對於無結構實驗單位的因子設計，Fries 與Hunter（1980）提出的最
小像差準則被廣泛運用在決定正規部分因子設計上。之後，許多相關研
究都集中在擁有多個誤差項的多層因子設計上，這些誤差項來自於複雜
的實驗單元結構。Chang 與Cheng (2018) 提出一種貝氏決策準則，它是
一個廣義版本的最小像差準則，並且可以運用在最佳化多層因子設計的
問題上。對於處理最佳化問題，粒子群優化演算法(PSO) 已是非常流行
並被廣泛應用於各種議題。在本篇論文中我們將提出了一個新版本的粒
子群優化演算法，來解決正規與非正規多層因子設計的最佳化問題。在
正規因子設計下，我們將定義字詞視為粒子群優化演算法中的粒子並將
粒子群優化演算法與設計鍵矩陣結合在一起。而在非正規的多層因子設
計下，則以處理組合做為演算法中的粒子。

For unstructured experimental units, minimum aberration in Fries and Hunter (1980) is a popular criterion for choosing regular fractional factorial designs. Following which, many related studies focused on multistratum
factorial designs with multiple error terms that arise from the complicated structures of experimental units. Chang and Cheng (2018) proposed a Bayesian criterion, which can be considered as a generalized version of the minimum aberration for selecting optimal multi-stratum factorial designs. Particle Swarm Optimization (PSO) algorithm is a popular optimization method that has been widely used in various applications. In this thesis, a new version of PSO is proposed to select regular and nonregular multi-stratum designs. We treat defining words as particles in PSO and link PSO with Design key matrix for selecting regular ones. For nonregular multi-stratum designs, we treat treatment combinations as particles in PSO.

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