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系統識別號 U0002-3007201312084100
中文論文名稱 應用雙演化法於結構最佳化設計之研究
英文論文名稱 Optimum Design of Structures by Dual Evolution Strategy
校院名稱 淡江大學
系所名稱(中) 航空太空工程學系碩士班
系所名稱(英) Department of Aerospace Engineering
學年度 101
學期 2
出版年 102
研究生中文姓名 張維恩
研究生英文姓名 Wei-En Chang
學號 600430580
學位類別 碩士
語文別 中文
口試日期 2013-07-02
論文頁數 79頁
口試委員 指導教授-張永康
委員-洪健君
委員-陳步偉
中文關鍵字 雙演化演算法  粒子群演算法  差分演化演算法  最佳化設計 
英文關鍵字 Dual Evolution Strategy  Particle Swarm Optimization  Differential Evolution  Optimum Design 
學科別分類 學科別應用科學航空太空
中文摘要 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。
英文摘要 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.
論文目次 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

參考文獻 參考文獻
[1] 三郎、杉江,北京,仿生學潛說,科學出版社,1982。

[2]高尚、楊靜宇,群智能算法及其應用,中國水利水電出版社,2006。

[3] Eberhart, R.C., and Kennedy, J., “Particle swarm optimization,” IEEE international conference on neural networks, Vol. 4, pp. 1942–1948, 1995.

[4] Eberhart, R.C., and Kennedy, J., “A New Optimizer Using Particle Swarm Theory,” Proceedings of the Sixth International Symposium on Micro Machine and Human Science, IEEE Service Center, pp. 39-43, 1995.

[5] Eberhart, R.C. and Shi, Y., “A modified particle swarm optimizer,” Proceedings of IEEE International Conference on Evolutionary Computation, 1998.

[6] 郭信川,張建仁,劉清祥,「粒子群演算法於最佳化問題之研究」,第一屆台灣作業研究學會學術研討會暨2004 年科技與管理學術研討會,419~432 頁,2004。

[7] Clerc, M., “The Swarm and the Queen: Towards a Deterministic and Adaptive Particle Swarm Optimization,” Proceedings of the Congress on Evolutionary Computation, Vol. 3, pp. 1951−1957, 1999.

[8] He, S., Wu, Q.H., Wen, J.Y., Saunders, J.R. and Paton, R.C., “A particle swarm optimizerwith passive congregation,” Biosystem, Vol. 78, pp. 135–47, 2004.

[9] Fourie, P.C. and Groenwold, A.A., “The particle swarm optimization algorithm in size and shape Optimization,” Struct Multidisc Optim 23, pp. 259–267,2002.

[10] Schutte, J.F. and Groenwold, A.A., “Sizing design of truss structures using particle swarms,” Struct Multidisc Optim 25,pp. 261–269 ,2003

[11] Perez, R.E. and Behdinan, K., “Particle swarm approach for structural design optimization,” Computers and Structures Vol. 85, pp. 1579–1588, 2007.

[12] 莊玟珊,PSO–SA混合搜尋法與其他結構最佳化設計之應用,國立中央大學土木工程研究所碩士論文,2007。

[13] 林大為,結合模擬退火之改良粒子群演算法於結構最佳化設計的研究,國立中央大學土木工程研究所碩士論文,2009。

[14] Storn, R. and Price, K., “Differential Evolution: A Simple and Efficient Adaptive Scheme for Global Optimization Over Continuous spaces,” Global Optimization, pp. 341-359, 1996.

[15] Sauer, J.G. and Coelho, L., “Discrete Differential Evolution with local search to solve the Traveling Salesman Problem: Fundamentals and case studies,” In Proceedings of the 7th IEEE International Conference on Cybernetic Intelligence Systems, pp. 1–6, 2008.

[16]Shao, Y. and Xu, H., “Solve Zero-One Knapsack Problem by Greedy Genetic Algorithm,” In Proceedings of the International Workshop on Intelligent Systems and Applications, pp.1140-1143, 2009.

[17] Chiou, J.P., Chang, C.F. and Su, C.T., “Variable scaling hybrid differential evolution for solving network reconfiguration of distribution systems,” In Proceedings of the IEEE Transactions on Power Systems, Vol. 20, No. 2, pp. 668-674, 2005.

[18]Cai, H.R., Chung, C.Y. and Wong, K.P., “Application of Differential Evolution Algorithm for Transient Stability Constrained Optimal Power Flow,” In Proceedings of the IEEE Transactions on Power Systems, Vol. 23, No. 2, pp. 719-728, 2008.



[19]Kicinger, R., Arciszewski, T. and Jong, K.D., “Evolutionary computation and structural design: A survey of the state-of-the-art,” Computers & Structures, Vol. 83, No. 23-24, pp. 1943-1978, 2005.

[20] 李維平,江長育,搭配擾動策略之差分演化演算法,中原大學資管研究所論文,2011。

[21]Salman, A., Engelbrecht, A.P. and Omran, M.G.H., “Empirical analysis of self-adaptive differential evolution,” European Journal of Operational Research, Vol. 183, No. 2, pp. 785-804, 2007.

[22]Hao, Z.F., Guo, G.H. and Huang, H., “A Particle Swarm Optimization Algorithm with Differential Evolution,” In Proceedings of the Sixth International Conference on Machine Learning and Cybernetics,, pp. 1031-1035, 2007.

[23]Abbass, H.A., “The self-adaptive Pareto differential evolution algorithm,” in Proceedings of the 2002 Congress on Evolutionary Computation, pp. 831-836, 2002.

