臺灣博碩士論文加值系統

本文藉由螞蟻之間相互合作和殘留費洛蒙的特性衍生出一個適合結構拓樸最佳化的螞蟻最佳化(ACO)，能快速收歛是其演算法之優點。而拓樸結構最佳化設計的優點則是能擺脫設計者主觀的束縛，在目標函數值設定的限制條件下，往往能搜尋出一反設計者思維的結果。以往蟻群最佳化常常使用在解決TSP、QAP、VRP等問題上，而使用在解決結構拓樸最佳化問題上的例子極少，本文正是利用蟻群最佳化來進行結構拓樸最佳化設計，主要是將拓樸結構上的網格當作是螞蟻搜尋食物的路徑，並依據路徑上費洛蒙的高低當作選取的機率，當搜尋完一個完整路徑後，進入商業軟體(ANSYS)進行分析並產生所需資料，藉由這些輸出的資料可以計算此完整路徑的目標函數值當做此路徑上螞蟻所殘留的費洛蒙值。本文最後成功利用多種螞蟻搜尋食物的機制來整合蟻群最佳化和結構拓樸最佳化，並且有效的搜尋出符合設計限制條件的設計結構，證明蟻群最佳化可以搜尋出最佳解。

The ant algorithm has been applied to solve the TSP, QAP, and VRP and there are only a few papers using it to solving problem of topology optimization. This study combines the topology optimization of structure with an ant algorithm that derives from specific pheromone and cooperation mechanism between ants. The best advantage of the ant algorithm is rapid convergence while the benefit of topology optimization can get rid of the subjective ideas of designers and provides them with unexpected results .The contribution of this paper is to integrate ant algorithm with commercial software ANSYS for finding the best results for topology optimization of structure.
A mesh topology of finite element model of structure was used as possible paths that ants find foods from. Every element of the model was treated as a node on the path for ant path. Then, the amount of accumulated pheromone deposited on every element(node) by different ants can be used to determine the probability of selection path for food-finding ants. After an ant completing a tour, the complete path was converted into a structure model and the software ANSYS was applied to analyze the structure. The output data was used to calculate the value of objective function that can be utilized as the amount of pheromone on each route trod by ants.
From the results of studies in this paper, ant algorithm provides an alternate optimization method that has high potential in finding the best design for topology optimization of structure successfully and efficiently.

中文摘要 i
英文摘要 ii
誌謝 iii
目錄 vi
圖目錄 viii
表目錄 ix
符號索引 x
第一章 緒論 1
1.1前言 1
1.2 文獻回顧 2
1.2.1 螞蟻演算法於拓樸結構最佳化 3
1.2.2 拓樸最佳化設計 3
1.3 研究動機 4
1.4論文架構 5
第二章 螞蟻演算法 6
2.1 螞蟻演算法簡介 6
2.2 螞蟻演算法應用在TSP問題 8
2.2.1 初始費洛蒙 9
2.2.2 路徑選擇 10
2.2.3費洛蒙更新 11
2.2.4終止條件 12
2.3 測試方程式驗證 13
2.3.1測試方程式結果與討論 14
第三章 適用於拓樸結構最佳化之蟻群最佳化 16
3.1拓樸結構最佳化介紹 16
3.2有限元素理論介紹 17
3.2.1有限元素分析的程序 18
3.3商用有限元素ANSYS軟體架構介紹 19
3.4 ANSYS結構分析程序 20
3.5應用於螞蟻演算法於拓樸最佳化設計 21
3.5.1路徑編碼 21
3.5.2初始機制 23
3.5.3搜尋路徑選擇機制 25
3.5.4懲罰機制 29
3.5.5更新費洛蒙 29
3.5.6 PTC機制 30
3.5.7 MMAS機制 31
3.5.8相似性判斷 31
3.5.9精英政策 32
3.5.10終止條件 32
第四章 結果與討論 34
4.1 邊界條件設定 34
4.2 蟻群最佳化應用於單目標結構拓樸最佳化設計執行結果 36
一、 比較螞蟻可搜尋方向的數量 36
二、 比較是否使用PTC機制 39
三、 比較目標函數是否標準化 42
四、 比較是否使用全域搜尋機制 45
五、 比較是否使用MMAS機制 49
六、 比較是否使用相似性判斷 52
4.3 總結 55
第五章 結論與未來展望 56
參考文獻 58

