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An adjusted gray map technique for Constructing Large Four-Level Uniform Designs

Journal of Systems Science & Complexity 2023年第1期36卷 433-456页

作者： ELSAWAH A M VISHWAKARMA G K MOHAMED H S FANG Kai-Tai Department of Statistics and Data Science Faculty of Science and TechnologyBeijing Normal University-Hong Kong Baptist University United International CollegeZhuhai 519087China Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science BNU-HKBU United International CollegeZhuhai 519087China Department of Mathematics Faculty of ScienceZagazig UniversityZagazig 44519Egypt Department of Mathematics&Computing Indian Institute of Technology DhanbadDhanbad 826004India College of Transportation and Civil Engineering Fujian Agriculture and Forestry UniversityFuzhou 350002China The Key Lab of Random Complex Structures and Data Analysis The Chinese Academy of SciencesBeijing 100190China

A uniform experimental design(UED)is an extremely used powerful and efficient methodology for designing experiments with high-dimensional inputs,limited resources and unknown underlying models.A UED enjoys the following two significant advantages:(i)It is a robust design,since it does not require to specify a model before experimenters conduct their experiments;and(ii)it provides uniformly scatter design points in the experimental domain,thus it gives a good representation of this domain with fewer experimental trials(runs).Many real-life experiments involve hundreds or thousands of active factors and thus large UEDs are *** large UEDs using the existing techniques is an NP-hard problem,an extremely time-consuming heuristic search process and a satisfactory result is not *** paper presents a new effective and easy technique,adjusted gray map technique(AGMT),for constructing(nearly)UEDs with large numbers of four-level factors and runs by converting designs with s two-level factors and n runs to(nearly)UEDs with 2^(t−1)s four-level factors and 2tn runs for any t≥0 using two simple transformation *** justifications for the uniformity of the resulting four-level designs are given,which provide some necessary and/or sufficient conditions for obtaining(nearly)uniform four-level *** results show that the AGMT is much easier and better than the existing widely used techniques and it can be effectively used to simply generate new recommended large(nearly)UEDs with four-level factors.

关键词： Aberration adjusted gray map technique gray map technique Hamming distance moment aberration threshold accepting algorithm uniform design

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