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Cross-Entropy Loss for Recommending Efficient Fold-Over Technique

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Abstract

Due to the limited resources and budgets in many real-life projects, it is unaffordable to use full factorial experimental designs and thus fractional factorial (FF) designs are used instead. The aliasing of factorial effects is the price we pay for using FF designs and thus some significant effects cannot be estimated. Therefore, some additional observations (runs) are needed to break the linages among the factorial effects. Folding over the initial FF designs is one of the significant approaches for selecting the additional runs. This paper gives an in-depth look at fold-over techniques via the following four significant contributions. The first contribution is on discussing the adjusted switching levels fold-over technique to overcome the limitation of the classical one. The second contribution is on presenting a comparison study among the widely used fold-over techniques to help experimenters to recommend a suitable fold-over technique for their experiments by answering the following two fundamental questions: Do these techniques dramatically lessen the confounding of the initial designs, and do the resulting combined designs (combining initial design with its fold-over) via these techniques have considerable difference from the optimality point of view considering the markedly different searching domains in each technique? The optimality criteria are the aberration, confounding, Hamming distance and uniformity. Many of these criteria are given in sequences (patterns) form, which are inconvenient and costly to represent and compare, especially when the designs have many factors. The third innovation is on developing a new criterion (dictionary cross-entropy loss) to simplify the existing criteria from sequence to scalar. The new criterion leads to a more straightforward and easy comparison study. The final contribution is on establishing a general framework for the connections between initial designs and combined designs based on any fold-over technique.

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Author information

Authors and Affiliations

  1. Division of Science and Technology, Beijing Normal University-Hong Kong Baptist University United International College, Zhuhai, 519085, China

    Lin-Chen Weng, A. M. Elsawah & Kai-Tai Fang

  2. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, 44519, Egypt

    A. M. Elsawah

  3. The Key Lab of Random Complex Structures and Data Analysis, Chinese Academy of Sciences, Beijing, 100190, China

    Kai-Tai Fang

Authors
  1. Lin-Chen Weng
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  2. A. M. Elsawah
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  3. Kai-Tai Fang
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Corresponding author

Correspondence to A. M. Elsawah.

Additional information

This research was supported by the Beijing Normal University-Hong Kong Baptist University United International College under Grant Nos. R201810, R201912 and R202010, and the Zhuhai Premier Discipline Grant.

This paper was recommended for publication by Editor ZHU Liping.

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Weng, LC., Elsawah, A.M. & Fang, KT. Cross-Entropy Loss for Recommending Efficient Fold-Over Technique. J Syst Sci Complex 34, 402–439 (2021). https://doi.org/10.1007/s11424-020-9267-9

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  • DOI: https://doi.org/10.1007/s11424-020-9267-9

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