A0467
Title: Effective algorithms for constructing two-level QB-optimal designs for screening experiments
Authors: Alan Vazquez - Tecnologico de Monterrey (Mexico) [presenting]
Weng Kee Wong - UCLA (United States)
Peter Goos - Universiteit Antwerpen (Belgium)
Abstract: Optimal two-level screening designs are widely applied in the manufacturing industry to identify factors that explain most of the product variability. These designs feature each factor at two settings 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 estimates for parameters in a large set of potential models as well. The optimal 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. Despite these attractive features, there are no good algorithms to construct these designs. Therefore, we propose two algorithms. The first algorithm, which is rooted in mixed-integer programming, guarantees convergence to the two-level QB-optimal designs. The second algorithm, which is based on metaheuristics, employs a novel formula to assess these designs and it is computationally efficient. Using numerical experiments, we demonstrate that our mixed integer programming algorithm is attractive to find small optimal designs, and our heuristic algorithm is an effective approach to constructing both small and large designs.
