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研究生:洪紹博
研究生(外文):Sau-Bor Hon
論文名稱:觀察不同微粒群優化法參數的設定與優化問題的關係之研究
論文名稱(外文):The Study of Investigation of the Relationship between Parameters of Particle Swarm Optimization and Related Optimization Problems
指導教授:周鵬程周鵬程引用關係
指導教授(外文):Pen-Chen Chou
口試委員:周鵬程許崇宜陳盛基
口試委員(外文):Pen-Chen ChouChung-I HsuSeng-Chi Chen
口試日期:2012-07-11
學位類別:碩士
校院名稱:大葉大學
系所名稱:電機工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:46
中文關鍵詞:突變微粒群優化法遺傳演算法
外文關鍵詞:MutationParticle Swarm optimization(PSO)Genetic Algorithm(GA)
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微粒群優化法(Particle Swarm Optimization, PSO)是在1995年的時候由Kennedy和Eberhart兩位教授所提出,由於參數的設定簡單,可以對許多問題進行優化,至今已成為許多學者熱烈討論的議題。
遺傳演算法(Genetic Algorithm, GA),其中的突變機制對於改善一些条件比較多的難題,使其跳脫局部陷阱有所幫助,是故PSO常加入突變以增進PSO的効力。但是有些難題還是会跳脫出局部陷阱,吾人發現加入強制突變機制可改善此困難。為了加速收斂,ω與ω_p的配對正確正可達成目的。
本篇文章將用我們的PSO與其它的PSO對解決函數問題進行比較,經過各種模擬測試之後的結果,來證明我們的PSO對於解決Maurice Clerc教授所提出之Mini-project問題有十分出色的能力。Clerc教授提出Standard PSO-2007版及VPSO版並加以比較,本論文提出對不同的問題,使用不同的PSO語法解問題,並与前述两方法比較,結果有所改良。

關鍵字:突變,微粒群優化法,遺傳演算法

Particle Swarm Optimization, PSO, proposed by Professor J. Kennedy and R. Eberhart in 1995, is one the current and attractive optimization algorithms studied all over the whole world at the present time. Due to its simplicity, that is the parameters to be set in PSO algorithm is few, it is a really benefit for optimization searches as a main PSO algorithm.

Another algorithm such as genetic algorithm uses evolution operators--- selection, crossover and mutation. In which, mutation mechanism can provide a capability of the search of optimal solution vector jumping out of the local trap in principle, therefore this mechanism can be combined well to PSO algorithm. Besides that, we introduce another mechanism called one-variable mutation to improve the former mentioned capability. In order to enhance the convergence rate of optimization search, different ω-ω_p pair is suggested in the specific PSO for specific problem.

This paper’s study is based on the mini-project of Professor Maurice Clerc in which he suggested that if a modified PSO is good or not, compared it with this paper. In that paper, two different PSO algorithms are listed, that is standard PSO-2007 and VPSO. With four different functions, such as, Tripod, Shifted Rosenbrock function, Compression spring, and Gear train, we have suggested four different specific PSO algorithms respectively. Comparisons show that our results are better than those listed in the paper.
Key Words:Particle Swarm optimization(PSO),Genetic Algorithm(GA),Mutation

目錄

簽名頁
中文摘要......................iii
英文摘要......................iv
誌謝........................v
目錄........................vi
圖目錄.......................viii
表目錄.......................ix
緒論
1.1簡介.......................1
1.2論文探討.....................2
1.3研究動機與目的..................3
微粒群優化法理論
2.1 微粒群優化法理論................4
2.2 PSO運算步驟及演算法流程圖 ...........7
2.3 PSO應用的情況.................10
2.4 PSO的優點與缺點................11
第三章 改良式微粒群優化法
3.1基本的微粒群優化法...............14
3.2線性遞減權重粒子優化機制............14
3.2.1線性遞減權重粒子優化機制運算步驟 ...... 15
3.3自適應權重粒子優化機制.............16
3.3.1 自適應權重粒子優化機制的運算步驟.....17
3.4學習因子異步變化優化機制............18
3.4.1學習因子異步變化粒子優化機制的運算步驟...19
3.5突變改良機制..................20
3.5.1突變改良機制................21
3.6強制型突變機制.................21
3.7ω與ω_p變動機制.................23
第四章 範例函數介紹
4.1 函數難度介紹..................25
4.2 難度1 Tripod function.............25
4.3 難度2 Rosenbrock F6 function..........26
4.4 難度3 Compression spring function.......27
4.5 難度4 Gear Train function...........29
第五章 模擬測試與比較
5.1 Tripod 模擬結果.................30
5.2 Rosenbrock_F6 模擬結果.............32
5.3 Compression Spring 模擬結果 ..........34
5.4 Gear Train模擬結果...............38
第六章 結論
6.1 Tripod函數模擬設定結論.............42
6.2 Rosenbrock_F6函數模擬設定結論..........43
6.3 Compression Spring函數模擬設定結論........43
6.4 Gear Train函數模擬設定結論............44
6.5 總結......................45
參考文獻......................46

