臺灣博碩士論文加值系統

粒子群最佳化法是近期興起的一種仿生演算法，它仿照鳥類群體行為去求解最佳化問題，本研究應用在連續結構拓樸問題上。首先描述粒子群最佳化法和二進位粒子群最佳化法的概要，再詳細介紹二進位粒子群最佳化法要如何演算結構拓樸。隨後，介紹本研究所提出的兩種粒子群最佳化法，改善式粒子群最佳化法和邏輯式粒子最佳化法的概念，去說明如何演算結構拓樸問題。使用四個結構拓樸的標準範例去找尋結構拓樸的多樣性，驗證所提出的演算法是有效性的。由結果可以觀察出本研究所提出的粒子群最佳化法是能有效處理拓樸問題，它能夠找出多樣性的結構拓樸。

The particle swarm optimization (PSO) algorithm, a relatively recent bio-inspired approach to solve combinatorial optimization problems mimicking the social behavior of birds flocking, is applied to problems of continuum structural topology design. An overview of the PSO and binary PSO algorithms are first described. A discretized topology design representation and the method for mapping binary particle into this representation are then detailed. Subsequently, modified binary PSO algorithm and logic binary PSO algorithm adopt the concept of genotype-phenotype representation are illustrated. Several well-studied examples from structural topology optimization problems of minimum weight and minimum compliance are used to demonstrate its efficiency and versatility. The results indicate the effectiveness of the proposed algorithm and its ability to find families of structural topologies.

ABSTRACT I
中文摘要 II
致謝 III
目錄 IV
圖目錄 VI
表目錄 VIII

第一章 緒論 1
1.1介紹 1
1.2研究動機與目的 4
1.3論文大綱 6

第二章 粒子群最佳化法 7
2.1粒子群最佳化發展的背景 7
2.2粒子群最佳化法 9
2.3二進位粒子群最佳化法 12
2.4改善式二進位粒子群演算法 15
2.5機率式二進位粒子群演算法 16
2.6邏輯式二進位粒子群演算法 17

第三章 粒子群最佳化設計連續結構拓樸 19
3.1結構拓樸最佳化設計 19
3.1.1連續結構拓樸編碼 19
3.1.2連續性定義 20
3.1.3連續性的修正 20
3.1.4適應值計算 22
3.1.5多群體記憶 24
3.2改善式粒子群演算結構拓樸最佳化 25
3.3邏輯式粒子群演算結構拓樸最佳化 28

第四章 模擬分析與結果討論 31
4.1結構拓樸範例 31
4.2改善式粒子群連續結構拓樸最佳設計結果 33
4.3邏輯式粒子群連續結構拓樸最佳設計結果 39
4.4結果和討論 44

第五章 結論與未來展望 45
5.1結論 45
5.2未來的研究方向與建議 45

參考文獻 47

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