The study of forced mutations to overcome the difficulty of finding optimization problem solutions w
潘仕濠、周鵬程
E-mail: [email protected]
ABSTRACT
The proposal of Particle Swarm Optimization(PSO) by James Kennedy and Russell Eberhart has been succeeded in solving for many optimization problems. PSO algorithm is one of new soft computing methods with great attentions. It has the features of rapid convergence speed and fewer parameters to be set. In the past research, PSO algorithm modified by appending mutation mechanism (from Gentic Algorithm) can solve optimization problems with high index of difficulty and high dimensions. However, if the
dimensionality of problem variables is high enough, the searched results will be trapped in local optima most of the time. In this case, we have tried adding the second mechanism of forced mutation to the above mentioned modified algorithm. We have found that this new modification can actually solve problems with high difficulty index and high dimensions. As for the least difficulty index
problems , the advantage is apparently not shown in our simulation result. In this thesis, problems using modified
mutation-appending PSO algorithm and modified forced mutation algorithm are compared to prove that the later algorithm actually works well, when problems with high difficulty index and high dimension of variables are to be optimized.
Keywords : Particle Swarm Optimization、Genetic Algorithm、Mutation Table of Contents
封面內頁 簽名頁 中文摘要．．．．．．．．．．．．．．．．．．．．．．．．iii 英文摘要．．．．．．．．．．．．
．．．．．．．．．．．．iv 誌謝．．．．．．．．．．．．．．．．．．．．．．．．．．v 目錄．．．．．．．．．
．．．．．．．．．．．．．．．．．vi 圖目錄．．．．．．．．．．．．．．．．．．．．．．．．．ix 表目錄．．．
．．．．．．．．．．．．．．．．．．．．．．x 第一章 緒論 1.1 簡介．．．．．．．．．．．．．．．．．．．． 1 1.2 研究動機與目的．．．．．．．．．．．．．1 第二章 粒子群優化法理論 2.1 群體智慧．．．．．．．．．．．．．
．．．．．4 2.2 粒子群優化法(PSO)理論．．．．．．．．．．． 5 2.3 PSO運算步驟及演算法流程圖．．．．．．．．．
8 2.4 PSO應用的情況．．．．．．．．．．．．．．． 11 2.5 PSO的優點與缺點．．．．．．．．．．．．． 12 第三章 PSO改良法介紹 3.1 基本粒子群優化法．．．．．．．．．．．．．15 3.1.1 基本粒子群優化法的原理介紹．．．．．15 3.1.2 基本粒子群優化法的運算步驟．．．．．15 3.2 PSO演算法 的設限．．．．．．．．．．16 3.2.1 PSO演算法在 的設 限的原理介紹．．16 3.3 線性遞減權重粒子群優化法．．．．．．．．17 3.3.1線性遞減權重粒子群優化法的運算步驟 ． 19 3.4 收縮因子式粒子群優化法．．．．．．．．．19 3.4.1 收縮因子k的原理介紹．．．．．．．．20 3.4.2 收縮因子k的 算法步驟．．．．．．．．21 3.5 擇優． ．．．．．．．．．．．．．．．．．21 3.5.1 擇優的原理介紹．．．．．．．
．．．．22 3.5.2 擇優的算法步驟．．．．．．．．．．．22 3.6 突變改良法．．．．．．．．．．．．．．．23 3.6.1 突 變改良法原理介紹．．．．．．．．．23 3.6.2 加入了突變改良法規則．．．．．．．．24 第四章 範例分析 4.1 難度分 析．．．．．．．．．．．．．．．． 25 4.1.1難度1 Sphere及Rastrigin function ． 25 4.1.2難度2 Rosenbrock function．．．
．．． 29 4.1.3難度3 Schaffer function．．．．．．． 30 第五章 強制型突變改良式PSO方法提出 5.1 強制型突變改良法
．．．．．．．．．．．． 35 5.2 加入強制型突變的粒子群優化法(難度容易) ． 39 5.3 加入強制型突變的粒子群優化法(難 度中等) ．．40 5.4 加入強制型突變的粒子群優化法(難度困難)．．40 第六章 模擬測試及效益研究 6.1 模擬結果．．．．
．．．．．．．．．．．．42 6.2 曲線適配．．．．．．．．．．．．．．．．59 第七章 結論．．．．．．．．．．．
．．．．．．．．． 61 參考文獻．．．．．．．．．．．．．．．．．．．．．． 67 圖目錄 圖2.1 PSO向量示意圖．．
．．．．．．．．．．．．．． 7 圖2.2 粒子群優化法的流程圖．．．．．．．．．．．．． 9 圖 4.1 二維Sphere函數的所 有解分佈圖．．．．．．．．．． 26 圖4.2 Sphere的俯視圖．．．．．．．．．．．．．．． 27 圖 4.3 二維Rastrigin函數 的所有解分佈圖．．．．．．．．． 28 圖4.4 Rastrigin的俯視圖．．．．．．．．．．．．．． 28 圖 4.5 二維Rosenbrock 函數的所有解分佈圖 ．．．．．． ． 29 圖4.6 Rosenbrock的俯視圖．．．．．．．．．．．．．． 30 圖 4.7 二維Schaffer 函數的所有解分佈圖．．．．．．．．．33 圖4.8 Schaffer的俯視圖．．．．．．．．．．．．．． 33 圖5.1 Schaffer函數 中突變機制加入了強制型突變．．．．36 圖5.2 強制型突變PSO 的流程圖 ．．．．．．．．．．． 38 圖6.1 、 在10維 與20維設置模擬結果直條圖 ．． 51 圖6.2 randxx在10維與20維設置模擬結果直條圖 ．． 53 圖6.3 Schaffer函數模擬結果直 條圖．．．．．．．．． 55 圖6.4 Schaffer函數模擬成功疊代平均次數直條圖 ．．． 55 圖6.5 Schaffer函數在突變機制20維 關係圖．．．．．． 56 圖6.6 Schaffer函數在加入強制型突變20維關係圖．．． 57 圖6.7 Schaffer函數在加入強制型突變14
維關係圖．．． 58 圖6.8 近似模擬24、26、28維的成功疊代平均次數 ．．．60 表目錄 表6.1 初始化參數設定 ．．．．．
．．．．．．．．．．．．42 表6.2 難度(1)Sphere函數模擬結果之比較 ．．．．．．．．43 表6.3 難度(1)Rastrigin函數模擬 結果之比較 ．．．．．．．45 表6.4 難度(2)Rosenbrock函數模擬結果之比較 ．．．．．．46 表 6.5 ， 在10維中的模擬實驗 結果 ．．．．．．．．．．49 表 6.6 ， 在20維中的模擬實驗結果 ．．．．．．．．．．50 表 6.7 randxx在10維中的模擬 實驗結果 ．．．．．．．．． 52 表 6.8 randxx在20維中的模擬實驗結果 ．．．．．．．．． 52 表6.9 難度(3)Schaffer函數 模擬結果之比較 ．．．．．．． 54 表6.10 曲線適配近似模擬結果．．．．．．．．．．．．．．60 表7.1難度(1)Sphere函 數模擬結果之比較．．．．．．．．．62 表7.2難度(1)Rastrigin函數模擬結果之比較．．．．．．． 63 表7.3難
度(2)Rosenbrock函數模擬結果之比較．．．．．．．64 表7.4難度(3)Schaffer函數模擬結果之比較．．．．．．．．65 REFERENCES
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