臺灣博碩士論文加值系統

摘 要
本文研究實數型進化演算法和倒傳遞類神經網路之結合，建立實數型進化演算法-倒傳遞類神經網路架構，應用於船舶設計資料之初步預估。
首先對單純形法、遺傳演算法和實數型進化演算法做探討比較，並對實數型進化演算法之參數分析，測試結果顯示族群數為20以上、更新數為70%對實數型進化演算法搜尋效率較好。再者，把實數型進化演算法測試於高維數香蕉函數問題(100~200維)，並與其他方法比較討論。
接著，針對三種類神經網路探討：1)倒傳遞類神經網路；2)實數型進化演算法-類神經網路；3)實數型進化演算法-倒傳遞類神經網路。首先以測試例對此三種類神經網路架構做比較，結果顯示以3)實數型進化演算法-倒傳遞類神經網路之訓練誤差和測試誤差為最小。
最後，應用實數型進化演算法-倒傳遞類神經網路，來做船舶設計資料之初步預估。將所建立的預估模型經測試顯示相當成功，可提供船舶初步設計一個相當省便又經濟的預估模型。
關鍵字：單純形法、遺傳演算法、實數型進化演算法、類神經網路、倒傳遞類神經網路、船舶初步設計資料。

Abstract
Combining the real-coded evolutionary algorithm with back- propagation networks for the preliminary prediction of ship design is proposed in this thesis. There are three parts in this thesis are examined and discussed.
First part, comparing with performance of global search among Nelder- Mead’s simplex method, binary coded genetic algorithms and real- coded evolutionary algorithms through some multi-modal problems. Their results show that for the searching performance the real-coded evolutionary algorithm is the best method among them.The influences of the parameter in the real-coded evolutionary algorithm on the performance are also studied and discussed. From the studied results, the faster convergent speed and better performance could be easily achieved by using the parameters in the real-coded evolutionary algorithm such as population over 20 and replacing rate about 70% of the population. And then applying the real-code evolutionary algorithm to examine the high-dimensional barnana function, dimensions 100 ~ 200, and compares the test results with those by means of some different methods.
The second part in the thesis, three artificial neural networks such as back-propagation network, real-code evolutionary algorithm-network, and hybridized real-coded evolutionary and back-propagation neural network, are examined through nonlinear functions. Comparison of the training performances of neural network shows that the hybridized real- coded evolutionary and back-propagation neural network is the best method among them.
Finally, the hybridized real-coded evolutionary and back- propagation neural network approaches is applied to the preliminary prediction for ship design. In this thesis, 29 container ship’s basic design data are collected. The hybridized neural network approach mentioned is used neural network learning and to obtain the better efficiency that the training error for these neural network model is acceptable. Using some different testing data for the learned neural network model, the predicted data approaches to ideal data or actual data closely. In other words, the established neural network model in the thesis for the preliminary prediction for ship design could be successful.
