Genetic algorithms developed in R software for finding optimal experimental designs
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Designing an experiment is important, since good designs are required to ensure the efficient estimation of a model that explains the relationship between response and explanatory variables. The reliability of conclusions from a model depends on the quality of data, apart from the model itself. More often the number of runs in an experiment has to be limited due to cost and resource constraints, and this can adversely affect the estimation of models that fit the data. However, choosing an optimal design with the limited runs will ensure the efficiency in such cases. Analytical methods of choosing an optimal design are not feasible when complex models are involved, and in such scenarios analytically finding an optimal design even with simple design criteria like D- optimality criterion becomes harder, let alone complex criteria, like minimax criteria. Therefore, numerical methods are required to perform the desired tasks. Several types of algorithms are available, and currently most popular among them are exchange algorithms. However, exchange algorithms have their limitations in finding experimental designs, especially with higher dimensional problems. In such situations, non-exchange type algorithms like genetic algorithms (GAs) found to be performing better and so GAs are gaining popularity in finding optimal designs. In this study GAs are created in R software and applied to some problems from literature, including exact G- optimal designs, which are based on minimax criteria. The optimal designs with D- and A- optimal criteria found using GAs are found to be very close to the theoretical optimal designs. The exact G- optimal designs for a two factor quadratic model are found to outperform such designs available in the published literature. Further study will be undertaken for problems with higher dimensionality, and for finding optimal designs for fractional polynomial models.