本論文應用改良式灰狼演算法於結構最佳化設計中，改良式灰狼演算法結合粒子群演算法及灰狼演算法並加入貪婪策略。粒子群演算法為仿生演算法收斂速度快、參數設定容易和具有記憶能力為他的特點。灰狼演算法學習狼群覓食的方式，在解空間中隨機生成初始值模擬狼群位置，利用包圍及攻擊的公式，趨近最佳解。改良式灰狼演算法藉由修改收斂係數，增加全域搜尋的比例，避免落入區域最佳解，加入記憶能力，提升收斂效率，加入針對不同位置之權重，使搜尋方向更加明確，並利用貪婪策略避免過多不必要的搜尋。在函數及結構數值分析中，結果顯示改良式灰狼演算法能夠獲得不錯的成效。

In this study, improved gray wolf algorithm is used in structural optimization design. Improved gray wolf algorithm is combined with particle swarm algorithm, gray wolf algorithm and greedy strategy. Particle swarm algorithm is a bionic technique with fast convergence, less parameter setting and memory ability. Gray wolf algorithm is conceptualized by grey wolves foraging behavior. The proposed method generates initial values randomly in the design space to simulate the position of the wolves and uses the encirclement and attack strateges to approach the best solution. Improved gray wolf algorithm reduces the probability of falling into the local best solusion by modifying the convergence coefficient to increase global searching, implement memory ability to improve the efficiency of convergence, adds weights for different positions to make the search direction clearer and uses greedy strategy to avoid unnecessary searches. In the numerical analysis of optimum design structures, the results show that the improved gray wolf algorithm can achieve good results.

目錄...............................iv
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...........................9
第二章粒子群演算法.  .................10
2.1基礎理論..........................10
2.2線性遞減慣性權重...................13
第三章  灰狼演算法....................14
3.1基礎理論..........................14
3.2改良收斂因子......................17
3.3自適應灰狼演算法...................19
第四章  最佳化設計....................20
4.1最佳化設計概念	....................20
4.2最佳化問題........................21
4.3適應值............................22
第五章  改良式灰狼演算法...............23
5.1概述..............................23
5.2基礎理論..........................24
5.2.1修改收斂係數.....................24
5.2.2加入 α,β,δ 權重.................26
5.2.3增加記憶能力.....................28
5.2.4貪婪策略........................29
5.3執行流程..........................30
第六章  函數數值分析..................33
6.1參數設定..........................33
6.2測試範例..........................34
6.3測試結果..........................34
第七章  結構數值分析..................39
範例一:十桿件桁架結構最佳化設計.........40
範例二: 二十五桿件桁架結構最佳化設計....42
範例三: 直升幾尾桁結構最佳化設計........44
範例四:十八桿件桁架結構最佳化設計.......46
範例五:二十二桿件桁架結構最佳化設計.....48
第八章  結論.........................50
參考文獻.............................70

圖目錄
圖 1 粒子群演算法........................12
圖 2 灰狼演算法..........................14
圖 3  a收斂曲線..........................18
圖 4  A分布圖............................25
圖 5 貪婪策略............................30
圖 6 改良式灰狼演算法執行流程..............32
圖 7 function 1.........................37
圖 8 function 2.........................37
圖 9 function 3.........................38
圖 10 function 4........................38
圖 11  範例一　十桿件桁架結構尺寸外型圖.....52
圖 12  範例二　二十五桿件桁架結構尺寸外型圖..53
圖 13  範例三　直升機尾桁結構尺寸外型圖.....54
圖 14  範例四  十八桿件桁架結構尺寸外型圖...55
圖 15  範例五　二十二桿件桁架結構尺寸外型圖..56


 
表目錄
表 1 參數設定.............................33
表 2 測試函數.............................34
表 3 測試結果.............................36
表 4　範例一　有限元素分析及最佳值比較.......57
表 5　範例二　二十五桁架結構各節點受力.......58
表 6　範例二　桿件分組.....................59
表 7　範例二　有限元素分析及最佳值比較.......60
表 8　範例三　桿件分組.....................61
表 9　範例三　直升機尾桁各節點受力..........62
表 10　範例三　有限元素分析及最佳值比較......63
表 11　範例四　十八桿件各節點受力...........64
表 12　範例四　桿件分組....................65
表 13　範例四　有限元素分析及最佳值比較......66
表 14 範例五　二十二桿件各節點受力..........67
表 15　範例五　桿件分組....................68
表 16　範例五　有限元素分析及最佳值比較......69

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