本研究應用蝙蝠特有的回聲定位能力，使其能藉由頻率、響度、脈衝發射率三者之間的改變，進行大範圍之搜尋並在滿足各種限制之條件後，進行最佳解的選擇，進而得到全域最佳解。但是傳統之蝙蝠演算法在搜尋多極值問題時，可能會侷限於區域性範圍。為了有效解決蝙蝠演算法易陷入局部最佳解的缺點，因此本研究在局部搜索時改採萊維飛行改良的蝙蝠演算法。萊維飛行具有小步距和偶爾長步距的搜尋特性。本研究同時根據不同的範例調整蝙蝠隨機飛行公式之頻率和萊維飛行的控制參數κ值控制萊維飛行的步距，以有效的達到尋求最佳解之能力。脈衝發射率可做為調整隨機飛行或局部最搜索的機率，響度參數之大小可作為接受新解的依據。改良後的演算法增加了蝙蝠位置的變化活力，提高了演算法的效率。由數值分析範例之結果，發現萊維飛行改良蝙蝠演算法於結構最佳化設計上可得到不錯的結果。

The unique echolocation capability of bats was applied to bat algorithm in this study. The proposed algorithm finds the distance between each bat and guides the bat’s movement by the bat position and velocity. With the help of frequency, loudness and pulse rate parameters during the search process, the optimum design can be obtained efficiently. However, searching for multi-extreme problems, the extreme point may be limited to the local optimum region. In order to improve the shortcomings that bat optimization is easy to fall into local optimum, the Lévy flight technique was applied to Bat algorithm in local search. Lévy flight has a small step and an occasional long step search. By controlling the frequency of the bat in random flight and parameter k value of Lévy flight, the ability of finding best solution can be achieved effectively. The pulse emissivity can be used to adjust the probability of random flight or local search and the acceptable new solution can be determined by the londness parameter. The improved algorithm increases the possibility of particle position and the efficiency of the algorithm. From the results of numerical analysis examples, it is found that the optimum designs obtained by the bat algorithm with Lévy Flight are better than other referances.

目錄I
圖目錄III
表目錄IV
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6
第二章蝙蝠演算法7
2.1基礎理論7
2.2蝙蝠演算法程序9
第三章萊維飛行12
3.1基礎理論12
3.2數學模型13
第四章結合萊維飛行的蝙蝠演算法16
4.1結合萊維飛行的蝙蝠演算法程序16
4.2結合萊維飛行的蝙蝠演算法流程19
第五章最佳化設計20
5.1最佳化概念20
5.2最佳化問題21
5.3適應值22
5.4程式執行流程23
第六章 數值分析24
6.1範例一:十桿件桁架結構最佳化25
6.2範例二:二十五桿件桁架結構輕量化設計27
6.3範例三:七十二桿件桁架結構輕量化設計29
6.4範例四:直升機尾桁結構輕量化設計31
6.5範例五:無人飛行載具機翼主樑之輕量化設計33
6.6範例六:四層壓電複合薄板結構之輕量化設計35
第七章結論39
參考文獻65
附錄69
圖一回聲定位期間所發出超聲波的類型變化40
圖二Pearson隨機遊走圖41
圖三(a)跳躍的蜘蛛猴(b)滿足萊維飛行的特徵42
圖四比較不同控制因子的萊維飛行43
圖五模擬的萊維飛行44
圖六結合萊維蝙蝠演算法流程45
圖七程式執行流程46
圖八範例一十桿件桁架結構尺寸圖47
圖九範例二二十五桿件桁架結構尺寸圖48
圖十範例三七十二桿件桁架結構尺寸圖49
圖十一範例四直升機尾桁結構外型及負載圖50
圖十二範例五無人飛行載具機翼主樑結構外型圖51
圖十三範例六四層壓電複合薄板結構外型圖52
表一範例一十桿件最佳值比較53
表二範例二二十五桿件桁架結構各節點受力54
表三範例二二十五桿件桁架結構節點座標55
表四範例二各桿件分類及桿件與節點關係56
表五範例二二十五桿件最佳值比較57
表六範例三七十二桿件桁架結構節點受力情形58
表七範例三七十二桿件結構各桿件分組59
表八範例三七十二桿件最佳值比較60
表九範例四直升機尾桁之桿件分組61
表十範例四直升機尾桁結構外型最佳值比較62
表十一範例五無人飛行載具主樑結構最佳值比較63
表十二範例六四層壓電複合薄板最佳值比較64

