Design Selection for Two-Level Multi-Stratum Factorial Experiments Based on Swarm Intelligence Optimization

基於蟲群智能最佳化之兩水準多階層因子實驗設計選取

Xie-Yu Li(李協諭)；Wei-Yang Yu(余維洋)；Ming-Chung Chang(張明中)

Minimum aberration ； Design key ； Block design ； Split-plot design ； Strip-plot design ； 最小混淆準則 ； 蟲群智能演算法 ； 多階層因子設計 ； 設計鍵

中國統計學報

61卷3期（2023 / 09 / 01）

178 - 206

英文;繁體中文

For unstructured experimental units, the minimum aberration due to Fries and Hunter (1980) is a popular criterion for choosing regular fractional factorial designs. Following which, many related studies have focused on multi-stratum factorial designs, in which multiple error terms arise from the complicated structures of experimental units. Chang and Cheng (2018) proposed a Bayesian-inspired aberration criterion for selecting multi-stratum factorial designs, which can be considered as a generalized version of that in Fries and Hunter (1980). However, they did not propose algorithms for searching for minimum aberration designs. The particle swarm optimization (PSO) algorithm is a popular optimization method that has been widely used in various applications. In this paper, we propose a new version of the PSO to select regular as well as nonregular multi-stratum designs. To select regular ones, we treat defining words as particles in the PSO and link the PSO with design key matrices. For nonregular multi-stratum designs, we treat treatment combinations as particles in the PSO. Several numerical illustrations are provided.

Fries and Hunter（1980）提出的最小混淆準則已廣泛被使用在無結構實驗單位之正規實驗設計上，許多後續研究試圖將之擴展至有多重誤差項的多階層因子設計。Chang and Cheng（2018）在貝氏觀點下提出對於多階層因子設計的最小混淆準則，其可視為Fries and Hunter（1980）的推廣，可是Chang and Cheng（2018）未探討計算層面的議題。本文使用蟲群智能演算法來克服計算上的問題，其中對於正規設計，我們將定義字視為該演算法的粒子，並與設計鍵做結合。對於非正規設計，我們將水準組合視為粒子，並在數值模擬上展現其效果。

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