An algorithmic approach to finding factorial designs with generalized minimum aberration |
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Authors: | Fasheng Sun Min-Qian Liu Wenrui Hao |
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Institution: | 1. Department of Statistics, School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China;2. Department of Scientific Computing and Applied Software, School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China |
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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. |
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Keywords: | Discrepancy Factorial design Generalized minimum aberration Quadratic penalty function Uniformity |
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