近年來，可靠度最佳化問題是一普遍受到重視的問題，而其中關於冗餘配置問題(Redundancy Allocation Problem, RAP)在可靠度最佳化問題裡更是一熱門研究領域。在文獻上，過去探討系統可靠度問題時大部分以串並聯系統作為考量並假設各個備品的可靠度為一個介於零到一之間的精準值，然而在新創的的工程系統下，沒有足夠資訊去確保備品的可靠度，加上串並聯系統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。在此篇論文中，本研究提出模擬最佳化為基礎的演算法，為粒群演算法為基礎之模擬最佳化(Particle-Swarm-Based Simulation Optimization Method)，使得本研究去解決上述複雜系統與備品可靠度不準確之冗餘備品問題，由於此問題的隨機變數龐大與可靠度只能以模擬的方式求得，為使求解速度更有效率，本研究提出之新方法為建立在粒群最佳化(Particle Swarm Optimization, PSO)並改良加入排序與選擇(Ranking and Selection, R&S)，使得每次求解過程都能以高信心水準向最佳解收斂。

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 series-parallel where the reliability of each components is considered as a precise value. Generalized redundancy allocation problem (GRAP) extends RAP to a more realistic situation where the reliabilities of the components are stochastic in nature and 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. In this paper, we proposed a new formulation of GRAP where the reliability of each component is modeled as a random variable with unknown distributions and developed particle-swarm-based simulation optimization method (PSSO) to identify the optimal solution efficiently. An extensive numerical study verifies the effectiveness and efficiency in realistic settings.

目錄
摘要 I
Abstract II
圖目錄 IV
表目錄 V
第一章 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 2
1.2 研究架構 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 11
第三章 數學模型 16
3.1 問題定義 16
3.2 符號定義 17
3.3 冗餘配置問題模型 17
第四章 求解方法 19
4.1 可靠度衡量 19
4.2 粒群演算法為基礎之模擬最佳化(Particle-Swarm-Based Simulation Optimization Method) 21
4.2.1 排序與選擇(Ranking and Selection) 26
第五章 數值分析 30
5.1 複雜網路 30
5.2 參數設定 32
5.3 數值分析 33
第六章 結論與未來研究 40
6.1結論 40
6.2未來研究 40
參考文獻 41

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