粒子群演算法的多極值工程最佳化

Multimodal Engineering Optimization Using Particle Swarm Algorithm

陳孝楷(Shiau-Kai Chen)

指導教授 ： 史建中

淡江大學/工學院/機械與機電工程學系碩士班/碩士(2010年)

https://doi.org/10.6846/TKU.2010.00286

摘要

由群體生物的行為智慧啟發，本研究模仿鳥類群體的飛行及鳥 類搜尋食物的智慧為理論基礎，發展同步求解多個極值解的粒子群 最佳化演算模型。其中假設搜尋空間裡隱藏著多個不同類型的食 物，此等不同類型的食物可對應到不同等級的極值解，使得數群鳥 在空間中找尋全部食物的原理為經由鳥類本身的傳遞訊息方式，及 視每隻鳥為無質量的粒子，進而開發仿生多極值粒子群最佳化設計 方法及程序。本文又以群集策略區分與重整求解過程中的多個極值 點，以目標值分辨各極值的等級，使得區域極值得以保存。經由多 類型多極值問題的檢驗與分析，證實本文之多極值粒子群最佳化方 法是有效可行的。 在對限制條件的處理方面，本文提出漸進飛向可行區的策略。在 求解程序裡，當粒子飛入不可行區時，依據該粒子的違反量作不同 的速度更新，使得在不可行區的粒子，能逐漸的飛回可行區，同時 提升了在限制邊界上搜尋求解的機會。 以本文所發展的多極值粒子群最佳化程序結合限制條件處理策 略，應用於桁架拓樸設計與分析。桁架結構設計方法分為兩階段， 第一階段為取得各類型桁架排列設計，再經由第二階段結構尺寸同 步設計程序，最後可得多種設計結果。由二維與三維桁架結構題目 進行檢驗，將分析與檢驗結果與文獻比較，可得與文獻相同或更佳 的解，也證實本文的多極值方法於多極值工程問題的適用性。

關鍵字

多極值最佳化 ； 拓樸結構設計 ； 粒子群最佳化 ； 群體智能

並列摘要

A theoretical hypothesis was made by the inspiration of searching food and flying behaviors of bird colony, a synchronous searching algorithm solving multiple local optimums has been developed in this thesis. Individual bird is defined as a particle without the mass and
volume. Such a group particles together food searching with a suitable algorithm is particle swarm optimization (PSO). Multiple food locations corresponding to multiple local optimums can be obtained by multiple population of birds’ colonial parallel search. A niche strategy used on
genetic algorithm (GA) is utilized herein for dealing with multi-modal particle swarm optimization (MPSO). Several benchmark problems are successfully examined by proposed MPSO.For treating the constraints handling problems, a direct method of flying modification has been developed based on the violation of constrained sum. Only those particles closing to search bound can beaffected by such strategy. Three levels of constrained violation
corresponding to three evolution strategies of particles. As a result,sequential particles will effectively approach into boundary region as well as optimizing the optimum performance. Consequently, this constraints handling technique based on biological bird’s mind merge to MPSO that results in an innovative constrained MPSO.Some illustrative examples have been examined by presented PSO
including such constraints handling approach. They also effectively apply to multi-modal topological truss optimization that arise several different layouts. A true global optimum can be obtained by proposed constrained MPSO as compared published papers. Some problems shows extra structure layout as compare to existing research work. The PSO containing constrained handling and multiple modal considerations presented in this thesis results in a relatively reliable and efficient optimization algorithm.

並列關鍵字

Particle swarm optimization ； Multiple optimization ； Swarm intelligence ； Topological structural design

參考文獻

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