[1]Altringham, J.D., ”Bats: Biology and Behaviour, ” Oxford University Press, 1996.
[2]Yang, X.S., ”A New Metaheuristic Bat-Inspired Algorithm,” Nature Inspired Cooperative Strategies for Optimization, Studies in Computa-tional Intelligence, Springer Berlin,Vol.284,pp.65-74, 2010.
[3]Yang, X. S., ”Bat Algorithm for Multi-objective Optimization, ” Int. J. Bio-Inspired Computation, Vol.3, No. 5,pp.267-274, 2011.
[4]Khan,K. and Sahai, A., ”A Comparison of BA,GA,PSO,BP and LM for Training Feed Forward Neural Networks in E-learning Con¬text,” Int. J. Intelligent Systems and Applications, Vol.4, No.7,pp.23-29, 2012.
[5]Komarasamy, G. and Wahi, A., ”An Optimized K-means Clustering Technique Using Bat Algorithm, ” Euro. J. Sci. Res., Vol. 84, No.2, pp.263-273, 2012.
[6]Yang, X.S. and Gandomi, A.H., ”Bat Algorithm: A Novel Approach for Global Engineering Optimization,” Engineering Computations, Vol.29,No.5, pp.464-483, 2012.
[7]Yang, X.S.and Fong, S., ”Bat Algorithm for Topology Optimization in Microelectronic Application,” IEEE, pp.150-155, 2012.
[8]Nakamura, R.Y.M., Pereira, L.A.M. and Costa,K.A., ”BBA:A BinaryBat Algorithm for Feature Selection, ” In:25th SIBGRAPI conference on graphics, patterns and images (SIBGRAPI), IEEE Publication, pp.291-297, 2012.
[9]Hasancebi, O., Teke, T. and Pekcan, O., ”A Bat-inspired Algorithm for Structural Optimization, ” Computers and Structures, Vol.128, pp.77-90, 2013.
[10]Gandomi, Amir H. and Yang, Xin-She, ”Chaotic Bat Algorithm,” Journal of Computational Science, JOCS.232, 2013.
[11]Taha,A.M. and Tang,A., ”Bat Algorithm for Rough Set Attribute Reduc-tion,” Journal of Theoretical and Applied Information Technology, Vol.51, pp.1-8, 2013.
[12]Yilmaz,S. and Kucuksille, E.U.,”A New Modification Approach on Bat Algorithm for Solving Optimization Problems,”Applied Soft Compu¬ting, Vol.28, pp.259-275, 2015.
[13]Yang, X.S. and Deb, S., ”Engineering Optimizations by Cuckoo Sea¬rch,” International Journal of Mathematical Modeling and Numerical Optimization, Vol.4, pp.330-343, 2010.
[14]Wang, Q. and Guo, X., ”Particle Swarm Optimization based on Lévy Flight,”Application Research of Computers, Vol.33, No.9, pp.2589-2591, 2016.
[15] Heidari, Ali Asghar and Pahlavani, Parham, ”An Efficient Modified Grey Wolf Optimizer with Lèvy Flight for Optimization Tasks,” Ap¬plied Soft Computing, Vol.60, pp115-134, 2017.
[16]吳忠信，蝙蝠的回聲定位，科學教育月刊第276期，2005年。
[17]Kirkpatrick, S., Gelatt, C.D., and Vecchi, M.P., ”Optimization by Simu-lated Annealing,” Science, Vol.220, pp.671-680, 1983.
[18]Porter, Mason A. and Renaud, Lambiotte, ”Random Walks and Diffusion on Networks,” Physics Reports, Vol.31, 2017.
[19]Rycroft, H. and Bazant, Z.,”Introduction to Random Walks and Diffu-sion,” Lecture 1, Department of Mathematics Class Note, MIT, 2005.
[20]Dienes, G.J. and Smoluchowski, R., ”Dynamics of Replacement Se-quences and Crowdions,” Journal of Physics and Chemistry of Sol¬ids, Vol.37, pp95-98, 1976.
[21]Barthelemy, P, Bertolotti, J. and Wiersma, Diederik S., ”A Lévy Flight for Light,”, Nature 453,pp.495-503, 2008.
[22]Sun, Zhaopeng and Zheng, Yujun, ”Trajectory Dynamics for Lévy Flight,” Highlights of Sciencepaper, Vol.10, No.13, pp.1519-1524, 2017.
[23]Lin, Jiann-Horng and Chou, Chao-Wei, ”A Chaotic Lévy Flight Bat Algorithm for Parameter Estimation in Nonlinear Biological Sys¬tems, ” Journal of Computer and Information Technology, Vol.2, No.2, pp.56-63, 2012.
[24]Yang,X.S. ”Firefly Algorithm, Lévy Flights and Global Optimization,” In:Research and Development in Intelligent Systems XXVI, pp.209-218, 2010.
[25]Yang,Xin-She and Deb, Suash, ”Multiobjective Cuckoo Search for De¬sign Optimization,” Applied Soft Computing, Vol.23, pp333-345, 2010.
[26]劉曉龍等，基於萊維飛行的鳥群優化算法，計算基測量與控制12期，pp.195-200,，2017年。
[27]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碩士論文，2010年。
[28]周于文，應用蜂群演算法於結構最佳化設計之研究，淡江大學航空太空工程學系研究所碩士論文，2013年。
[29]陳炫光，應用蝙蝠演算法於結構最佳化設計之研究，淡江大學航空太空工程學系研究所碩士論文，2016年。
[30]Perez, R. E. and Behdinan, K., “Particle Swarm Approach for Structural Design Optimization,” Computers and Structures 85, pp.1579-1588, 2007.
[31]陳景文，改良式移動漸進線法於結構之最佳化設計，淡江大學航空太空工程學系研究所碩士論文，2009年。
[32]郭純孜，應用移動漸進線法於結構之最佳化設計，淡江大學航空太空工程學系研究所碩士論文，2008年。
[33]柯星竹，遺傳演算法與類神經網路於結構最佳化設計之研究，淡江大學航空太空工程學系研究所碩士論文，2006年。