Keyword: Nelder-Mead’s simplex method, Genetic Algorithms, Real-coded Evolutionary Algorithm, Artificial Neural network, Back-Propagation Network, Preliminary Prediction for Ship Design

目 錄
摘要………………………………………………………………………..I
Abstract………………………………………………………………….II
目錄……………………………………………………………………….III
圖目錄…………………………………………………………………….VI
表目錄………………………………………………………………………IX
第一章 緒論………………………………………………………………1
1.1 研究動機與目的……………………………………………….1
1.2 搜尋演算法……………………………………………………….1
1.3 類神經網路……………………………………………………….3
1.4 研究方向與論文大綱…………………………………………….4
第二章 全域性搜尋演算法…………………………………………..….6
2.1 遺傳演算法………………….……………………….…………..….6
2.1.1 位元編碼與解碼方式…………….…..…………………..….6
2.1.2 遺傳演算法之基本運算子……………….…………………….7
2.1.3 遺傳演算法之流程……………………………………….……10
2.1.4 遺傳演算法之流程圖……………………………………….…11
2.2 單純形法…………………………………………………………………12
2.2.1 單純形法之搜尋機制………………..……………………...13
2.2.2 單純形法之流程……….………..………………………………...15
2.2.3 單純形法之流程圖……….………..……………………………...17
2.3實數型進化演算法………..…………….…………………………...18
2.3.1 實數型進化演算法之基本運算子………………….………...18
2.3.2 實數型進化演算法之流程…………………………………....19
2.3.3 實數型進化演算法之流程圖………………………….……...20
第三章 實數型進化演算法之搜尋特性………………………………..21
3.1實數型進化演算法之特性………………………………………21
3.1.1初始族群之隨機探討…….……….…………….…...21
3.1.2 族群數………………………………………………....25
3.1.3 更新數………………………………………………....33
3.1.4 利用視覺化找出特性…………………………………...40
3.2 與遺傳演算法之比較……………………………………..…...45
3.3 與單純形法之比較………………………………………..…...49
第四章實數型進化演算法應用於高維問題………………………………..54
4.1 挑戰高維問題之瓶頸………..………………………….…...54
4.2 局部改善策略…………………………………………………….54
4.21 隨機產生……………………………………………..…..57
4.22 方向性產生………………………………………….…...57
4.3 與改善前之比較……….………………………………….….…57
第五章 類神經網路………..…………………………………..…….…..61
5.1 類神經網路………………………………………………......61
5.1.1類神經網路原理……….………….…………………...62
5.1.2 類神經網路模型………………………………………...67
5.2 倒傳遞類神經網路……………………………………………..69
5.3實數型進化演算法(REA)於類神經網路之訓練……..………...73
5.3.1 網路架構………..………………………………………………...73
5.3.2 REA-NN處理流程………..…………………………..…….…….74
5.4 實數型進化演算法(REA)於倒傳遞類神經網路之訓練……...76
5.4.1網路架構………..……………………………….……...76
5.4.2 REA-BP…………………………………………………...77
5.5 三種類神經網路之比較……………………..……………...79
5.5.1 資料的擷取………………….………………….…...79
5.5.2 資料範例之處理…………………………….……...81
5.5.3 結果………………………..…………....….……...83
第六章 應用於船舶初步設計之預估……………………………………...86
6.1 構想…………………….……………………………………...86
6.2 船舶設計之初步預估流程…………………………….……...86
6.3 類神經網路於船舶設計基本資料處理………..……………...87
6.4 預估模型之建立….………………….…….………………..93
6.5 預估測試….………………….……….………………………..94
6.6 訓練範例數目多寡之影響….………………………….……..96
6.7 不同訓練範例之誤差探討….…………………………….……100
第七章 結論及未來展望……….…………………………………………112
