System No. U0002-1902201418490000 仿生免疫演算法的限制最佳化及應用 The Development of Immune Algorithms for Constrainted Optimization and Applications 淡江大學 機械與機電工程學系碩士班 Department of Mechanical and Electro-Mechanical Engineering 102 1 103 蔡仲達 Chong-Da Tsai 600370893 碩士 Traditional Chinese 2014-01-20 91page advisor - 史建中 co-chair - 林志豐 co-chair - 鍾添東 仿生最佳化 限制免疫演算法 轉換目標策略 拓樸桁架最佳化 結構最佳化 Biological based optimization constrained immune algorithm objective transform strategy topological truss optimization structural optimization ```本文主要為發展適用於免疫演算法的限制條件處理策略。免疫演算法的原理是模仿B細胞表面受體上的Y型重鏈及輕鏈基因結構，藉由基因的高度突變完成病原體的解碼，達到最佳化的求解。處理限制的轉換目標策略是將限制條件的違反量轉換為另一目標函數，將此另一目標函數與原目標函數進行非支配排序，可得到Pareto前沿解，當另一個函數值為0的點即表示符合所有的限制條件。本文以發展完成的限制免疫最佳化演算法(CIA)，進一步發展處理含限制的雙目標最佳化問題及含限制的多極值最佳化問題。並以多個數值例題呈現及檢驗解題的精確性及演算法的穩健性及效率。 含限制的免疫最佳化應用於電熱微致動器的最佳化工程設計，應用到有限元素軟體(ANSYS)與免疫最佳化演算連結，設計微致動器的結構及輸入電壓以達到最大的位移效果。另一個設計問題是含三種材料的震動台，最小化成本達到最大震動效果的雙目標最佳化設計，應用到ANSYS與免疫演算法做連結，結果為多組解可供設計者選擇。含限制的多極值免疫最佳化程序，被應用於桁架拓樸設計與分析，本文採用了二階段設計程序。第一階段為排列桁架可能的型態，再經第二次型態與結構尺寸同步設計程序，最後可得到多種型態的設計結果，每種排列結構相當於不同尺寸的區域最佳解。其中包含平面及空間桁架結構設計，結果與參考文獻結構相同或較佳。``` ```The presenting thesis mainly proposes a constraints handling strategy applied for immune system algorithm (IA). The theory of such an IA simulates the gene structures of Y-shape heavy chain and light chain on B-cell receptor. The key decoded operator is somatic mutation where the gene evolves to the final optimum. In dealing with constraints, an objective transform strategy is proposed where all violations are organized to an additional objective function. Then, the non-dominate method is utilized for two objective function problem. The final optimum converge at when the additional objective function evolving to zero. This constraints handling technique is further applied and adapted to double-objective constrained optimization problem. The other application of the proposed constraints handling is applied to the multimodal constrained problems. The engineering designs presented in the thesis include single-arm and two-arm micro electromechanical actuators design and analysis. The I-beam and vibrating platform structural design contain two-objective functions and constraints. The result shows that the proposed method is reliable and efficient. Several constrained topological truss design are illustrated by presented constrained multimodal algorithm. The better performances can be obtained as compared published papers.