
3.2 符號定義.............................................16
3.3 一般化數學模型........................................17
第四章 求解方法...................................................18
4.1 可靠度之估計方法......................................18
4.2 定義信賴區域..........................................20
4.3 決策變數之轉換........................................21
4.4 Nelder-Mead單形法(Nelder-Mead Simplex Method).......21
4.5 成本限制式檢驗........................................25
4.6 鄰域解績效評估........................................25
4.7 延伸找到暫時點........................................31
4.8 更新信賴區域..........................................32
4.9 提出之演算法..........................................33
第五章 數值結果...................................................35
5.1 簡單橋狀系統..........................................35
5.2 複雜網路系統..........................................39
第六章 結論與未來研究.............................................45
6.1 結論.................................................45
6.2 未來研究..............................................45
參考文獻..........................................................46

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