7.1 結論….…………………………….……………………………112
7.2 未來展望….…………………………….………………………113
參考文獻………..………………………………….…………………….114
圖目錄
圖2.1遺傳演算法之流程圖………………………………………………….11
圖2.2單純形法示意圖………………………………..……………..…..13
圖2.3單純形法之流程圖…………………………………………………..17
圖2.4實數型進化演算法之流程圖…………………………………..……20
圖3.A f2(x)族群數……………………………………………..…………32
圖3.B f3(x)族群數…………………………………………………..……32
圖3.C f2(x)更新數……………………………………………..…………39
圖3.D f3(x)更新數…………………………………………..…………39
圖3.1 f1(x) 二維多極值函數 (Branin RCOS)…………………….…….22
圖3.2第Ⅰ種情形，初始族群點分佈●、最後族群點分佈▲與最佳解■。…..23
圖3.3第Ⅱ種情形，初始族群點分佈●、最後族群點分佈▲與最佳解■。…..23
圖3.4第Ⅲ種情形，初始族群點分佈●、最後族群點分佈▲與最佳解■。…..23
圖3.5第Ⅳ種情形初始族群點分佈●、最後族群點分佈▲與最佳解■。……...23
圖3.6第一角隅，初始族群點分佈●、最後族群點分佈▲與最佳解■。…..….24
圖3.7第二角隅，初始族群點分佈●、最後族群點分佈▲與最佳解■。……...24
圖3.8第三角隅，初始族群點分佈●、最後族群點分佈▲與最佳解■。……...24
圖3.9第四角隅，初始族群點分佈●、最後族群點分佈▲與最佳解■。……...24
圖3.10f2(x)一維多極值函數…………………………………..…….…26
圖3.11 f3(x)二維多極值函數………………………………………..…26
圖3.12族群數目=5，X=5.832742，f2(x)= -3.366327……….……..…27
圖3.13族群數目=10，X= -0.4369638，f2(x)= -3.372897………….…27
圖3.14族群數目=15，X= -13.00306，f2(x)= -3.372897………….….28
圖3.15族群數目=20，X= -13.003032，f2(x)= -3.372896………….…28
圖3.16族群數目=25，X= -0.4369085，f2(x)= -3.372898…………….28
圖3.17族群數目=30，X= -0.4369082，f2(x)= -3.372898………….…28
圖3.18族群數目=35，X= -0.4369103，f2(x)= -3.372898…………….29
圖3.19族群數目=50，X= 5.421505，f2(x)= -3.372897……………….29
圖3.20族群數目=5，f3(x)= -3.753128…………………………………29
圖3.21族群數目=10，f3(x)= -3.765869……..…………………………30
圖3.22族群數目=15，f3(x)= -3.782829…..…………………..……..30
圖3.23族群數目=20，f3(x)= -3.776457……………………………..…30
圖3.24族群數目=25，f3(x)= -3.775952…………………..……………30
圖3.25族群數目=30，f3(x)= -3.760258…………………..……..…..31
圖3.26族群數目=35， f3(x)= -3.783714………………….……….…..31
圖3.27族群數目=50， f3(x)= -3.783669……………….………..….31
圖3.28 更新數為20%，X=-0.4366631，f2(x)= -3.372897……………33
圖3.29 更新數為30%，X=-0.436885，f2(x)= -3.372898………………33
圖3.30 更新數為40%，X=5.846474，f2(x)= -3.372897……..…………34
圖3.31 更新數為50%，X=-0.4369082，f2(x)= -3.372898.…..……,..34
圖3.32 更新數為60%，X=12.12934，f2(x)= -3.372897………………34
圖3.33 更新數為70%，X=-0.4367532，f2(x)= -3.372898………………35
圖3.34更新數為80%，X=-0.4368472，f2(x)= -3.372898………………35
圖3.35 更新數為90%，X=-0.4369794，f2(x)= -3.372897….. ………35
圖3.36更新數為20%，X1= -3.792454，X2= -3.311016，f3(x)= -3.758288,,,,,,6
圖3.37 更新數為30%，X1= 2.97333，X2= 2.018428，f3(x)= 2.995423…………..36
圖3.38 更新數為40%，X1= 2.983797，X2= 2.013445，f3(x)= 2.992197………....36
圖3.39更新數為50%，X1= -3.77151，X2= -3.267184，f3(x)= -3.760258…………37
圖3.40 更新數為60%，X1= -3.793158，X2= -3.28279，f3(x)= -3.781812………...37
