摘要
本文藉由比較粒子群演算法、正交學習粒子群演算法來計算六個不同的適應函數，說明何種粒子群演算法的計算較為精確，接著比較圖形處理器和中央處理器之間的速度差異，解釋粒子群演算法和正交學習粒子群演算法在平行化運算中的狀況。
首先，我們先簡單介紹粒子群演算法，粒子群演算法是一種計算最佳化問題的方法，而粒子群演算法又能透過加入正交學習以及正交實驗設計，演變形成正交學習粒子群演算法。
接下來我們使用圖形處理器進行加速計算的工具，圖形處理器擁有比中央處理器更多個計算核心，藉由圖形處理器可以達到平行化計算的效果，使得粒子能夠分散在多個區塊中，同時進行運算的處理，讓程式能夠加速計算函數。
最後，我們可以得到正交學習粒子群演算法無論是在搜尋速度或者最佳解的精確度上都比粒子群演算法來的好，尤其是使用在計算複雜函數的最佳化問題時，效果更為顯著。

Abstract
This thesis compares the performance of two optimization methods, the standard particle swarm optimization (PSO) and orthogonal learning particle swarm optimization (OLPSO), through six different fitness functions. Based on PSO, OLPSO incorporated the orthogonal experimental design is proposed to construct the better guidance exemplar to enhance convergence toward the global optima. We also perform parallel OLPSO using Graphic Processing Unit (GPU) architecture which has more computational cores than Central Processing Unit (CPU). We distribute the orthogonal learning process of each particle to GPU threads. The results shows that the OLPSO algorithm outperforms the tranditional PSO in finding the optimal solutions.

1.緒論 1
2.正交學習粒子群演算法 2
2.1粒子群演算法介紹 2
2.2正交學習粒子群演算法介紹 5
3.程式介紹 11
3.1 CPU版本程式呈現 11
3.2 GPU版本程式呈現 22
4.適應函數介紹 34
5.數值結果 36
5.1 CPU的演算法比較- Unimodal 36
5.2 CPU的演算法比較- Multimodal 37
5.3 CPU的演算法比較- Rotated And Shifted 38
5.4 CPU與GPU比較 39
6.參考文獻 40

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