博碩士論文 90322009 詳細資訊




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姓名 張慰慈(Wei-Tze Chang)  查詢紙本館藏   畢業系所 土木工程學系
論文名稱 DLM-GA混合搜尋法於結構離散最佳化設計之應用
(A DLM-GA Hybrid Searching Algorithm for Discrete Sizing Optimization of Structures)
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摘要(中) 中文摘要
本文主要是針對含離散設計變數之結構最佳化設計問
題,提出一種結合離散拉格朗日法(DLM)和遺傳演算法(GA
)的混合式全域搜尋法。DLM為一種鄰點搜尋法,過去的研
究結果顯示此法在中、小型結構問題上的求解能力極佳,
惟處理多極值之大型問題時,雖然求解的品質不錯,但因
屬局部搜尋法,故若參數調整不當,則仍有落入較差局部
最佳解的缺憾。GA為一隨機搜尋法,具全域搜尋之能力,
但所使用之策略及可調整之參數甚多、處理大型結構相當
耗時、且缺乏強固數學理論所建立之收斂準則,故即使所
得之解為一局部最佳解,卻無從驗證。因此,本研究嘗試
利用GA全域搜尋的能力,配合DLM具備強固之數學收斂準
則,將此兩種演算法加以整合,以改善整體的搜尋效能。
研究中,首先針對大型結構提出一種合向量移動策略
,來加速DLM的求解效率,並提出一種淘汰策略和調整懲
罰參數的方法,藉以改善傳統GA求解的穩定性,最後再根
據結構最佳化設計問題的特性,提出一種連續次區域搜尋
觀念,同時修改DLM的鄰點搜尋方法,發展出GA-NB和DLM-
GA-NB兩種混合搜尋法。數個結構輕量化設計問題將分別
用來探討各種搜尋方法的適用性和影響各方法求解品質與
效率的相關參數,並藉由和文獻設計結果之比較來印證本
文所發展之搜尋方法的優缺點。結果顯示:(1) 合向量移
動策略可以大幅改善DLM求解大型結構問題的效能;(2)
連續次區域搜尋之GA-NB法較傳統GA具備更為強健且快速
的搜尋能力,非常適合求解中、小型結構系統的最佳化問
題;(3) DLM-GA-NB混合求解策略則可進一步改善DLM的求
解品質,非常適合求解中、大型結構系統之離散最佳化問
題。
摘要(英) Abstract
This report is devoted to the presentation of
two hybrid search algorithms, namely GA-NB and
DLM-GA-NB, for discrete sizing optimization of
structures. The structure is subject to stress and
displacement constraints under multiple load
cases. The DLM (discrete Lagrangian method) is an
adaptation of the usual Lagrange multiplier method
for continuous problems. Previous applications of
the method to structural optimization problems
using available sections have shown that it is
robust and validate for solving small- to medium-
scale structures. Although good quality solution
for large-scale structures can also be acquired
using the method, it strongly depends on the
weighting parameter selected by the user. On the
other hand, GA has the ability in performing
global search. However, the solution quality of
the method relies on many factors, such as selec-
tion, crossover and mutation schemes, probabili-
ties of crossover and mutation, and so on. It is
also computational expensive for solving large-
scale structures. To enhance the efficiency and
robustness of the search for optimal structural
design problems, an enhancing schemes for accele-
rating the search speed of the DLM and, the two
hybrid search algorithms are proposed. A novel se-
quential regional GA searching concept is also
developed and been implemented into the hybrid
search algorithms presented in this report. More
than ten typical structures studied in the litera-
ture are used to validate the effectiveness of the
algorithms. It is shown that the algorithms pro-
posed in the report are valid and robust in de-
signing structures of weight minimization problems
using available sections.
關鍵字(中) ★ 結構輕量化設計
★ 離散拉格朗日法
★ 遺傳演算法
★ 混合搜尋法
★ 離散變數
關鍵字(英) ★ genetic algorithm
★ hybrid search algorithms
★ discrete variables
★ discrete Lagrangian method
★ optimum structural design
論文目次 目錄
中文摘要 .......................................................... i
英文摘要 .......................................................... iii
目錄 .............................................................. v
表目錄 ............................................................ xiii
圖目錄 ............................................................ xix
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 分岔及限值法 ........................................... 5
1.2.2 模擬鍛鍊法 ............................................. 7
1.2.3 遺傳演算法 ............................................. 8
1.2.4 離散拉格朗日演算法 ..................................... 13
1.2.5 其他 ................................................... 15
1.3 研究方法與內容 ............................................. 16
第二章 DLM演算法 ................................................. 19
2.1 離散最佳化問題之數學模式 ................................... 19
2.2 DLM理論回顧 ................................................ 20
2.2.1 加權離散拉格朗日函數 ................................... 20
2.2.2 鄰點 ................................................... 21
2.2.3 離散梯度 ............................................... 23
2.2.4 離散鞍點 ............................................... 24
2.2.5 轉換函數 ............................................... 24
2.2.6 收斂準則與一階搜尋公式 ................................. 25
2.2.7 DLM搜尋程序 ............................................ 29
2.3 合向量移動策略 ............................................. 31
2.4 合向量移動策略之數學算例 ................................... 36
2.4.1 10桿平面桁架 ........................................... 36
2.4.2 25桿空間桁架 ........................................... 42
2.4.3 200桿平面桁架(I) ....................................... 49
2.5 討論 ....................................................... 53
第三章 遺傳演算法 ................................................ 55
3.1 引言 ....................................................... 55
3.2 GA的搜尋策略 ............................................... 56
3.2.1 族群 ................................................... 56
3.2.2 束制函數的處理和適應函數 ............................... 57
3.2.3 離散變數的處理 ......................................... 61
3.2.4 運算子 ................................................. 64
3.2.5 其他演化策略的運用運算子 ............................... 70
3.2.6 收斂準則 ............................................... 73
3.3 數值算例 ................................................... 73
3.3.1 10桿平面桁架 ........................................... 74
3.3.2 36桿空間桁架 ........................................... 76
3.3.3 22桿平面桁架 ........................................... 79
3.4 討論 ....................................................... 82
第四章 DLM-GA混合設計程序 ........................................ 83
4.1 引言 ....................................................... 83
