本研究應用PSO-SA混合法於結構多目標最佳化設計中，粒子群演算法是種模仿自然界鳥類覓食的現象進行問題求解之步驟，屬於仿生演算法一種，此演算法具有快速搜尋且較為簡易設定的優點並具有全域搜尋之特色。模擬退火法主要是根據統計熱力學的原理，模擬材料在進行退火的過程中，逐漸達到最低溫狀態的現象，並透過波茲曼函數判斷問題解被接受機率，如此能有助於跳脫區域最佳解往全域最佳解靠近的機會。 
  
     本研究將結構多目標最佳化問題轉換為數學函數，利用線性遞減式慣性權重更新搜尋速度及位置以獲得最佳值，再應用模擬退火法判斷是否跳脫此最佳解以避免落入區域最佳解之中。在求解過程中，發現本方法應用於多目標結構最佳化設計問題時，能有效的在多目標問題中搜尋出最佳解並且同時滿足限制條件。
  
   


本研究以FORTRAN程式與ANSYS有限元素分析軟體中的APDL語法結合成一系統程式。並透過六個不同範例驗證了PSO-SA混合法於結構多目標最佳化設計上皆有不錯之成效。

The PSO-SA hybrid method was applied to multiobjective optimum design of structure in this study. Particle Swarm Optimization is to mimic the behavior of birds finding a good path to the food, which is one of the artificial biological algorithms. Thus, it has the merits of converge efficiently and programming easily. The advantage of Particle Swarm Optimization (PSO) is it global search technique. The Simulated Annealing (SA) method is based on the principle of statistical thermodynamic. That is material during the annealing process can be reached most cryogenic state phenomenon. The possibility of local optimum jump to global optimum can be determined by the probability of the Bozeman function.
The structural optimization problem can be transformed into a mathematical function. The new design can be obtained by using the linear decreasing inertia weight to update velocity and position of particles. After the optimal solution was obtained, the strategy of SA method is initiated to determine whether this optimal solution should be neglected or not . In the Numerical examples, the study showed that the computational efficiency can be improved and the constraint is satisfied.
　　A systematic program was developed by FORTRAN and APDL of ANSYS software. The optimum results of six different multiobjective examples showed that the PSO-SA hybrid methods are reasonable compared to other references.

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	 研究方法....................................................................................6
第二章 粒子群演算法.............................................................................7
2.1 引言............................................................................................7
2.2 理論基礎.....................................................................................7
    2.3 常數慣性權重............................................................................9
    2.4 線性遞減式慣性......................................................................10
    2.5 壓縮因子………..........................................................................11
    2.6 最大速度限制..........................................................................12
2.7  PSO之演算程序…………………………………………………………………12


第三章 模擬退火法...............................................................................14
3.1 理論基礎...................................................................................14
3.2 模擬退火法…………………...........................................................15
第四章 最佳化設計............................................. .................................18
    4.1 最佳化設計概念……………………………………………………………..……18
4.2 最佳化問題..............................................................................19
4.3 多目標適應函數………………………………………………………….…..…..20
4.4 Pareto 最佳解………………………………………………………..……………..21
    4.5 程式執行流程………………………..................................................22
   
第五章 數值分析……………………………………………………………………………….24
 5-1 範例一:十桿件桁架多目標結構最佳化設計………….…..……..25
 5-2 範例二:二十五桿件桁架多目標結構最佳化設計…………..….27
    5-3 範例三:四桿件桁架多目標結構最佳化設計……………………….29
    5-4 範例四:直升機尾桁結構多目標最佳化設計……………….………31
    5-5 範例五:單層懸臂薄板多目標結構最佳化設計……..….………..35
    5-6 範例六：四層壓電複合薄板結構之最佳化設計….……….….….38
第六章 結論............................................................................................43
參考文獻..................................................................................................67

圖目錄
圖一 粒子速度及位置更新意示圖........................................................45
圖二 粒子群演算法流程圖……………………………………………………..…………46
圖三 模擬退火法跳出局部最佳解示意圖............................................47
圖四 模擬退火法被接受機率之函數關係圖........................................47
圖五 模擬退火法流程圖.......................................................................48
圖六 多目標最小化意式圖………………………………………………………………..49
圖七 程式執行流程圖…………………………....................................50
圖八 PSO-SA混合法流程圖…………..................................................51
圖九 範例一 十桿件桁架結構尺寸外型圖……...………………………………52
圖十 十桿件桁架之Pareto solution……………………………………..…….………52
圖十一 範例二 二十五桿件桁架結構尺寸外型圖………….………..……..53
圖十二 二十五桿件桁架之Pareto solution…………….………………………….53
圖十三 範例三 四桿件桁架結構尺寸外型圖…………………………..………54
圖十四 四桿件桁架之Pareto solution……………………………………………….54
圖十五 範例四 直昇機尾桁結構外型及負載圖……………………………….55
圖十六 範例五 單層懸臂薄板結構外型圖……………………………………….56
圖十七 範例六 四層壓電複合薄板結構外型圖…………..…………………..57



 表目錄
表一 範例一 有限元素分析初始值與最佳值比較..............................58
表二 範例二 二十五桿件桁架結構桿件截面積分組..........................59
表三 範例二 二十五桿件桁架結構各節點受力..................................59
表四 範例二 二十五桿件桁架結構節點座標......................................60
表五 範例二 有限元素分析初始值與最佳值比較..............................61
表六 範例三 有限元素分析初始值與最佳值比較..............................62
表七 範例四 直升機尾桁之桿件分類..................................................63
表八 範例四 有限元素分析初始值與最佳值比較………………….….......64
表九 範例五 有限元素分析初始值與最佳值比較..............................65
表十 範例六 有限元素分析初始值與最佳值比較……………………………66

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