TY - JOUR

T1 - Constructing two-level QB -optimal screening designs using mixed-integer programming and heuristic algorithms

AU - Vazquez, Alan R.

AU - Wong, Weng Kee

AU - Goos, Peter

N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2023/2

Y1 - 2023/2

N2 - Two-level screening designs are widely applied in manufacturing industry to identify influential factors of a system. These designs have each factor at two levels and are traditionally constructed using standard algorithms, which rely on a pre-specified linear model. Since the assumed model may depart from the truth, two-level QB-optimal designs have been developed to provide efficient parameter estimates for several potential models. These designs also have an overarching goal that models that are more likely to be the best for explaining the data are estimated more efficiently than the rest. However, there is no effective algorithm for constructing them. This article proposes two methods: a mixed-integer programming algorithm that guarantees convergence to the two-level QB-optimal designs; and, a heuristic algorithm that employs a novel formula to find good designs in short computing times. Using numerical experiments, we show that our mixed-integer programming algorithm is attractive to find small optimal designs, and our heuristic algorithm is the most computationally-effective approach to construct both small and large designs, when compared to benchmark heuristic algorithms.

AB - Two-level screening designs are widely applied in manufacturing industry to identify influential factors of a system. These designs have each factor at two levels and are traditionally constructed using standard algorithms, which rely on a pre-specified linear model. Since the assumed model may depart from the truth, two-level QB-optimal designs have been developed to provide efficient parameter estimates for several potential models. These designs also have an overarching goal that models that are more likely to be the best for explaining the data are estimated more efficiently than the rest. However, there is no effective algorithm for constructing them. This article proposes two methods: a mixed-integer programming algorithm that guarantees convergence to the two-level QB-optimal designs; and, a heuristic algorithm that employs a novel formula to find good designs in short computing times. Using numerical experiments, we show that our mixed-integer programming algorithm is attractive to find small optimal designs, and our heuristic algorithm is the most computationally-effective approach to construct both small and large designs, when compared to benchmark heuristic algorithms.

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U2 - 10.1007/s11222-022-10168-1

DO - 10.1007/s11222-022-10168-1

M3 - Article

AN - SCOPUS:85142472532

SN - 0960-3174

VL - 33

JO - Statistics and Computing

JF - Statistics and Computing

IS - 1

M1 - 7

ER -