[1]D. E. Goldberg, “Genetic Algorithm in Search, Optimization, and Machine Learning”, Addison Wesley 1989
[2]de Castro, L. N., and von Zuben, F. J., ”Artificial Immune Systems：Part I-Basic Theory and Applications,” Technical Report TR-DCA 01/99, 1999.
[3]J. Kennedy, R. Eberhart, “Particle Swarm Optimization”, From Proc. IEEE Int’l. Conf. on Neural Networks (Perth, Australia), IEEE Service Center, Piscataway, NJ, IV:1942-1948.(1995).
[4]M. Dorigo, V. Maniezzo, A. Colorni, Ant System: Optimization by a Colony Cooperating Agents, IEEE TRANSACTION ON SYSTEM, Man, and Cybernetics, Part B: Cybernetics, vol. 26, no. 1, pp.1-13, 1996.
[5]M. Dorigo and L. M. Gambardella, “Ant Colony System : A cooperative learning approach to the traveling salesman problem” IEEE Transactions on Evolutionary Computation, 1(1) : 53-66, 1997.
[6]T. Stützle and M. Dorigo, “ACO algorithms for the traveling salesman problem.” In K.Miettinen, M. M. Makela, P.Neittaanmaki,and J. Periaux, editors, Evolutionary Algorithms in Engineering and Computer Science, pages 163-183. John Wiley &Sons, Chichester, UK, 1999 .
[7]Vittorio Maniezzo and Alberto Colorni, “The Ant System Applied to the Quadratic Assignment Problem”, IEEE TRANSACTION ON KNOWLEDGE AND DATA ENGINEERING, VOL. 11, NO. 5, SEPTEMBEWR/OCTORBER 1999 .
[8]Chen Baowen, Song Shen-min, Chen Xinglin, Shan Zhizhong, “A Multi-Ant Colony System for Vehicle Routing Problems”, Proceeding of the 25th Chinese Control Conference 7-11 August, 2006, Harbin, Heilongjiang .
[9]Zhou Pin, Li Xiao-ping, Zhang Hong-fang,”An Ant Colony Algorithm for Job Shop Scheduling Problem“, Proceedings of the 5th Congress on Intelligent Control and Automation , June 15-19, 2004, Hanghou,P.R. China .
[10]Guan-Chun Luh, Chun-Yin Wu, Chun-Yi Lin, “Multi-model topological optimization of structure using ACO algorithms”, 7th International Conference on Computational Intelligence and Natural Computing in conjunction with 8th Joint Conference on Information Sciences, VOL 479-482, july 21-26, 2005,Salt Lake City, Utah .
[11]S.-C. Chu, C.-S. Shieh, and J. F. Roddick, “A tutorial on meta-heuristics for optimization,”in J.-S. Pan, H.-C. Huang, and L. C. Jain (Eds.), Intelligent Watermarking Techniques, World Scientific Publishing Company, Singapore, Chapter 4, pp. 97-132, 2004.
[12]S. Zheng, G. Zhang and Z. Zhou, “Ant Colony Optimization based on Pheromone Trail Centralization” IEEE, Proceedings of the 6th World Congress on Intelligent Control and Automation, Vol 3349-3352, June 21-23, 2006, Dalian, China.
[13]T. Stützle and H. H. Hoos, “The MAX-MIN Ant System and local search for the traveling salesman problem.”, In T. Back, Z. Michalewicz, and X. Yao, editor, Proceedings of the IEEE International Conference on Evolutionary Computation(ICEC’97), pages 309-314, IEEE Press, Piscataway,NJ , USA, 1997
[14]Fabricio Olivetti de Franca and Fernando J. Von Znben, “Max Min Ant System and Capacitcted p-Medians : Extension and Improved Solution”, Informatica 29(2005) pages 163-171 .
[15]T. Stützle and S. Linke, “Experiments with Variants of Ant Algorithms”, Mathware & Soft Computing 7,Vol 1-15, 2000
[16]H. Kawamur , M.Yamamoto, K.Suzuki, A.Ohuchi, “Multiple Ant Colonies Algorithm Based on Colony Level Interactions ”, IECE TRANS. FUNDAMENTALS, VOL. E83-A, NO.2 FEBURARY 2000 .
[17]J. Sun, S.W. Xiong, F. M. Guo, “A NEW PHEROMONE UPDATING STRATEGY IN ANT COLONY OPTIMIZATION”, Proceedings of the Third International Conference on Material Learning and Cybernetics, Shanghai, 26-29 August 2004 .
[18]R.Meziane, Y. Massim, A. Zeblah, A. Ghoraf, R. Rahli, “Reliability optimization using ant colony algorithm under performance ant cost constraints”, Electric Power System Research 76(2005) 1-8 .
[19]P.S.Shelokar, V.K.Jayaraman,B.D.Kulkarni, “An ant colony classifier system: application to some process engineering problems”, Computers and Chemical Engineering 28(2004) 1577-1584
[20]D.Merkle, M. Middendorf , H. Schmeck, “Pheromone Evaluation in ant Colony Optimization”, Institute for Applied Computer Science and Formal Description Methods(AIFB) .
[21]B. Li , X. Song, “Improved Ant Colony Algorithm with Pheromone Mutation and its Application in Flow-shop Problems” , Proceeding of the 6th World Congress on Intelligent Control and Automation , June 21-23,2006,Dalian,China .
[22]H. Fredricson, “Structural topology optimization: an application review”, Int. J . Vehicle Design, Vol. 37, No. 1, 2005.
[23]B J G Kidd , Topology Optimization Used To Achieve Frequency Targets Of An Engine Beacket , Altair Engineering Ltd , 2000
[24]S. Kota, J. Hetrick, Z. Li, and L. Saggere , “ Tailoring Unconventional Actuators Using Compliant Transmissions : Design Methods and Applications ”IEEE/ASME TRANSACTION ON MECHATRONICS, VOL. 4, NO. 4, DECEMBER 1999 .
[25]F. Ratnieks , Outsmarted by ants , Nature , Vol.436, 2006
[26]M. J. Jakiela, C. Chapman, J. Duda, A. Adewuya, K. Saitou, ”Continue structure topology design with genetic algorithms”, Comput. Methods Appl. Mesh. Engrg. 186(2000) 339 – 356
[27]陳精一 , “ANSYS 電腦輔助工程分析”, 全華科技圖書, 2003
[28]曾科颖,”多值域與多目標結構拓樸最佳化-遺傳演算法之應用”,碩士論文,機械工程研究所,大同大學,2003.
[29]古志強,”應用分散式類免疫演算法於多值域結構拓樸最佳化”,碩士論文,機械工程研究所,大同大學,2004.
[30]林耀乾,” 應用拓樸最佳化於撓性為夾具設計” ,碩士論文,機械工程研究所,大同大學,2006.