近年來有許多的超啟發式演算法被不同學者所提出來解決分群問題，以及尋找分群問題中的近似解。為了了解量子啟發式演算法在分群問題上的表現能力，以及改善分群結果，本篇研究提出了一個改良式的量子啟發式演算法（iQEA）。在更新量子位元時，改良式量子啟發式演算法使用一個會隨著演算法演化代數改變的角度來影響量子閘，並旋轉所有的量子位元。實驗結果顯示，在與其它超啟發式演算法比較之下，改良式量子啟發式演算法在分群問題上能夠有更好的分群表現以及分群品質。

Many metaheuristic algorithms have been presented to find an approximate solution for the data clustering problem in recent years. To understand the capability of quantum-based algorithm in solving the clustering problem and to improve the quality of the clustering results, an improved quantum-inspired evolutionary algorithm (iQEA) is presented in this thesis. Unlike the original QEA that fixes the rotation degree of Q-gate, the rotation degree of iQEA is changed at different iterations. The experimental results show that the iQEA is able to find a better result than the original QEA and all the other metaheuristic algorithms compared in this thesis in terms of the quality of the clustering results.

論文審定書 i
誌謝 iii
摘要 v
Abstract vi
List of Figures x
List of Tables xii
Chapter 1
Introduction 1
1.1 Motivation 3
1.2 Contributions 4
1.3 Organization 4
Chapter 2
Related Works 6
2.1 Clustering Problem and k-means 6
2.1.1 Clustering Problem 6
2.1.2 The k-means Algorithm 9
2.2 Metaheuristic Algorithms 10
2.2.1 The Genetic Algorithm 11
2.2.2 The Particle Swarm Optimization 13
2.3 Quantum-Inspired Evolutionary Algorithm 14
2.3.1 Background 15
2.3.2 Details of Quantum-Inspired Evolutionary Algorithm 16
2.4 Summary 22
Chapter 3 Improved Quantum-Inspired Evolutionary Algorithm for Clustering Problems 24
3.1 The Basic Idea 24
3.1.1 Encoding 24
3.1.2 Rotation Degree 26
3.1.3 iQEA Hierarchy 27
3.2 Algorithm 29
3.2.1 Initialization 29
3.2.2 Observation 29
3.2.3 Repair 29
3.2.4 LocalSearch 30
3.2.5 Evaluation 32
3.2.6 Update 32
3.2.7 Selection 33
3.2.8 Migration 33
3.2.9 Catastrophe 34
3.2.10 OutputResults 34
3.3 Summary 35
3.4 Example 35
3.4.1 Initialization 36
3.4.2 Observation, Repair, LocalSearch and Evaluation 37
3.4.3 Update and Selection 39
3.4.4 Migration and Catastrophe 40
3.4.5 OutputResults 41
Chapter 4 Experimental Results 42
4.1 Environment, Datasets and Parameters Setting 42
4.1.1 Environment 42
4.1.2 Datasets 42
4.1.3 Parameters Setting 43
4.2 Simulation Results 45
4.2.1 Analysis 45
4.2.1.1 Rotation Degree 46
4.2.1.2 Population Size 47
Chapter 5 Conclusions and Future Works 52
Bibliography 53

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