本論文提出一種新的方法來改善螞蟻群聚最佳化(ant colony optimization, ACO)，稱為
雙重費洛蒙表格的螞蟻群聚最佳化演算法(ant colony optimization with dual pheromone
tables, ACODPT)，主要作法是在ACO中加入『負面』的費洛蒙表格，以避免演算法過
易落入區域最佳解(local optima)。演算法透過負面的費洛蒙表格刪除在搜尋新的結果的
過程中最不可能的路徑，藉此提昇剩餘路徑被選擇的機率以及解答的品質。為了能夠
表達此演算法的效能，ACODPT將在分群問題(clustering problem)上與一些最先進的演
算法做比較，實驗結果顯示此方法能防止ACO在前期的計算中落入區域最佳解，因此
能夠在多數情況下提供較好的結果。

This thesis presents a novel algorithm called ant colony optimization with dual pheromone tables
(ACODPT) for improving the quality of ant colony optimization (ACO). The proposed
algorithm works by adding a so-called “negative” pheromone table to ACO to avoid the problem
of ACO easily falling into local optima. By using the “negative” pheromone table to
eliminate the most impossible path to search for the new solution, the probability of selecting
the remaining paths is increased, and so is the quality. To evaluate the performance of the proposed
algorithm, ACODPT is compared with several state-of-the-art algorithms in solving the
clustering problem. The experimental results show that the proposed algorithm can eventually
prevent ACO from falling into local optima in the early iterations, thus providing a better result
than the other algorithms in many cases.

論文審定書i
Acknowledgments iii
摘要iv
ABSTRACT v
List of Figures viii
List of Tables x
Chapter 1 Introductions 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Contributions of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Organization of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Chapter 2 Related Works 3
2.1 Clustering Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Clustering Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.1 k-means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.2 Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.3 Genetic k-means Algorithm . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.4 Ant-based Clustering Algorithm . . . . . . . . . . . . . . . . . . . . . 9
2.2.5 Ant Colony Optimization . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.5.1 Ant System . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.5.2 Ant Colony System . . . . . . . . . . . . . . . . . . . . . . 13
2.2.5.3 ACO-based Algorithm for Clustering . . . . . . . . . . . . . 14
2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Chapter 3 The Proposed Algorithm 16
3.1 The Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 The Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3 Ant Colony Optimization with Dual Pheromone Tables . . . . . . . . . . . . . 18
3.3.1 The Negative Pheromone . . . . . . . . . . . . . . . . . . . . . . . . . 21
Chapter 4 Experimental Results 23
4.1 Datasets and Parameter Settings . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2.1 Iris . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.2.2 Wine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.2.3 Abalone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.2.4 Yeast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Chapter 5 Conclusion and Future Works 29
5.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.2 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Bibliography 30

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