圖目錄

圖(2.1) PSO向量圖....................6
圖(2.2) PSO運算步驟及演算法流程圖............7
圖(3.1)線性遞減權重粒子優化機制的運算步驟圖......15
圖(3.2)自適應權重粒子優化機制的運算步驟圖.......17
圖(3.3)學習因子異步變化粒子優化機制的運算步驟圖....19
圖(3.4) Gear Train函數的適應值變動圖...........24
圖(4.1) Tripod 3D圖...................26

表目錄

表5.1難度(1)Tripod 函數改變參數結果...........31
表5.2難度(1)Tripod 進入第2段的疊代次數調整.......32
表5.3 難度(2) Rosenbrock_F6函數參數模擬結果.......33
表5.4難度(2) Rosenbrock_F6的Popusize為300、350、400增加次數統計.........................34
表5.5難度(3) Compression Spring 函數模擬參數結果.....36
表5.6難度(3) Compression Spring 針對Popusize為300跟400進行模擬結果........................37
表5.7難度(4) Gear Train ω與ω_p三段參數設定的模擬測試..39
表5.8難度(4) Gear Train ω與ω_p參數的設定........40
表5.9難度(4) Gear Train PopuSize模擬與比較........41
表6.1 結果與比較....................45

參考文獻

[1]Kennedy J. and Eberhart R.C. ,“Particle Swarm Optimization”, Proceedings of the IEEE international joint conference on neural networks, 1942-1948,(1995).
[2]Shi Y. and Eberhart R.C. ,“A Modified Particle Swarm Optimizer” , Proceedings of the IEEE International Conference on Evolutionary Computation, pp. 69-73,(1998).
[3]林奕辰 ,“微粒優化法的理論探討及演算法改良之研究”,大葉大學電機研究所, (2010).
[4]周鵬程、潘仕濠 ,“Principle of Ant Colony Optimization and Traveling Salesman Problem Application” 海峽兩岸四地無線電科技研討會, (2010).
[5]Shi Y. and Eberhart R.C. , “A Modified Particle Swarm Optimizer. IEEE International Conference on Evolutionary Programming”, Alaska, May 4-9, (1998).
[6]Shi Y. and Eberhart R.C. , “Empirical study of particle Swarm optimization” .Proceedings of the Evolutionary Computation 1999 Congress, Vol 3, pp.1945-1950, (2010).
[7]Maurice Clerc. ,“The swarm and the queen: towards a deterministic and adaptive particle swarm optimization”, Proc. CEC 1999, Washington, DC, pp. 1951-1957,(1999).
[8]龔純、王正林 ,精通Matlab最優化設計,電子工業出版社,北京(2009).
[9]董維倫 ,“對微粒優化法的主要參數應用於不同問題時,其效之研究” ,大葉大學電機研究所, (2010).
[10]周鵬程、周宇辰、董維倫 , “基因演算法的介紹” ,海峽兩岸三地無線電科技研討會,(2009).
[11]周鵬程 ,遺傳演算法原理與應用,修訂版,全華科技圖書股份有限公司(2001).
[12]PenChen Chou. and SauBor Hon. ,“Modified Particle Swarm Optimization for Sphere”,Rastrigin Schwefel and schaffer functions.IEEE.pp.1716-1719,(CSQRWC,2001,26-30 July).
[13]Maurice Clerc. ,“Particle Swarm Optimization”. ISTE (International Scienticand Technical Encyclopedia),(2006).
[14]Louis Gacôgne. ,“Steady state evolutionary algorithm with an operator family” .In EISCI, pages 373379, Kosice, Slovaquie, (2002).
[15]Godfrey C. Onwubolu and B. V. Babu. ,“New Optimization Techniques in En-gineering”. Springer, Berlin, Germany, (2004).
[16]E. Sandgren. ,“Non linear integer and discrete programming in mechanical design optimization”. ISSN 0305-2154, (1990).
[17]Yun-Wei Shang .and Yu-Huang Qiu. ,“A note on the extended rosenbrock function. Evolutionary Computation”,14(1) 119-126, (2006).
[18]Shi Y. and Eberhart R. C. ,“Parameter Selection in Particle Swarm Optimization” , V. W. Porto, N. Saravanan, D. Waagen, and A. E. Eiben (eds), Lecture Notes in Computer Science, 1447, Evolutionary Programming VII, Springer, Berlin, pp. 591-600 (1998).
[19]Shi Y. and Eberhart R.C. ,“Tracking and optimizing dynamic systems with particle swarms” , Proceedings of the 2001 Congress on Evolutionary Computation ,Vol. 1, pp 94-100,(2001).
[20]潘仕濠 ,“強制型突變改良粒子群演算法對高維度尋優問題的研究”,大葉大學電機研究所, (2011).
[21]Maurice Clerc. ,“A Mini-benchmark” ,clerc.maurice.free.fr/pso/
,(2010).

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