An algorithmic approach to finding factorial designs with generalized minimum aberration

Authors:
Fasheng Sun;Min-Qian Liu;Wenrui Hao
Affiliations:
Department of Statistics, School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China;Department of Statistics, School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China;Department of Scientific Computing and Applied Software, School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China
Venue:
Journal of Complexity
Year:
2009

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An effective algorithm for generation of factorial designs with generalized minimum aberration

Journal of Complexity

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Abstract

Factorial designs are arguably the most widely used designs in scientific investigations. Generalized minimum aberration (GMA) and uniformity are two important criteria for evaluating both regular and non-regular designs. The generation of GMA designs is a non-trivial problem due to the sequential optimization nature of the criterion. Based on an analytical expression between the generalized wordlength pattern and a uniformity measure, this paper converts the generation of GMA designs to a constrained optimization problem, and provides effective algorithms for solving this particular problem. Moreover, many new designs with GMA or near-GMA are reported, which are also (nearly) optimal under the uniformity measure.