分群問題是一個經典問題，其研究價值在於許多工程或科學甚至醫學及經濟學等，都存在這類問題，且常被使用來作為初步分析的解決方案。在解決分群問題時許多的演算法容易受到初始解或陷入區域最佳解等問題，使搜尋的最佳解品質不穩定。因此，本研究我們提出了一個以搜尋經驗為基礎的演算法架構稱為「潛力預測演算法」，其主要的概念是透過以往的搜尋資訊進行分析及推測，預測較有機會搜尋出較佳解的位置，並結合k-means 演算法作為區域搜尋的機制，以提昇分群演算法的搜尋品質。為了驗證潛力預測演算法的搜尋效能，本研究將利用潛力預測演算法與其他啟發式演算法演算法進行模擬實驗及比較分析，再更進一步的對於潛力預測演算法的參數分別進行測試實驗並整理分析結果。模擬實驗結果說明，潛力預測演算法能提昇分群結果的品質，並使搜尋品質更佳的穩定。

Clustering is a classical problem that has been a valuable research topic because it exists in many fields, such as engineering, computer science, medical science, and economics, and it has been widely used as the initial stage in solving these problems. Many algorithms for clustering are likely to fall into local optima easily or are extremely sensitive to the initial solution of the clustering problem, thus making the quality of the end result quite unstable. Therefore, we proposed a search-experience-based algorithm, called potential forecast algorithm (PFA). The underlying idea of the proposed algorithm is to use not only the past searched information to forecast the potential positions which may end up with better solutions, it also uses k-means as a local search mechanism to improve the quality of the end result. To evaluate the performance of PFA, we compare it with other state-of-the-art algorithms. We also test and analyze the influence of all the parameters. The simulation results indicate that PFA can provide not only a better solution but also a more stable quality of the end result.

論文審定書 i
誌謝 iii
摘要 iv
Abstract v
List of Figures ix
List of Tables x
Chapter 1 簡介 1
1.1 動機 3
1.2 論文貢獻 4
1.3 論文架構 4
Chapter 2 相關文獻探討 5
2.1 分群問題 5
2.1.1 資料分群 5
2.1.2 分割式分群法 6
2.2 演化式演算法及分群算法 7
2.2.1 k-means Algorithm 7
2.2.2 Genetic k-Means Algorithm 9
2.2.3 Particle Swarm Optimization 11
2.2.4 Firefly Algorithm and k-means 12
2.2.5 Black Hole Algorithm 13
2.3 結論 14
Chapter 3 潛力預測演算法 16
3.1 演算法的設計概念 16
3.2 演算法架構及流程 17
3.3 潛力預測演算法解分群問題 26
3.4 潛力預測演算法時間複雜度分析 31
3.5 結論 33
Chapter 4 實驗結果 34
4.1 實驗環境及參數設定 34
4.2 模擬實驗及分析 35
4.3 參數分析 38
4.3.1 收斂實驗分析 38
4.3.1.1 儲存集合大小分析 39
4.3.1.2 分組數量分析 41
4.3.1.3 k-means疊代次數分析 44
4.3.2 非收斂實驗分析 46
4.3.2.1 儲存集合大小分析 48
4.3.2.2 分組數量分析 48
4.3.2.3 k-means疊代次數分析 50
4.4 總結 53
Chapter 5 結論與未來展望 57
5.1 結論 57
5.2 未來展望 58
Bibliography 59
Chapter A 潛力預測演算法完整虛擬碼 64
Chapter B 演算法模擬實驗結果分析說明 66
B.1 Abalone 66
B.2 Balance Scale 67
B.3 Ecoli 68
B.4 Haberman’s Survival 70
B.5 Iris 72
B.6 Letter Recognition 72
B.7 Liver Disorders 74
B.8 SPECT Heart 76
B.9 SPECTF Heart 77
B.10 Wine 78
B.11 Yeast 80
B.12 Statlog (Shuttle) 80

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