``` ```致謝………………………………………………………………...I 中文摘要………………………………………………………….II 英文摘要…………………………………………………………IV 目錄………………………………………………………………VI 圖目錄………………………………………………………….VIII 表目錄…………………………………………………………….X 符號表……………………………………………………………XI 第一章 緒論……………………………………………………..1 1.1 動機與目的………………………………………...1 1.2 文獻回顧…………………………………………...1 1.3 本文架構…………………………………………...4 第二章 含限制免疫系統最佳化………………………………..5 2.1 免疫系統的原理…………………………………...5 2.2 免疫系統演算法………………………………….11 2.3 轉換目標策略的原理及方法…………………….16 2.4 含限制的免疫演算法…………………………….20 第三章 含限制雙目標免疫系統最佳化………………………33 3.1 雙目標免疫系統演算法………………………….33 3.2 含限制雙目標免疫系統演算法………………….37 第四章 含限制多極值免疫系統最佳化………………………47 4.1 多極值免疫演算法原理及技術………………….47 4.2 含限制多極值免疫演算法……………………….53 第五章 含限制免疫最佳化工程設計…………………………63 5.1 電熱微致動器單目標最佳化設計……………….63 5.2 震動台雙目標最佳化設計……………………….74 5.3 桁架型態及結構多極值最佳化設計…………….78 第六章 結論……………………………………………………88 6.1 結論……………………………………………….88 6.2 未來展望………………………………………….89 參考文獻…………………………………………………………90 圖目錄 圖2.1 B 細胞辨識抗原示意圖………………………………………...8 圖2.2 B 細胞表面受體Y 型結構示意圖……………………………..9 圖2.3 B 細胞重鏈突變方式示意圖…………………………………..9 圖2.4 株落選擇過程…………………………………………………10 圖2.5 非支配排序法示意圖………………………………………..16 圖2.6 雙目標最佳化的Pareto 前沿………………………………..17 圖2.7 數值例題一目標求解迭代圖………………………………..26 圖2.8 數值例題二目標求解迭代圖………………………………..29 圖2.9 數值例題三目標求解迭代圖………………………………..31 圖3.1 本文轉換目標策略Pareto 解………………………………..44 圖3.2 摘自文獻[9]Pareto 解………………………………………...44 圖3.3 I 型樑設計圖…………………………………………………..45 圖3.4 本文I 型樑最佳化設計Pareto 圖解…………………………46 圖3.5 摘自文獻[9]Pareto 圖解……………………………………...47 圖4.1 平均值為0，標準差為1 的常態分佈函數機率分佈圖………50 圖4.2 群集搜尋示意圖……………………………………………...51 圖4.3 Rastrigin 函數一與限制條件示意圖………………………….60 圖4.4 Rastrigin 函數二與限制條件示意圖………………………….62 圖5.1 單臂電熱式微致動器示意圖………………………………….65 圖5.2 單臂電熱微致動器迭代圖…………………………………….69 圖5.3 文獻單臂電熱微致動器迭代圖……………………………….69 圖5.4 雙臂電熱式微致動器示意圖………………………………….70 圖5.5 雙臂電熱微致動器迭代圖…………………………………….73 圖5.6 文獻雙臂電熱微致動器迭代圖……………………………….73 圖5.7 震動台的材料結構圖………………………………………….75 圖5.8 文獻[18]之Pareto 圖解………………………………………..78 圖5.9 本文Pareto 圖解……………………………………………….78 圖5.10 39 桿桁架結構圖……………………………………………..81 圖5.11 平面39 桿桁架型態與結構設計程序圖…………………….83 圖5.12 39 桿結構文獻[4]與本文結果比較圖……………………….84 圖5.13 空間24 桿桁架結構圖……………………………………….85 圖5.14 空間24 桿桁架型態與結構設計程序圖……………………..87 表目錄 表2.1 數值例題一之數值結果……….………………………………27 表2.2 數值例題二之數值結果……………………………………….30 表2.3 數值例題三之數值結果……………………………………….32 表4.1 Rastrigin 函數一所得極值點結果表…………………….……60 表4.2 Rastrigin 函數二所得極值點結果表………………….………62 表5.1 多晶矽材料性質……………………………………………….67 表5.2 設計變數與範圍……………………………………………….67 表5.3 設計變數與範圍……………………………………………….71 表5.4 震動台的材料性質及價錢…………………………………….75 表5.5 對稱39 桿桁架設計結果比較表……………………………...84 表5.10 空間24 桿桁架求解結果表………………………………….88``` ```[1]De Castro, Leandro N., and Fernando J. 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Finite elements in analysis and design, Vol. 37, No. 5, 2001, pp. 447-465.``` Within Campus： On-campus access to my hard copy thesis/dissertation is open immediately Release immediately Outside the Campus： I grant the authorization for the public to view/print my electronic full text with royalty fee and I donate the fee to my school library as a development fund.Release immediately