本論文提出結合粒子群演算法與差分演化演算法的雙演化演算法於結構最佳化設計中。粒子群演算法為仿生演算法，其特點為收斂速度快、參數設定少、搜尋範圍廣及具有記憶性。差分演化演算法為演化式演算法，其優勢在於參數設定及架構簡單、能維持母體的多樣性、高效能及高精確度等。雙演化演算法則是利用粒子群演算法與差分演化演算法兩者同時進行運算，優點在於互相補足缺點，利用差分演化演算法的多樣性使其跳脫區域最佳解，而利用粒子群演算法的記憶性使局部搜尋更加完善，利用兩者不同的搜尋方式，並將兩者演算法之最佳值做比較及分享，以獲得最佳值。本文中針對粒子群演算法提出變速因子的改良機制，藉由判斷粒子的區域最佳解與全域最佳解的距離來改變搜尋的步伐，以改善搜尋過程之收斂效率。本研究在差分演化演算法中，選取適合的突變方式可增加解的多樣性以彌補粒子群演算法之不足。
    本研究將ANSYS有限元素分析軟體中的APDL語法與FORTRAN程式結合成一系統程式，並以五種不同的範例執行結構最佳化設計。範例中將結構最佳化問題轉為數學函數，再利用雙演化演算法對結構系統執行最佳化設計。由數值分析範例之結果，顯示雙演化演算法求出的解比單獨使用粒子群演算法和差分演化演算法求出的解為佳且應用在結構之最佳化設計上皆可得到不錯的結果。

The PSO-DE Dual Evolution Strategy was applied to optimum design of structures in this study. Particle Swarm Optimization (PSO) algorithm is a bionic technique which has fast convergence, less parametric setting and wide search range with memory. Differential Evolution (DE) algorithm is an evolutional technique that has advantages of easy to implement, little parameter tuning requirement, and also exhibits reliable, accurate and fast convergence. In this study, a Dual Evolution Strategy that includes an improved Particle Swarm Optimization algorithm and a Differential Evolution algorithm is proposed for structural optimal design. The improved Particle Swarm Optimization algorithm adopts an alternation velocity factor that changes with the particle distance between the local and the global optimal solution. In the Differential Evolution algorithm, an appropriate mutation is selected to increase domain flexibility and improve the deficiency of Particle Swarm Optimization algorithm. This Dual Evolution Strategy utilizes the domain flexibility offered by the Differential Evolution algorithm and the local search memory of the Particle Swarm Optimization algorithm. The two algorithms are computed independently , the best result is obtained and shared between the two algorithms at each iteration. Numerical analysis showed that the results obtained from the Dual Evolution Strategy are better than those obtained individually from the Particle Swarm Optimization algorithm or Differential Evolution algorithm.

目錄
中文摘要	I
英文摘要	III
目錄	V
圖目錄	VII
表目錄	VIII
第一章 緒論	1
1.1研究動機	1
1.2文獻回顧	3
1.3本文架構	8
第二章 粒子群演算法	10
2.1理論基礎	10
2.2常數式慣性權重(Constant Inertia Weight)	13
2.3線性遞減式慣性權重(linearly Decreasing Inertia Weight)	14
2.4 壓縮因子(Constriction Factor)	14
2.5 被動聚集因子(Passive Congregation)	15
2.6變速因子(Alteration Velocity Factor)	17
2.7粒子群演算法執行流程	18
第三章 差分演化演算法	20
3.1理論基礎	20
3.2差分演化演算法執行流程	25
第四章 雙演化演算法	27
4.1理論基礎	27
4.2雙演化演算法執行流程及步驟	28
第五章 數值分析	30
5.1範例一：十桿件桁架結構輕量化設計	31
5.2範例二：無人飛行載具機翼主樑輕量化設計	33
5.3範例三：無人飛行載具機翼主樑承受扭矩之輕量化設計	36
第六章 太陽能無人飛機之最佳化設計	38
6.1問題一：太陽能無人飛行載具之結構輕量化設計	41
6.2問題二：太陽能無人飛行載具之自然振動頻率最大化設計	43
第七章 結論	45
參考文獻	66
論文簡要	72


圖目錄
圖一 粒子群位置及速度更新示意圖	47
圖二 粒子群演算法流程圖	48
圖三 合成向量交配示意圖	49
圖四 差分演化演算法之流程圖	50
圖五 雙演化演算法之流程圖	51
圖六 範例一 十桿件桁架結構尺寸圖	52
圖七 範例二 無人飛行載具機翼主樑結構外型圖	53
圖八 範例二 無人飛行載具機翼位移及應力分析圖	54
圖九 範例三 受扭矩之無人飛行載具主樑結構外型圖	55
圖十 範例三 無人飛行載具主樑結構位移及應力分析圖	55
圖十一 太陽能動力飛機「鸑鷟」之結構設計圖	56
圖十二 太陽能動力飛機「鸑鷟」之完成圖	56
圖十三 問題一 UAV之位移與結構應力分析圖	57
圖十四 問題二 UAV結構之第一模態自然振動頻率	58
圖十五 問題二 UAV最佳化後之第一模態自然振動頻率	59





表目錄
表一 範例一 本研究與文獻最佳值比較	60
表二 範例二 本研究與文獻最佳值比較	61
表三 範例三 本研究與文獻最佳值比較	62
表四 碳纖維材料係數表	63
表五 巴爾沙木材料係數表	63
表六 問題一 UAV結構之初始值與最佳值	64
表七 問題二 UAV自然振動頻率之初始值與最佳值	65

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