本文利用單目標與多目標粒子群演算法探討於二維層流流場中，多個橢圓柱的隊形在不同雷諾數下最佳化之問題，首先介紹粒子群演算法(Particle Swarm Optimization)，將多目標粒子群演算法(MOPSO)與計算流體力學軟體ANSYS FLUENT結合，計算不同橢圓隊形所受到的阻力，經由多目標粒子群演算法求出最佳化的隊形。同時亦比較單目標與多目標粒子群演算法求出結果之差異，並以此最佳化隊形以及本研究撰寫出的程式架構，做為未來探討鳥類飛行隊伍的研究方法。
　　本研究以Microsoft Visual Studio 2008中的C#為程式架構的主體，以其撰寫粒子群演算法，並利用C#自動操控繪圖軟體Rhino建模，進行橢圓位置移動改變隊形之後，再將檔案匯入ANSYS FLUENT計算，利用計算出來的結果回傳至C#程式，作為修正下一次計算隊形的參考。
　　本研究目的在於研究自動最佳化計算的主要架構，使其可以利用來演算不同物體的最佳化隊形，只需要建立一開始的模型，經由程式自動化迭代計算之後，即可得到最小阻力的隊形。將來亦可將橢圓模型置換成鳥類、船等物體，利用隊形減少阻力節省效能，作為軍事或長途航行之用途，達到省時省能的效果。

　　This research uses the single objective particle swarm optimization (PSO) and multiobjective PSO (MOPSO) to implement the optimization for elliptic cylinders in formation in the two-dimesional laminar flow. We start from introducing PSO and MOPSO, and combine MOPSO with ANSYS FLUENT to calculate different formations. Finally we obtain an optimizing formation and also discuss the difference of results between the PSO and MOPSO. In the future, we will take this program to research the V-formation of birds.
　　The framewok of program is written in Microsoft Visual Studio 2008 C#, including PSO algorithm, changing the positons of elliptic cylinders, importing the files to ANSYS FLUENT and returning the data of forces back to PSO in order to correct the next calculation.
　　The main pupose to the research is to automate the optimizing framework of PSO, Rino and ANSYS FLUENT. To study different kinds of bodies, we only have to build an initial model in this program. If we obtain the formation of birds or ships, our research can use the optimizing formation to reduce drag force. We believe it can achieve decreasing fuel consumption in application of military or long-distance navigation.

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