圖3.41 更新數為70%，X1= -3.791316，X2= -3.283575，f3(x)= -3.783036………37
圖3.42 更新數為80%，X1= -3.783069，X2= -3.284333，f3(x)= -3.78231…….….38
圖3.43 更新數為90%，X1=-2.823297，X2=3.131748，f3(x)= -2.8125………..….38
圖3.44族群遷移進化圖(族群數目7個)………………,,,,,………………42
圖3.45族群遷移進化圖(族群數30個)………………………….………….43
圖3.46：族群數目=40，收斂次數(NF)與函數值(FX)…………………..46
圖3.47：族群數目=20，收斂次數(NF)與函數值(FX)……………………46
圖3.48：族群數目=10，收斂次數(NF)與函數值(FX)………………..…47
圖3.49：族群數目=5，收斂次數(NF)與函數值(FX)…………….…..…47
圖3.50：族群數目=40，收斂次數(NF)與函數值(FX)…………………….47
圖3.51：族群數目=20，收斂次數(NF)與函數值(FX)……. ……………47
圖3.52：族群數目=10，收斂次數(NF)與函數值(FX)………………..….48
圖3.53：族群數目=5，收斂次數(NF)與函數值(FX)…………………..…48
圖3.54 X1X2方向……………………..……………..………….….…51
圖4.1 f4(x) Rosenbrock 香蕉函數……………………………………..55
圖4.2 Hybrid Model = REA-GRID………….……………………….…56
圖5.1: 生物神經元結構………………………..……..………….…….63
圖5.2: 人工神經元架構………………………..……..…….…....….63
圖5.3: 感知機網路架構………………………..………...……….…67
圖5.4: 倒傳遞網路架構……………………………………………...….70
圖5.5 f5(x) 二維單極值函數………………..………………….…….80
圖5.6 f6(x) 二維單極值函數………………..………………...…..80
圖5.7 類神經網路輸入、輸出資料…………………..……..………….81
表目錄
表3.1單純形與實數型進化演算法比較表…………..……………………51
表3.1a 單純形法之搜尋結果………………………………………..…….50
表3.1b 實數型進化演算法I之搜尋結果……..…..………………..…..51
表3.1c 實數型進化演算法II之搜尋結果…..……..……………….……51
表4.1a 各種演算法之比較。MEAN：收斂之計算次數；SD：標準差；SUCC：搜尋成功次數；BF：搜尋之最好之函數值。…………………...58
表4.1b 各種演算法之比較。MEAN：收斂之計算次數；SD：標準差；SUCC：搜尋成功次數；BF：搜尋之最好之函數值。……………..….59
表5.1 f5(x)訓練、測試誤差……...……..………………....………85
表5.2 f6(x) 訓練、測試誤差……..……..…..……..…………………85
表6.1貨櫃船輸入資料…………....………..…………..……….89
表6.2 貨櫃船輸出資料…..……..…….………………………...………90
表6.3 尺度化貨櫃船輸入資料…………..…..…..…..……..………..91
表6.4尺度化貨櫃船輸入資料…..…………………..……..……..……92
表6.5 五組輸出之訓練誤差…..……..……..…………………..………94
表6.6 預估船舶資料……..……..………………….,,,,,,,,,,,,,,,,,95
表6.7 預估輸出資料與誤差…..……..……..……..……………………95
表6.8 五組REA-BP學習訓練之均方根誤差(I)…..……..……..……..96
表6.9 貨櫃船輸入資料(粗斜體為插入之隨機20筆).………..…………97
表6.10貨櫃船輸出資料(粗斜體為插入之隨機20筆)…………..…………98
表6.11 預估輸出資料與誤差……………..…..…..……..……..……99
表6.13 Lpp之誤差(29筆資料)…..…….....……..……..………..101
表6.14 Bm之誤差(29筆資料)…..……..…….……..……..………..102
表6.15 d之誤差(29筆資料)…..……..……….…..……..………..103
表6.16 BHP之誤差(29筆資料.……..……….…..……..……….,,,104
表6.17 FOC之誤差(29筆資料)…..……..………..……..………..105
表6.18 Lpp之誤差(49筆資料)…..……..……....……..……..…..106
表6.19 Bm之誤差(49筆資料)…..……..……....……..……..…..107
表6.20 d之誤差(49筆資料)…..……..……..……..…….…..…..108
表6.21 BHP之誤差(49筆資料)…..…...……..……..…..…..…..109
表6.22 FOC之誤差(49筆資料)…..………...……..……..………..110
表6.23 平均值與標準偏差……....……..……..……..……..……111

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