在不了解資料的情況下要事先決定分群數對於資料分群問題而言是一件困難的研究議題。一個有效率的多目標演化式分群演算法被提出來克服上述的問題並且提供了更好的分群結果。我們所提出的演算法已經不同於傳統的演化式演算法只使用一個交配運算和一個突變運算，而是使用超過一個的交配運算和突變運算，而這些運算被各自放入交配候選池和突變候選池中，在每次突變及交配運算時以供隨機挑選用來增加每代搜尋的多樣性。最後利用多個著名的資料集來估算本文所提出的演算法效能，實驗結果顯示此演算法不僅能夠自動決定分群的數量，並且相較我們在此所比較的分群演算法能夠提供較好的分群結果。

Automatically determining the number of clusters without a priori knowledge is a difficult research issue for data clustering problem. An effective multiobjective evolutionary algorithm based clustering algorithm is proposed to not only overcome this problem but also provide a better clustering result in this study. The proposed algorithm differs from the traditional evolutionary algorithm in the sense that instead of a single crossover operator and a single mutation operator, the proposed algorithm uses a pool of crossover operators and a pool of mutation operators that are selected at random to increase the search diversity. To evaluate the performance of the proposed algorithm, several well-known datasets are used. The simulation results show that not only can the proposed algorithm automatically determine the number of clusters, but it can also provide a better clustering result.

論文審定書i
誌謝iii
摘要iv
Abstract v
List of Figures viii
List of Tables ix
Chapter 1 簡介1
1.1 動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 論文貢獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 論文架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Chapter 2 文獻探討5
2.1 分群問題. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 多目標最佳化問題. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.1 支配(domination)觀念. . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.2 柏拉圖最佳化(pareto optimality) . . . . . . . . . . . . . . . . . . . . 9
2.3 多目標最佳化演算法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.1 NSGA-II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.2 PESA-II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 多目標分群演算法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4.1 MOCK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.2 VRJGGA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.3 VAMOSA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5 總結. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Chapter 3 新的自動決定群數多目標演化式分群演算法17
3.1 多個資訊交換的多目標分群演算法. . . . . . . . . . . . . . . . . . . . . . 17
3.1.1 染色體表示方式. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.1.2 初始化. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.3 目標函式. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.4 多種資訊交換突變運算. . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1.5 多種資訊交換交配運算. . . . . . . . . . . . . . . . . . . . . . . . . 24
3.1.6 最後解挑選方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Chapter 4 實驗結果28
4.1 環境，參數設定，資料集合. . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.2 實驗結果. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.2.1 分群品質. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.2.2 正確分群次數. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Chapter 5 結論與未來展望34
Bibliography 35

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