臺灣博碩士論文加值系統

高維度與多極值最佳化問題會隨著維度之增加與解空間之擴大而使其問題之困難度較低維度問題時高得多。粒子群演算法雖然可以相當有效率的應用於各領域最佳化問題，但應用於高維度與多極值問題時，常發生粒子群聚過快收斂於局部極值無法跳脫，以及在最佳值附近收斂過慢的缺點。本研究是針對三種改良型粒子群演算法，包括之分群式粒子群演算法(KPSO)、文化分群式粒子群演算法(CKPSO)與吸引排斥型粒子群演算法(ARPSO)等，應用於求解高維度基準測試函數，探討分群搜索與文化知識保存功能應用於提升粒子群演算法的效用。確認KPSO能否有效的增加粒子的探索能力；CPKSO能否有效加速收斂能力；ARPSO能否在收斂後加速調整粒子朝向聚集或是分散的方向移動進而得到最佳解。而由本研究實驗證明，改良型粒子群演算法應用於高維度與多極值基準測試例題，具備擴大搜索與加速收念的特性。

The difficulty to solve a high dimensional optimization problem will be much more than low dimensional problems due to the increasing of solution space. The Particle Swarm Optimization (PSO) has been applied extensively to various fields.. However, there are weaknesses in adopting PSO in high dimensional problems. For examples, PSO is easily trapped into local extreme resulting in low optimizing precision or failure, and even though in the surroundings of extreme solution, the rate of convergence need to be improved. This study is focused on the performance of swarm intelligence in modified particle swarm optimization for K-means PSO (KPSO), culture K-means PSO (CKPSO), attractive and repulsive PSO (ARPSO) in high dimensional problems. The comparisons of results of benchmark functions among the argorithms up to 100 dimensions valid that the modified PSO adopted in High dimensional and multi-extremum problems, and can ensure the rate of effective convergence.

摘　要 i
Abstract ii
目　錄 iii
表目錄 vi
圖目錄 viii
第一章 緒論 1
1-1 研究背景與動機 1
1-2 文獻回顧 3
1.2.1 PSO 粒子群最佳化演算法 3
1.2.2 分群式粒子群演算法 4
1.2.3 文化分群式粒子群演算法 4
1.2.4 吸引排斥型粒子群演算法 5
1-3 研究目的 5
1-4 論文架構與流程 6
第二章 研究方法 8
2-1 粒子群最佳化演算法 8
2.1.1 粒子群演算法基本原理 8
2.1.2 加入慣性權重 粒子群演算法 12
2.1.3 加入壓縮因子 粒子群演算法 12
2-2 分群式粒子群演算法 13
2-3 文化分群式粒子群演算法 16
2.3.1文化分群式粒子群演算法設計 17
2-4 吸引排斥型粒子群演算法 20
第三章 實驗設計及測試 23
3-1 測試函數 23
3.1.1 Spherical 24
3.1.2 Schwefel 25
3.1.3 Rosenbrock 25
3.1.4 Ackley 27
3.1.5 Griewank 28
3-2 改良型粒子群演算法驗証分析 30
3.2.1 分群式粒子群演算法計算結果 30
3.2.2文化分群式粒子群演算法計算結果 32
3.2.3 吸引排斥型粒子群演算法計算結果 33
第四章 高維度實證分析 36
4.1 高維度問題 36
4.2 分群式粒子群演算法於高維度實證分析 37
4.2.1 實驗結果 38
4.2.2 實驗分析 39
4.2.3 參數組配分析 39
4.3 文化分群式粒子群演算法於高維度實證分析 41
4.3.1實驗結果 41
4.3.2實驗分析 42
4.3.3 參數組配分析 43
4.4 吸引排斥型粒子群演算法於高維度實證分析 45
4.4.1 實驗結果 46
4.4.2實驗分析 47
4.5 綜合分析與比較 48
4.5.1在Spherical函數中適應值比較 48
4.5.2在Schwefel函數中適應值比較 50
4.5.3在Rosenbrock函數中適應值比較 52
4.5.4在Ackley函數中適應值比較 54
4.5.5在Griewank函數中適應值比較 56
第五章 結論及未來展望 58
5.1 結論 58
5.2 未來展望 58
參考文獻 60

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