蟻群演算法系統已成功地應用於求解優化問題上。尤其是，蟻群演算法被証實是有效率的找到近似最佳解於離散解空間的問題上。但如果所面臨到的問題是存在於連續型解空間之上，它就不是那麼適合的使用原來蟻群演算法來解決它。本論文因此提出了兩種擴充蟻群演算法來求解於連續變量的問題。第一個蟻群演算法基於二元編碼用以提供一個標準化的流程來解決連續型空間上的問題。它首先將連續型解空間對應到一個二元編碼的解空間(一個蟻群搜尋圖)，再利用這個搜尋圖來搜尋出可行解。不同於之前用以解決連續型空間的螞蟻演算法，提出的二元編碼蟻群演算法可以保留傳統蟻群演算法所有的運算，使得其特點和優點得以保留。另外，這個演算法是很容易實作和應用在數學相關的問題和其它不同的問題之上。本論文提出另一個演算法為動態路徑蟻群演算法，相較於二元編碼蟻群演算法，它可以動態地生成位於兩個節點之間的邊，並通過費洛蒙分佈函數來得到費洛蒙的濃度。此外，利用費洛蒙分佈函數映射傳統蟻群演算法的編碼和運算子是非常容易的。由於這個演算法所定義的編碼空間是真實對應連續解空間的，所以它可以確保全域最佳解被定義於編碼空間之內。
此論文將所提出的動態路徑蟻群演算法應用於模糊數據挖掘上。數據挖掘主要的目的是要從大型的數據資料庫中找尋有意思且有價值的知識和資訊。最後，本文提出一個Hadoop的框架用以來減少動態蟻群演算法的運算時間。
最後實驗結果証明，所提出的方法顯示了在連續型解空間之上求解數學式問題和模糊數據挖掘上皆有優秀的效能表現。

Ant colony systems (ACS) have been successfully applied to solve optimization problems. Especially, they are effective in finding nearly optimal solutions to discrete search spaces. When the solution spaces of the problems to be solved are continuous, it is not so appropriate to use the original ACS. This dissertation thus proposes two extended ACS algorithm for solving continuous variables problems. The first approach based on binary coding provides a standard process for solving problems with continuous variables. It first encodes the solution space for a continuous domain into a discrete binary coding space (searching map), and then a modified ACS is applied to find the solution. Different from the previous ant-based algorithms for continuous domain, the proposed binary coding ACS (BCACS) could retain the original operators and keep the benefits and characteristics of the traditional ACS. Besides, it is easy to implement, and could be applied in different kinds of problems in addition to mathematical problems. The other proposed algorithm is dynamic-edge ACS (DEACS). Different from BCACS, it can dynamically generate edges between two nodes and give a pheromone measure through distribution functions. In addition, it maps the encoding representation and the operators of the original ACS into continuous spaces easily. The encoding of solution space in this algorithm is a real continuous space. Thus, the global best solution is assured to be in the solution space.
The proposed DEACS is also applied to fuzzy data mining for finding out interesting and meaningful linguistic patterns from large databases. Finally, this dissertation presented a Hadoop framework for DEACS in order to reduce the computation time. Experimental results on mathematical functions and fuzzy data miming show the good performance of the proposed approaches in the continuous solution space.

目錄
中文審定書 ............................................................................................................... i
英文審定書 .............................................................................................................. ii
誌謝 ......................................................................................................................... iv
中文摘要 .................................................................................................................. v
ABSTRACT ............................................................................................................ vi
Chapter 1 INTRODUCTION ........................................................................... 1
1.1. Background and Motivation ......................................................................... 1
1.2. Contributions .................................................................................................... 5
1.3. Thesis Organization ........................................................................................ 5
Chapter 2 REVIEW OF RELATED WORKS ................................................. 7
2.1. Review of Ant Colony Systems ................................................................... 7
2.1.1. Ant Algorithm ............................................................................................... 7
2.1.2. Ant Colony System ..................................................................................... 8
2.1.3. Existing Ant-related Algorithms for Continuous
Solution Spaces ......................................................................................... 11
2.2. Review of Fuzzy Data Mining .................................................................. 14
2.3. Review of Map-Reduce .............................................................................. 16
Chapter 3 GENERALIZED BINAEY -CODING ACS ALGORITHM ......... 19
3.1. Encoding and Searching Map for BCACS ............................................ 19
3.2. Proposed BCACS Algorithm .................................................................... 22
ix
3.3. An Example for BCACS ............................................................................ 24
Chapter 4 DYNAMIC EDGE ACS ALGORITHM ....................................... 27
4.1. Pheromone Distribution Functions .......................................................... 27
4.2. Global Updating Rule in DEACS ............................................................ 29
4.3. Local Updating Rule in DEACS .............................................................. 35
4.4. Generating Dynamic Edges ....................................................................... 38
4.5. Dependency between Variables ................................................................ 40
4.6. Proposed DEACS Algorithm .................................................................... 42
4.7. An Example for DEACS ............................................................................ 45
Chapter 5 APPLICATION AND EXTENSION OF DEACS ........................ 47
5.1. Proposed Map-Reduce Framework for DEACS ................................. 47
5.2. Fuzzy Data Miming Based on DEACS .................................................. 51
5.3. Proposed DEACS Algorithm for Miming Membership
Function ......................................................................................................... 52
5.4. An Example for DEACS Algorithm for Miming
Membership Function ................................................................................ 55
Chapter 6 EXPERIMENTAL RESULTS ....................................................... 59
6.1. Experimental Results for Mathematical Functions in
BCACS ........................................................................................................... 59
6.2. Experimental Results for Mathematical Functions in
DEACS ........................................................................................................... 64
x
6.3. Experimental Results for Map-Reduce Framework ........................... 72
6.4. Experimental Results for Fuzzy Data Mining ...................................... 73
Chapter 7 CONCLUSION AND FUTURE WORK ...................................... 77
REFERENCE ......................................................................................................... 81

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