Construction of Optimal Mixed-Level Uniform Designs

CHATTERJEE Kashinath, LIU Min-Qian, QIN Hong, YANG Liuqing

Journal of Systems Science & Complexity ›› 2024, Vol. 37 ›› Issue (2) : 841-862.

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Journal of Systems Science & Complexity ›› 2024, Vol. 37 ›› Issue (2) : 841-862. DOI: 10.1007/s11424-024-2379-x

Construction of Optimal Mixed-Level Uniform Designs

  • CHATTERJEE Kashinath1, LIU Min-Qian2, QIN Hong3, YANG Liuqing2
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Abstract

The theory of uniform design has received increasing interest because of its wide application in the field of computer experiments. The generalized discrete discrepancy is proposed to evaluate the uniformity of the mixed-level factorial design. In this paper, the authors give a lower bound of the generalized discrete discrepancy and provide some construction methods of optimal mixed-level uniform designs which can achieve this lower bound. These methods are all deterministic construction methods which can avoid the complexity of stochastic algorithms. Both saturated mixed-level uniform designs and supersaturated mixed-level uniform designs can be obtained with these methods. Moreover, the resulting designs are also χ2-optimal and minimum moment aberration designs.

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Generalized discrete discrepancy / Hadamard matrix / mixed-level design / orthogonal array / supersaturated design

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CHATTERJEE Kashinath , LIU Min-Qian , QIN Hong , YANG Liuqing. Construction of Optimal Mixed-Level Uniform Designs. Journal of Systems Science & Complexity, 2024, 37(2): 841-862 https://doi.org/10.1007/s11424-024-2379-x

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Funding

This work was supported by the National Natural Science Foundation of China under Grant Nos. 12131001, 12226343, 12371260, and 12371261, National Ten Thousand Talents Program of China, and the 111 Project under Grant No. B20016.
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