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)，主要應用在許多大型且複雜的系統，像是電子系統、電力網路、通訊系統以及製造系統，是考慮在某些資源限制之下，探討如何在每一個子系統(subsystem)中藉由決定備品(component)種類或是增加備品的方式，使得整個系統在滿足特定可靠度條件下最小化總系統成本。在本論文中，我們主要針對兩個面向做討論。第一，我們考慮此問題在一個一般化拓撲結構的系統中，因在文獻中此類問題的系統大多都是考慮串並聯系統(series-parallel system)，但實務問題的系統中連接方式可能含有邏輯判斷，所以不能用簡單的串並聯系統做描述。第二，此問題存在機會約束(chance constraint)，需在滿足特定可靠度的前提下進行最佳化，而機會約束本身為一相當複雜之問題，當決策變數維度上升，將大幅提升其求解難度。而我們提出了一個以模擬最佳化為基礎的方法，使得我們可以考慮此問題為一般化拓撲結構的系統，且能有效率的在滿足機會約束下進行系統成本之最小化。並在數值分析中證明我們提出之方法能有效率的搜尋最佳解，且優於現存之求解方法。

Redundancy allocation problem (RAP), which aims to minimize the system total cost subject to some constraints on system reliability, represents an important problem in system design with many applications in areas such as electronic systems, power systems, telecommunication systems and manufacturing systems. In this paper, we extend RAP to a more generalized situation, First, the network topology is generalized, i.e., the components in the system can be of any logical relationship. Second, there exist chance constraints that the overall system reliability is required to exceed a prescribed value. 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.

摘要..................................I
Abstract.............................II
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
第三章 數學模型.......................13
3.1問題定義...........................13
3.2符號定義...........................14
3.3冗餘配置問題模型....................14
第四章 求解方法.......................16
4.1可靠度之估計方法....................17
4.2 STRONG及運用之概念.................18
4.3定義設計區域........................20
4.4搜尋方向分割........................20
4.5決策變數之轉換......................21
4.6提出之演算法........................23
第五章 數值結果.......................29
5.1簡單網路系統........................29
5.1.1簡單網路系統─參數設定...........30
5.1.2簡單網路系統─演算法之參數設定....31
5.1.3簡單網路系統─數值結果............32
5.2複雜網路系統........................34
5.2.1複雜網路系統─參數設定...........35
5.2.2複雜網路系統─演算法之參數設定....36
5.2.3複雜網路系統─數值結果...........37
第六章 結論及未來目標.................39
6.1結論...............................39
6.2未來研究...........................39
參考文獻..............................41

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