4.2 次區域 ..................................................... 84
4.3 收斂準則 ................................................... 87
4.4 混合演算程序 ............................................... 87
4.4.1 GA-NB .................................................. 88
4.4.2 DLM-GA-NB .............................................. 89
第五章 數值算例及參數研究 …...................................... 93
5.1 結構離散最佳化問題之目標函數與束制條件 ..................... 93
5.2 測試流程介紹 ............................................... 95
5.3 GA NB參數研究 .............................................. 97
5.3.1 參數研究:族群及菁英之多寡 ............................. 97
5.3.2 參數研究:編碼方式 ..................................... 99
5.3.3 參數研究:動態懲罰函數之係數 .......................... 100
5.3.4 參數研究:汰除率Pe ..................................... 102
5.3.5 參數研究:選擇法 ....................................... 103
5.3.6 參數研究:交配法 ....................................... 104
5.3.7 參數研究:突變率一致性C ................................ 105
5.3.8 參數研究:突變率 ....................................... 105
5.3.9 參數研究:移民政策 ..................................... 106
5.3.10 參數研究:NB鄰點間距b ................................. 107
5.3.11 參數研究:NB合向量nCV ................................. 107
5.3.12 參數研究:NB鄰點間距b 配合合向量nCV ................... 108
5.4 GA-NB 設計結果 ............................................. 109
5.4.1 10桿平面桁架 ........................................... 109
5.4.2 25桿空間桁架 ........................................... 112
5.4.3 72桿空間桁架 ........................................... 115
5.4.4 36桿空間桁架 ........................................... 117
5.4.5 22桿平面桁架 ........................................... 120
5.4.6 132桿穹頂桁架 .......................................... 121
5.4.7 200桿平面桁架(II) ...................................... 127
5.4.8 101桿平面桁架 .......................................... 130
5.4.9 單跨雙層平面構架 ....................................... 134
5.4.10 雙跨五層平面構架 ...................................... 137
5.4.11 單跨八層平面構架 ...................................... 142
5.4.12 討論 .................................................. 146
5.5 DLM-GA-NB 設計結果 ......................................... 146
5.5.1 132桿穹頂桁架 .......................................... 147
5.5.2 200桿平面桁架(II) ...................................... 151
5.5.3 101桿平面桁架 .......................................... 156
第六章 結論與建議 ................................................ 161
6.1 結論 ....................................................... 161
6.2 未來研究方向 ............................................... 163
參考文獻 .......................................................... 165
附錄A 25桿平面桁架細部資料及設計結果 ............................. 177
A.1 細部設計資料 ............................................... 177
A.2 DLM設計結果 ................................................ 178
A.3 GA NB設計結果 .............................................. 179
附錄B 72桿平面桁架細部資料及設計結果 ............................. 181
B.1 細部設計資料 ............................................... 181
B.2 GA NB設計結果 .............................................. 183
附錄C 10桿平面桁架細部資料及設計結果 ............................. 185
C.1 細部設計資料 ............................................... 185
C.2 DLM-GA-NB設計結果 .......................................... 186
附錄D 36桿平面桁架細部資料及設計結果 ............................. 187
D.1 細部設計資料 ............................................... 187
D.2 GA設計結果 ................................................. 189
D.3 GA-NB設計結果 .............................................. 190
附錄E 22桿平面桁架細部資料及設計結果 ............................. 191
E.1 細部設計資料 ............................................... 191
E.2 GA設計結果 ................................................. 192
E.3 GA-NB設計結果 .............................................. 193
附錄F 132桿穹頂桁架細部資料及設計結果 ............................ 195
F.1 細部設計資料 ............................................... 195
F.2 GA-NB設計結果 .............................................. 199
F.3 DLM設計結果 ................................................ 204
F.4 DLM-GA-NB設計結果 .......................................... 209
附錄G 200桿平面桁架(II)細部資料及設計結果 ........................ 215
G.1 細部設計資料 ............................................... 215
G.2 GA-NB設計結果 .............................................. 218
G.3 DLM設計結果 ................................................ 224
G.4 DLM-GA-NB設計結果 .......................................... 230
附錄H 101桿平面桁架細部資料及設計結果 ............................ 237
H.1 細部設計資料 ............................................... 237
H.2 GA-NB設計結果 .............................................. 239
H.3 DLM設計結果 ................................................ 241
H.4 DLM-GA-NB設計結果 .......................................... 243
附錄I 200桿平面桁架(I)細部資料及設計結果 ......................... 245
I.1 細部設計資料 ............................................... 245
I.2 DLM設計結果 ................................................ 248
附錄J 單跨雙層平面構架細部資料及設計結果 ......................... 255
J.1 細部設計資料 ............................................... 255
J.2 GA-NB設計結果 .............................................. 256
附錄K 雙跨五層平面構架細部資料及設計結果 ......................... 257
K.1 細部設計資料 ............................................... 257
K.2 GA-NB設計結果 .............................................. 259
K.3 DLM設計結果 ................................................ 261
附錄L 單跨八層平面構架細部資料及設計結果 ......................... 263
L.1 細部設計資料 ............................................... 263
L.2 GA-NB設計結果 .............................................. 270
L.3 DLM設計結果 ................................................ 271
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指導教授 莊德興(Der-Shin Juang) 審核日期 2003-7-8
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