本文探討與發展含改良突變機制的粒子群最佳化演算法，除了能避免最終解落入區域極值的可能。本文又探討三種處理限制條件的方法，第一種是改良飛回策略的。第二種是利用量測限制違反量分區的策略。第三種是應用求解多目標最佳化的技術。經由數值例題，檢驗本文所提之三種策略，都能有效及可行的在粒子群最佳化演算法中處理限制條件。
另外，本文應用非支配排序法於粒子群演算法，求解多目標最佳設計的問題。先以無限制的多目標數值例題，探討粒子群演算法求解的可行性，再探討含有限制條件的多目標粒子群演算法。最後，以多目標粒子群最佳化程序，應用於含限制條件的工程設計問題，例如四桿桁架設計，I型樑的截面設計及焊接樑的設計。本研究的含限制之多目標粒子群最佳化程序亦結合有限元素分析軟體ANSYS，再對工程例題進行多目標最佳化的設計，加強本文粒子群最佳化設計具有實用性。 由本文所發展的含限制或不含限制的多目標粒子群最佳化程序，可得到平滑的Parato曲線，亦得到精確的數值。

A particles swarm algorithm (PSA) including improving mutation for global optimization is presented in this thesis.  The presented global PSA can simplify the solution process.  Three constraints handling strategies in such a global PSA are proposed to construct a constrained particles swarm optimization (CPSO).  The first strategy is applied the concept of flying back with modification.  The second strategy is to modify the measurement technique of constraints violation.  The third strategy is the application of the technique of multiobjective optimization in which all constraints are integrated and transformed to an additional objective.  
The non-dominated concept is applied for dealing with particles swarm multiobjective optimization (PSMO) problem.  The PSMO in the thesis contains those three constraints handling strategies with some illustrative examples and structural design optimization problems.  The results shows that all constrained PSO for single or double objective problems are successful to obtain the results and satisfied Pareto front.

目錄
致謝......................................................I
中文摘要.................................................II
英文摘要.................................................IV
目錄.....................................................VI
圖目錄..................................................VIII
表目錄...................................................XI
符號說明................................................XII
第一章 緒論...............................................1
1.1 研究動機與目的........................................1
1.2 文獻回顧..............................................2
1.3 本文架構..............................................4
第二章 含突變機制的改良粒子群演算法.......................5
2.1 基本粒子群原理........................................5
2.2 粒子群的數學模型......................................7
2.3 含突變機制的粒子群演算法.............................10
第三章 粒子群最佳化限制條件的處理........................20
3.1 對已知限制條件處理方法的改善.........................21
3.2以多目標策略處理限制條件的方法........................24
3.3 含限制條件的單目標數值例題分析.......................31
第四章 粒子群的多目標最佳化..............................47
4.1 無限制條件的多目標最佳化流程.........................47
4.2 有限制條件的多目標最佳化流程.........................51
4.3 多目標數值例題分析...................................54
第五章 粒子群的多目標工程最佳化..........................63
5.1 應用ANSYS的有限元素分析..............................63
5.2 結合有限元軟體ANSYS的粒子群最佳化....................70
5.3 四桿桁架的粒子群雙目標最佳化設計.....................74
5.4  I型樑的粒子群雙目標最佳化設計.......................80
5.5 焊接樑的粒子群雙目標最佳化設計.......................87
第六章 結論..............................................96
6.1 綜合討論與結論.......................................96
6.2 未來展望.............................................98
參考文獻.................................................99

