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

TL;DR

This paper introduces a swarm intelligence-based optimization method to select optimal multi-stratum factorial designs, addressing both regular and nonregular cases with novel algorithmic approaches.

Contribution

It develops a new PSO-based algorithm for selecting multi-stratum factorial designs, extending previous criteria without existing search algorithms.

Findings

Effective in selecting optimal designs for complex multi-stratum experiments

Applicable to both regular and nonregular factorial designs

Demonstrated through numerical illustrations

Abstract

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.