本研究提出整體最佳解引導的多樣性控制差分演算法(whole best leaded diversity control differential evolution algorithm, WBDDE)來解決差分演算法(differential evolution, DE)在使用上會遇到參數設定、演化停滯、收斂速度過慢等三項問題。WBDDE包含三項機制：整體最佳解(whole best, WB)引導演化、適應性調整廣度多樣性(extent diversity, ED)、控制個體均勻度多樣性(uniform diversity, UD)。
WB比全域最佳解(global best, GB)可以更快得到族群內部的情況，提供更多演化資訊與加快收斂速度。適應性調整ED可以提高個體ED值，也有助於探索突變策略演化出較佳的解。控制UD的機制創造出不同於傳統突變策略的收斂曲線、UD曲線。不但減少演化停滯，也加快收斂速度。
WBDDE與其他DE變化型比較結果可發現WBDDE在合成函數的表現較佳。除解決參數設定，加快收斂速度，減少演化停滯外，WBDDE還有增加DE個體演化資訊、兩面向量測多樣性、驗證單目標最佳化問題演化結果也會受到多樣性的影響以及主動控制多樣性等學術貢獻與特色。
WBDDE是設計用來解決最佳化問題，因此WBDDE可以使用於最佳化問題的應用，例如：排程、系統鑑定等等。

This study proposes the whole best leaded diversity control differential evolution algorithm (WBDDE) to solve three problems when using differential evolution algorithm (DE): parameters setting, evolutionary stagnation, and slow convergent speed when solving optimization problems. WBDDE contains three mechanisms: whole best (WB) leaded evolution, adaptively turning extent diversity (ED) and controlling uniform diversity (UD).
WB gets the evolutionary situations fast, offers more evolutionary information, and increases convergent speed than global best (GB). This adaptive tuning mechanism of ED increases ED and helps with finding superior solutions for exploration mutation strategies. The mechanism of controlling UD creates different paths of convergence curves and UD curves from conventional mutation strategies. This mechanism mitigates the evolutionary stagnation and speeds up the convergence.
Comparing WBDDE with other DE variants, WBDDE has superior performances for composition functions. In addition to increasing convergent speed, mitigating evolutionary stagnation and setting parameters, WBDDE also has other contributions and features: increasing the evolutionary information, measuring diversity in two ways, indicating the performance also being affected by the diversity of individuals for single objective optimization problems.
WBDDE is designed to solve optimization problems so that user can apply WBDDE to any optimization problems, such as scheduling, identified systems, and so forth.

摘要 i
ABSTRACT iii
致謝 v
Contents vii
List of Figures xi
List of Tables xv
List of Abbreviation xix
List of Symbols xxi
Chapter 1 Introduction 1
1-1 Overview 1
1-2 Terminologies in This Dissertation 3
1-3 Motivation 4
1-3-1 Three Common Evolutionary Problems in DE 5
1-3-2 The Relationship between Individual Diversity and Evolution 7
1-4 Contributions and Features 8
1-5 Organization of this dissertation 10
Chapter 2 Background Knowledge 13
2-1 Differential Evolution Algorithm 13
2-1-1 Classical DE Algorithm 14
2-1-2 Exploitative and Explorative Mutation Strategies 16
2-1-3 Explorative, Exploitative Mutation Strategies, and Diversity 19
2-2 Fuzzy Inference System 19
2-3 Evaluated Functions in This Study 22
2-4 Summary 25
Chapter 3 Whole Best Leaded Mutation 27
3-1 Increasing the Mutant Information 27
3-2 The Whole Best Leaded Mutation in DE 29
3-2-1 Center of Solutions, Best Center of Solutions and Whole Best 29
3-2-2 Modified Mutation Strategies and Flow of WB Leaded DE 31
3-3 Experiments 35
3-3-1 Experimental Settings 35
3-3-2 Experimental Results 36
3-3-3 Discussion 39
3-4 Summary 41
Chapter 4 Adaptive Tuning Extent Diversity 73
4-1 Crossover Rate and Extent Diversity 73
4-2 Adaptive Tuning Mechanism of Extent Diversity 75
4-2-1 Evaluation of Adaptive Tuning Extent Diversity 75
4-2-2 Fuzzy Inference System Design 75
4-2-3 The Flow of DE with adaptive tuning mechanism of ED 79
4-3 Experiments 81
4-3-1 Experimental Settings 81
4-3-2 Experimental Results 82
4-3-3 Discussion 86
4-4 Summary 87
Chapter 5 Control Individual Uniform Diversity 119
5-1 Uniform Diversity and Its Measurements 119
5-2 Control Mechanism of Uniform Diversity 122
5-2-1 Proposed Mutation Strategy 122
5-2-2 Fuzzy Inference System Design 124
5-2-3 The Flow of DE with Uniform Diversity Control 126
5-3 Experiments 128
5-3-1 Experimental Settings 128
5-3-2 Experimental Results and Discussion of Different Uniform Diversity Goals 131
5-3-3 Experimental Results and Discussion of Different Mutation Strategies 135
5-4 Summary 138
Chapter 6 Whole Best Leaded Diversity Control Differential Evolution Algorithm 173
6-1 Differential Evolution Variants 173
6-2 Whole Best Leaded Diversity Control Differential Evolution Algorithm 178
6-3 Experiments 180
6-3-1 Experimental Settings 180
6-3-2 Experimental Results and Discussion of Different Uniform Diversity Goals 180
6-3-3 Experimental Results and Discussion of Different DE variants 185
6-4 Summary 188
Chapter 7 Conclusions and Future Works 215
7-1 Conclusions 215
7-2 Future Works 217
References 219
Vita 225

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