[24]Deng, C., Zhao, B., Deng, A. and Hu, R., “New Differential Evolution Algorithm with a Second Enhanced Mutation Operator,” In Proceedings of the International Workshop on Intelligent Systems and Applications, pp. 1-4, 2009.

[25]Luitel, B. and Venayagamoorthy, G.K., “Differential evolution particle swarm optimization for digital filter design,” In Proceedings of the IEEE Congress on Evolutionary Computation, pp. 3954-3961, 2008.

[26] Eberhart, R.C., Kennedy, J. and Shi, Y., “Swarm Intelligence,” Evolutionary Computation, Morgan Kaufmann, Los Altos, CA, pp.187-219, 2001.

[27] Eberhart, R.C., and Shi, Y., “Parameter Selection in Particle Swarm Optimization,” Porto, V.W., Saravanan, N., Waagen, D. and Eiben, A.E. (eds), Lecture Notesin Computer Science, 1447, Evolutionary Programming VII, Springer, Berlin,pp. 591−600, 1998.
[28] Eberhart, R.C. and Shi, Y., “Comparing Inertia Weights and Constriction Factors in Particle Swarm Optimization,” In Proceedings of the 2000 Congress on Evolutionary Computation, Vol. 1,pp.84−88, 2000.

[29] Carlisle, A., and Dozier, G., “An off-the-shelf PSO,” In Proceedings of the Workshop on Particle Swarm Optimization, Vol. 1, pp. 1−6, 2001.

[30] Parrish, J.K. and Hamner, W.M., “Animal Groups in Three Dimensions,” Cambridge University Press, Cambridge, UK, 1997.

[31]洪冠豪,改良式粒子群優化演算法於桁架結構最佳化設計之應用,國立交通大學土木工程系碩士班碩士論文,2010。

[32]王永富,應用混合型差分進化演算法於多區域電力系統之經濟調度與運轉,國立中正大學電機工程研究所,2004。

[33] Růžek, B. and Kvasnička, M., “Differential Evolution Algorithm in the Earthquake Hypocenter Location,” Pure and Applied Geophysics, pp. 1420-9136, 2001.

[34] Storn, R., Price, K. and Lampinen, J., “Application of Differential Evolution to the Analysis of X-Ray Reflectivity Data,” Differential Evolution, Springer Berlin Heidelberg , pp. 463-478, 2005.

[35] Mayer, D.G., Kinghorn, B.P. and Archer, A.A., “Differential Evolution – an easy and efficient evolutionary algorithm for model optimization,” Agricultural Systems, Vol. 83, pp. 315-328, 2005.

[36] Ali, M. M. and Torn, A., “Population set-based global optimization algorithms: some modifications and numerical studies,” Computers and Operations Research, Vol. 31, No. 10, pp. 1703-1725, 2004.

[37]Salman, A., Engelbrecht, A.P., and Omran, M.G.H., “Empirical Analysis of Self-adaptive Differential Evolution,” European Journal of Operational Research, Vol. 183, No. 2, pp. 785-804, 2007.

[38]Luitel, B., and Venayagamoorthy, G.K., “Differential Evolution Particle Swarm Optimization for Digital Filter Design.” In Proceedings of the IEEE Congress on Evolutionary Computation, pp. 3954-3961, 2008.

[39]Abbass, H.A., “The Self-adaptive Pareto Differential Evolution Algorithm. in Evolutionary Computation,” In Proceedings of the 2002 IEEE Congress on Evolutionary Computation, 2002.

[40]李維平,簡璟蔚,蔡宛庭,改良突變權重的差分進化演算法,先進工程學刊 第六卷 第四期,2011。

[41] Gong, W., Cai, Z. and Jiang, L., “Enhancing the performance of differential evolution using orthogonal design method,” Applied Mathematics and Computation, Vol. 206, No. 1, pp. 56-69, 2008.

[42]Qin, A.K. and Suganthan, P.N., “Self-adaptive differential evolution algorithm for numerical optimization,” in Proceedings of the 2005 Congr. on Evol. Comput., Vol. 2, pp. 1785-1791, 2005.

[43] Storn, R., “Differential evolution research – trends and open questions,” Studies in Computational Intelligence, Vol. 143, pp. 1-31, 2008.

[44]Xu, R., Venayagamoorthy, G. K. and Wunsch, D. C., “Modeling of gene regulatory networks with hybrid differential evolution and particle swarm optimization,” ESCI on Neural Networks Vol. 20, pp. 917-927, 2007.

[45]吳盈志,雙演化演算法之研究,中原大學資訊管理研究所,2009。

[46] Zhang, W.J, and Xie, X.F ,"DEPSO Hybrid Particle Swarm with Differential Evolution Operator", In Proceeding of the 2003 IEEE Internatuonal Conference on Systems, 2003.

[47]Omran, M. G. H., Engelbrecht, A. P. and Salman, A., “Differential Evolution Based Particle Swarm Optimization,” In Proceedings of the 2007 IEEE on Swarm Intelligence Symposium, pp. 112–119, 2007.

[48]劉敬文,結合基因演算法與線性規劃法於結構最佳化設計,淡江大學航空太空工程學系研究所,2010。

[49]戴伯勳,3D桁架最佳化設計平台,國立台灣科技大學機械工程系研究所,2006。

[50]王興正,應用粒子群演算法於無人飛行載具結構系統之最佳化設計,淡江大學航空太空工程學系研究所,2012。
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