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

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