過去幾十年很多基於生物啟發的演算法被提出,這些以群體為基礎的演算法 之適應學習能力已經被證實可以有效地解決許多最佳化問題。在這些演算法中, 粒子群演算法是一個很流行且常用的策略,因為它具有易於實作等優點。早期的 粒子群演算法通常只使用單一群去執行運算,然而隨著粒子群演算法的發展,採 用多個子群來求解問題的方式也被提出來,並常用於如平行處理,多極值最佳化, 多目標最佳化等問題上。在本篇論文中,我們首先回顧並探討當粒子群演算法使 用多子群執行時的一些有趣特性,並提出一個多子群演算法,調查當總粒子數固 定時,不同的子群數對效能產生的影響,而該演算法在本質上也很適合做平行處 理。接著我們提出一個可階層式執行的粒子群策略,經由分層的執行並在各層之 間加入一些運算來使得整體的效能變的更好。我們也探討該策略在不同的執行架 構下對於效能的影響。此外,我們提出一個粒子群演算法的動態遷徙策略,它可 以動態的決定遷徙發生的時機。我們並將動態的遷徙策略使用在階層式粒子群演 算法上,藉著額外使用遷徙,合併,重新初始化這些操作來增加粒子間演化的多 樣性以獲得更好的效能。最後我們經由一些實驗來驗證所提方法之效能。

In the past decades, many global optimization algorithms based on biologically-inspired strategies have been developed. Most of them are population-based algorithms and their abilities of adaptive learning have shown they can solve optimization problems effectively. Particle swarm optimization (PSO) is a very popular and common-used strategy among them since it is easily implemented. In the early days, PSO was usually performed on a single swarm. Along with the development of variant PSO technologies, multiple-swarm schemes were also adopted for some purposes such as parallel processing, multimodal optimization and multi-objective optimization. In the thesis, we first revisit and discuss some interesting characteristics of PSO for multiple sub-swarm processing. We then propose a multi-sub-swarm algorithm, in which the original particle swarm is divided into several sub-swarms with the same total size, to investigate the variation of performance with different sub-swarm numbers. The algorithm is very suitable to be parallelized in nature. We then propose a hierarchical PSO strategy called HPSO, which executes the PSO algorithm in hierarchical levels and uses some operations to increase the performance. Different execution structures of HPSO are discussed as well. Furthermore, we propose a dynamic migration mechanism for PSO, which can automatically determine when to migrate a portion of particles from one sub-swarm to its neighbor. Finally, we apply the dynamic migration mechanism on the HPSO to check the effects of combination. By additionally using some operations such as migration, merge and re-initialization, the particles can increase diversity effectively and thus obtain good results. Experiments are also made to show the performance of the proposed approaches.

論文審定書 ....................................................................................................................... i
致謝 .................................................................................................................................. ii
摘要 ................................................................................................................................. iii Abstract............................................................................................................................ iv
Contents ............................................................................................................................ v
List of Figures................................................................................................................. vii
List of Tables ................................................................................................................... ix
CHAPTER 1 Introduction ............................................................................................. 1
1.1 Motivation ........................................................................................................ 1
1.2 Contributions.................................................................................................... 2
1.3 Organization of Thesis ..................................................................................... 4
CHAPTER 2 Related Works ......................................................................................... 5
2.1 Particle Swarm Optimization ........................................................................... 5
2.2 Sub-Swarm of PSO ........................................................................................ 10
2.3 Hierarchical Structure .................................................................................... 12
2.4 Migration strategy .......................................................................................... 14
CHAPTER 3 Balance of Local Search and Diversity in Sub-swarms of PSO............ 17
3.1 Introduction .................................................................................................... 17
3.2 The proposed Multi-Sub-Swarm Algorithm .................................................. 18
3.3 An Example of Multi-Sub-Swarm Algorithm ............................................... 23
3.4 Parallel Implementation of Proposed Multi-Sub-Swarm Algorithm ............. 28
CHAPTER 4 Particle Swarm Optimization with Hierarchical Execution .................. 30
4.1 Introduction .................................................................................................... 30
4.2 The Proposed PSO with Hierarchical Execution Algorithm ......................... 31
4.3 An example of PSO with Hierarchical Execution Algorithm........................ 36
CHAPTER 5 Particle Swarm Optimization with migration strategy .......................... 42
5.1 Introduction.................................................................................................... 42
5.2 The Proposed Dynamic Migration Strategy................................................... 42 v
5.3 Applied Dynamic Migration Strategy in HPSO ............................................ 47
5.4 An example of HE-DMPSO Algorithm......................................................... 49
CHAPTER 6 Experimental Evaluation ....................................................................... 54
6.1 Introduction .................................................................................................... 54
6.2 Experimental Benchmarks ............................................................................. 54
6.3 Parameter Settings.......................................................................................... 57
6.4 Experimental Results of multi-sub-swarm..................................................... 57
6.5 Experimental Results of HPSO ...................................................................... 62
6.6 Experimental Results of DMPSO .................................................................. 63
6.7 Comparison .................................................................................................... 65
CHAPTER 7 Conclusion and Future Work ................................................................ 68 References ...................................................................................................................... 69

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