質群演算法(PSO)於多組解方程最佳化問題之研究

Modified Particle Swarm Optimization for Solving the Global Optimization of Continuous Multimodal Functions

邱怡瑛(Yi-Yin Chiu)

指導教授 ： 范書愷

元智大學/工程學院/工業工程與管理學系/碩士(2004年)

摘要

質群演算法（PSO）發展至今，許多由原始型改善而得之變化型亦有學者陸續發表。PSO的整體概念既簡單易懂，又能夠以較快速又較節省成本的方式獲得結果，便成為研究的初步動機；再加上原始型PSO於多組解最佳化問題的求解效率與收斂速度不佳，更促使本論文針對多組解最佳化問題展開研究，並且提出一適用於求解大型多組解最佳化問題的PSO方法。
在研究初期，使用實驗設計（DOE）的技術用以探討PSO的主要參數對整體演算法效果與效率之影響，由實驗設計的全因子分析所得之參數效果圖表與數據結果，提出一改善方案，稱為DW-PSO（Decreasing Weight Particle Swarm Optimization）。演算法的成功率和運算次數作為衡量指標，實驗結果顯示DW-PSO能夠解決多組解方程最佳化問題，除此之外，更進一步地將各式多組解最佳化方程同樣地套用於DW-PSO與其他學者所提出的PSO方法，由其比較結果可知，DW-PSO對大型多組解最佳化問題的求解表現與其他PSO方法相較之下，成功尋找總體最佳解之效果尤其顯著。

關鍵字

質群演算法 (PSO) ； 多組解最佳化 ； 實驗設計 (DOE)

並列摘要

The development of the Particle Swarm Optimization (PSO) has been almost ten years since 1995. From that time on, a variety of modifications of the original PSO has been proposed by many PSO researchers. The evolutionary concept of PSO, simple in concept, easy to implement and computational efficient, is partly the motivation of this thesis. The performance of the original PSO on the solution quality and convergence speed becomes much aggravated while optimizing multimodal functions with higher dimension. This is the main objective of this research such that we would like to develop a modified PSO suitable for solving large-scale multimodal optimization problems.
In this study, design of experiments (DOE) has been conducted to investigate the influences of each parameter in PSO. Based the computation results in the DOE stage, a modified PSO, termed Decreasing Weight Particle Swarm Optimization (DW-PSO), has been addressed. The success rate and number of function evaluation are considered performance measures. The experimental results show that the DW-PSO shows great promise in solving multimodal functions. The computational comparisons with PSO variants further reveal that DW-PSO has significant advantages, especially when it is performed to solve high dimension problems.

並列關鍵字

Particle Swarm Optimization (PSO) ； Multimodal Function ； Design of Experiments (DOE)

參考文獻

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