圖目錄
圖2.1  速度更新示意圖................................8
圖2.2  MPSA演算流程圖...............................15
圖3.1  非支配排序法示意圖...........................27
圖3.2  Pareto front示意圖...........................28
圖3.3  目標函數值與限制條件總合由非支配排序法排序...28
圖3.4  收歛最佳示意圖...............................30
圖3.5  本文改良飛回策略的數值例題1求解迭代圖........33
圖3.6  本文改良相對法的數值例題1求解迭代圖..........33
圖3.7  本文多目標策略的數值例題1求解迭代圖..........34
圖3.8  本文改良飛回策略的數值例題2求解迭代圖........37
圖3.9  本文改良相對法的數值例題2求解迭代圖..........37
圖3.10 本文多目標策略的數值例題2求解迭代圖..........38
圖3.11 10桿桁架結構圖...............................38
圖3.12 為飛回策略[6]求解10桿桁架迭代圖..............42
圖3.13 本文改良飛回策略求解10桿桁架迭代圖...........43
圖3.14 本文改良飛回策略求解10桿桁架迭代圖...........43
圖3.15 本文改良飛回策略求解10桿桁架迭代圖...........44
圖3.16 本文改良飛回策略求解10桿桁架迭代圖...........44
圖3.17 改良飛回策略(含突變)求解10桿桁架迭代圖.......45
圖3.18 本文改良相對法(含突變)求解10桿桁架迭代圖.....45
圖3.19 本文多目標處理法(含突變)求解10桿桁架迭代圖...46
圖4.1  無限制條件多目標最佳化流程圖.................50
圖4.2  含限制條件多目標最佳化流程圖.................53
圖4.3  SCH測試函數之Pareto解........................55
圖4.4  POL測試函數之Pareto解........................57
圖4.5  摘自文獻[18]POL測試函數之Pareto解............57
圖4.6  利用改良飛回策略.............................59
圖4.7  利用改良相對法...............................60
圖4.8  利用多目標策略處理限制條件...................60
圖4.9  摘自文獻[19]測試函數之Pareto解...............61
圖4.10 三種限制條件處理方法求解比較圖...............61
圖5.1  四桿桁架結構及受力圖.........................64
圖5.2  四桿例題分析範例.............................64
圖5.3  I型樑外型及受力圖............................66
圖5.4  I型樑分析範例................................67
圖5.5  焊接樑結構及受力圖...........................68
圖5.6  焊接樑分析範例...............................69
圖5.7  整合粒子群最佳化與有限元軟體流程圖...........73
圖5.8  用解析式的四桿Pareto結果.....................78
圖5.9  連結ANSYS的四桿Pareto結果....................79
圖5.10 摘自文獻[18]四桿Pareto的結果.................79
圖5.11 用解析式及改良相對法的I型樑Pareto結果........84
圖5.12 連結ANSYS及改良飛回法的I型樑Pareto結果.......85
圖5.13 連結ANSYS及改良相對法的I型樑Pareto結果.......85
圖5.14 連結ANSYS及多目標策略的I型樑Pareto結果.......86
圖5.15 摘自文獻[21]I型樑Pareto的結果................86
圖5.16 連結ANSYS的I型樑Pareto結果比較圖.............87
圖5.17 用解析式及改良飛回的焊接樑Pareto結果.........92
圖5.18 連結ANSYS及改良飛回法的焊接樑Pareto結果......93
圖5.19 連結ANSYS及改良相對法的焊接樑Pareto結果......93
圖5.20 連結ANSYS及多目標策略的焊接樑Pareto結果......93
圖5.21 摘自文獻[20]求解焊接樑Pareto的結果...........94
圖5.22 連結ANSYS焊接樑Pareto比較圖..................95

表目錄
表2.1 PSO參數設定表................................16
表2.2 求解Rastrigin函數(n=10)的30次分析結果.........17
表2.3 Rastrigin函數設計點結果表....................17
表2.4 求解Griewank函數(n=10)的30次分析結果..........18
表2.5 Griewank函數設計點結果表.....................19
表3.1 數值例題1最佳化10次分析結果表.................32
表3.2 數值例題1最佳化分析結果表.....................32
表3.3 數值例題2最佳化10次分析結果表.................36
表3.4 數值例題2最佳化分析結果表.....................36
表3.5 10桿桁架結構最佳化分析結果表.................41
表3.6 由含突變機制改良飛回求出的應力值..............41
表3.7 由含突變機制改良飛回求出的位移量..............42

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