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Math. Comput. Appl. 2018, 23(2), 25; https://doi.org/10.3390/mca23020025

The Construction of a Model-Robust IV-Optimal Mixture Designs Using a Genetic Algorithm

1
Department of Mathematics and Statistics, Walailak University, Thasala, Nakhon Si Thammarat 80160, Thailand
2
Department of Statistics, Kasetsart University, Chatuchak, Bangkok 10903, Thailand
3
Department of Mathematical Sciences, Montana State University, Bozeman, MT 59717, USA
*
Author to whom correspondence should be addressed.
Received: 10 April 2018 / Revised: 7 May 2018 / Accepted: 16 May 2018 / Published: 17 May 2018
(This article belongs to the Special Issue Numerical and Evolutionary Optimization)
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Abstract

Among the numerous alphabetical optimality criteria is the IV-criterion that is focused on prediction variance. We propose a new criterion, called the weighted IV-optimality. It is similar to IV-optimality, because the researcher must first specify a model. However, unlike IV-optimality, a suite of “reduced” models is also proposed if the original model is misspecified via over-parameterization. In this research, weighted IV-optimality is applied to mixture experiments with a set of prior weights assigned to the potential mixture models of interest. To address the issue of implementation, a genetic algorithm was developed to generate weighted IV-optimal mixture designs that are robust across multiple models. In our examples, we assign models with p parameters to have equal weights, but weights will vary based on varying p. Fraction-of-design-space (FDS) plots are used to compare the performance of an experimental design in terms of the prediction variance properties. An illustrating example is presented. The result shows that the GA-generated designs studied are robust across a set of potential mixture models. View Full-Text
Keywords: mixture experiments; single component constraints; genetic algorithm; IV-optimality criterion mixture experiments; single component constraints; genetic algorithm; IV-optimality criterion
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Limmun, W.; Chomtee, B.; Borkowski, J.J. The Construction of a Model-Robust IV-Optimal Mixture Designs Using a Genetic Algorithm. Math. Comput. Appl. 2018, 23, 25.

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