混合型人工蜂群演算法之發展與應用

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呂宜倫(Yi-lun Lu) 查詢紙本館藏

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土木工程學系

論文名稱

混合型人工蜂群演算法之發展與應用

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摘要(中)

本文主要是針對連續變數、離散變數、混合變數之最佳化設計問題，提出以人工蜂群演算法(Artificial Bee Colony Algorithm, ABC)為基礎，結合Nelder-Mead單純形法(Nelder and Mead Simplex Method, NM)以及擾動機制(Perturbation, PT)的三種混合啟發式搜尋法，並分別稱為ABC-NM、ABC-PT以及ABC-NM-PT。ABC為一種全域的隨機搜尋法，藉由模擬蜜蜂覓食的過程，依靠個體之間的資訊交換進行平行式的搜索，進而找到問題的最佳解，然而ABC和其他高階啟發式搜尋法類似，在求解最佳化問題時存在著局部搜索能力差，接近最佳解時搜索效率下降，以及求解高度非線性問題時可能陷入局部最佳而使演化停滯等缺失。為了改善此缺失，本文採用NM演算法來取代ABC偵察蜂的階段的隨機產生個體機制，期望藉由NM優異的局部搜尋能力，改善ABC局部搜索能力較差之缺失並提高搜索效能。而考慮到NM反覆搜尋的機制可能導致搜尋時間增加，因此本研究另外引入PT擾動機制取代NM，希望達到降低適應值計算次數。最後，本文亦參考GCM的作法，以垃圾桶模型整合ABC、NM及PT，各取其優點來提升求解能力。在本文中，藉由不同類型的設計例，包含數學式及結構設計的問題，探討本文方法之優劣。比較算例之結果發現ABC-NM、ABC-PT與ABC-NM-PT在求解連續變數及離散變數之最佳化問題時都較ABC穩定，求解品質也較佳。

摘要(英)

This article is devoted to the presentation of hybrid heuristic searching algorithms, namely ABC-NM, ABC-PT and ABC-NM-PT, for the optimum design with discrete, continuous and mixed variables. ABC (Artificial Bee Colony Algorithm) is a random search method that mimics the process of food foraging of honeybees. Honeybees pick the honey by each other and share the message of food sources, and then they find the best food source. However, ABC is similar to other meta-heuristic algorithms that have a poor search in local. When it becomes the best solution or is applied to complex problems, it will fall into local optimum and the algorithm stops. To overcome the drawback of the method, this report proposes the hybrid heuristic algorithm called ABC-NM which combined ABC and NM (Nelder-Mead Simplex Method) to raise the searching efficiency. The repeatedly search by NM may cost a lot of time, so this research replaces NM by PT (Perturbation) and when an aim to reduce the time of fitness calculating. At last, this research combines ABC, NM and PT by GCM (Garbage Can Model), namely ABC-NM-PT, for combining their advantages in order to enhance the searching ability. The design examples including mathematical problems and structure design demonstrate the effectiveness of the hybrid heuristic searching algorithms. The results show the ABC-NM-PT algorithm is reliable, and the solution quality in the literature is comparable to other optimal methods.

關鍵字(中)

★ 人工蜂群演算法
★ Nelder-Mead單純形法
★ 擾動機制
★ 混合型啟發式搜尋法

關鍵字(英)

★ Artificial bee colony algorithm
★ Nelder-Mead simplex method
★ Perturbation
★ Hybrid heuristic search algorithm

論文目次

中文目錄 I
英文目錄 III
目錄 V
表目錄 X
圖目錄 XIII
第一章緒論 1
1.1 研究動機與目的 1
1.2 文獻回顧 5
1.2.1 結構最佳化設計方法 5
1.2.2 遺傳演算法(Genetic Algorithm, GA) 6
1.2.3 粒子群演算法(Particle Swarm Optimization, PSO) 7
1.2.4 差分演化法(Differential Evolution, DE) 8
1.2.5 和聲搜尋法(Harmony Search Method, HS) 9
1.2.6 人工蜂群演算法(Artificial Bee Colony Algorithm, ABC) 10
1.3 研究方法與內容 12
第二章 ABC演算法、NM演算法及PT擾動機制 14
2.1 最佳化問題之數學模式 14
2.2 限制函數的處理和適應函數 15
2.3 人工蜂群演算法(ABC) 16
2.3.1 ABC基本模式 16
2.3.2 ABC之演算程序 18
2.4 NELDER-MEAD 單純形法 20
2.4.1 引言 20
2.4.2 Nelder-Mead單純形法之演算程序 22
2.5 PERTURBATION擾動機制(PT) 24
第三章混合搜尋法 27
3.1 引言 27
3.2 ABC-NM混合式搜尋法 27
3.3 ABC-PT混合式搜尋法 30
3.4 ABC-NM-PT混合式搜尋法 33
第四章數值計算例 38
4.1 分析流程 38
4.2 數學式的算例 39
4.2.1 Constrained Function I 41
4.2.2 Constrained Function II 42
4.2.3 Constrained Function III 45
4.2.4 Constrained Function IV 47
4.2.5 Pressure Vessel Design 49
4.3 結構設計問題 52
4.3.1 10桿平面桁架 54
4.3.2 25桿空間桁架 59
4.3.3 36桿空間桁架 64
4.3.4 72桿空間桁架 69
4.3.5 132桿空間桁架 75
4.3.6 160桿空間桁架 81
4.3.7 單跨雙層平面構架 88
4.3.8 雙跨五層平面構架 94
4.3.9 單跨八層平面構架 99
4.4 小結 105
第五章結論與建議 111
5.1 結論與建議 111
5.2 未來研究方向 112
參考文獻 114
附錄A　10桿平面桁架細部資料及設計結果 124
A.1　細部設計資料 124
A.2　設計結果 124
附錄B　25桿空間桁架細部資料及設計結果 126
B.1　細部設計資料 126
B.2　設計結果 127
附錄C　36桿空間桁架細部資料及設計結果 128
C.1　細部設計資料 128
C.2　設計結果 129
附錄D　72桿空間桁架細部資料及設計結果 131
D.1　細部設計資料 131
D.2　設計結果 132
附錄E　132桿穹頂桁架細部資料及設計結果 135
E.1　細部設計資料 135
E.2　設計結果 136
附錄F　160桿空間桁架細部資料及設計結果 145
F.1　細部設計資料 145
附錄G　單跨雙層平面構架細部資料及設計結果 161
G.1　細部設計資料 161
G.2　設計結果 161
附錄H　雙跨五層平面構架細部資料及設計結果 163
H.1　細部設計資料 163
H.2　設計結果 164
附錄I　單跨八層平面構架細部資料及設計結果 167
I.1　細部設計資料 167
I.2　設計結果 173

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指導教授

莊德興(Der-shin Juang)

審核日期

2013-7-4

推文