以時變學習因子策略改良粒子群演算法

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蔡憲文(Hsien-wen Tsai) 查詢紙本館藏

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電機工程學系

論文名稱

以時變學習因子策略改良粒子群演算法
(Improvement of Acceleration Coefficients on Particle Swarm Optimization Algorithm)

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摘要(中)

本文為了改善粒子群演算法工作性能且解決不易選取合適的學習因子,提出了一個以自適應模糊粒子群演算法[5]為基礎的改良式演算法稱之為TV-PSO。大多粒子群演算法選擇學習因子方式是以疊代的方式來決定c1、c2值。即在初期希望有較高的探索能力,使得粒子能分佈於解空間當中,而不是往區域最佳解方向找尋,而後期有較高的收斂能力,讓粒子進可能收斂於最佳解中。但是這樣的方式會造成有一種強迫收斂的行為產生, 容易導致粒子收斂於區域最佳解,我們在此將一種新概念導入粒子群演算法內,粒子根據前一代最佳解和目前此代最佳解來選擇目前所需c值,每一次疊代中粒子根據最佳解找尋狀況決定是否該繼續探索新區域或者轉入局部搜尋加速收斂,可避免落入區域最佳解。最後我們將提出的新方法分別測試14種經典不同複雜之函數評估此演算法效率,並與傳統粒子群演算法、自適應模糊粒子群演算法和近幾年熱門的方式PSO-TVAC、TA- PSO做比較,最後結果顯示TV-PSO在搜尋能力和性能表現皆優於其他演算法,證明此演算法是可行的。

摘要(英)

In order to improve the performance of Particle Swarm Optimization (PSO) algorithm and to overcome the difficulty of selecting the appropriate acceleration coefficients, this thesis proposes an improved algorithm based on adaptive-fuzzy PSO algorithm [5], TIME-VARYING Particle Swarm Optimization, called TV-PSO. First, an adaptive-fuzzy PSO is adapted to generate the curves of the acceleration coefficients versus the differences between the consecutive values of two consecutive fitness functions. Then, each curve is simplified to three line segments to present the time-varying acceleration coefficients.
Finally, 14 classic functions with different complexities are utilized to test our proposed algorithm. As compared with the traditional PSO algorithm, Adaptive-fuzzy PSO Algorithm, PSO-TVAC and TA-PSO, it is found that the proposed time-varying coefficients are easy to be applied in the PSO algorithm and a better performance is obtained.

關鍵字(中)

★ 粒子群演算法
★ 自適應
★ Fuzzy
★ 學習因子

關鍵字(英)

★ Particle Swarm Optimization
★ acceleration coefficients
★ adaptation
★ Fuzzy

論文目次

摘要……………………………………………………………………………………………………………………………………….i
Abstract…………………………………………………………………………………………ii
Acknowledgement………………………………………………………………………………………………………………iii
Symbol table…………………………………………………………………………………………………………………iv
Table of Content……………………………………………………………………………..vi
List of Figures………………………………………………………………………………viii
List of Tables…………………………………………………………………………………x
Chapter 1 Introduction………………………………………………………………………1
1.1 Motivation…………………………………………………………………..……….1
1.2 Objectives…………………………………………………………………………4
1.3 Framework of the study……………………………………………………………5
Chapter 2 PSO and adaptive fuzzy PSO algorithms…………………………………………6
2.1 Mathematical model for optimization………………………………………………6
2.2 Particle Swarm Optimization………………………………………………………7
2.2.1 Basic model for PSO………………………………………………………7
2.2.2 Flowchart and Basic Code for PSO………………………………………9
2.2.3 PSO work flowchart…………………………………………………………12
2.2.4 Inertia weight for constants…………………………………………………13
2.2.5 Liner inertia reduction………………………………………………………13
2.2.6 Limitation of maximum velocity…………………………………………14
2.2.7 Constriction factor…………………………………………………………15
2.3 Adaptive Fuzzy Particle Swarm Optimization (AF-PSO)………………………….16
Chapter 3 TV-PSO……………………………………………………………………………19
vii
3.1 Introduction…………………………………………………….…………………19
3.2 Essential design principle and procedure of TV-PSO……………………………22
3.3 Ci(dfn) for TV-PSO……………………………………………………………….26
3.3.1 Ci(dfn) testing results for 10-D……………………………….……………28
3.3.2 Ci(dfn) testing results for 30-D……………………………………………35
3.3.3 Operation flow and basic code for TV-PSO…………………………………46
3.3.4 TV-PSO flowchart………………………………………………………49
Chapter 4 Experimental results………………………………………………………………50
4.1 Test procedure and methods………………………………………………………50
4.2 Testing Results for 10-D…………………………………………………………..52
4.3 Testing Results for 30-D………………………………………………………….57
Chapter 5 Conclusions and future perspectives……………………………………………….63
5.1 Conclusions…………………………………………………………………………63
5.2 Future perspectives…………………………………………………………………64
Reference……………………………………………………………………………………66

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指導教授

莊堯棠(Yau-tarng Juang)

審核日期

2010-7-26

推文