New orders of 2k factorial designs generated by simulated annealing adapted to optimality criteria

Abstract

The excessive changes in factor levels can lead to a high cost in practice and make it difficult to conduct the experiment, in addition to adding a higher computational cost and loss of the orthogonality property, resulting in numerical proble

Excessive changes in factor levels can lead to a high cost in practice and hinder the conduction of experiments, in addition to adding a higher computational cost and loss of the orthogonality property, resulting in numerical problems in estimating the parameters of a model. The sequential specification of experimental points, seen as treatments in a 2^k factorial design, results in a high-order bias in some factors, which is caused by the accumulation of −1 or +1 signals. This study aimed to propose new designs generated by the simulated annealing technique, respecting the main A-optimal and D-optimal optimality criteria as random execution orders that minimize the order bias. This approach allowed the generation of 2⁴ and 2⁵ factorials, which were compared to the designs in standard order. The simulated annealing technique is a viable method to generate optimal designs with the same efficiency as the usual designs to obtain A-optimal and D-optimal designs with new execution orders, which minimize the effect of order bias relative to standard order designs. Regarding efficiency, the generated designs were precise in the variance of model parameter estimates, similar to the original designs.

ms in the estimation of the parameters of a model. The sequential specification of the experimental points, seen as treatments in a 2^k factorial design, results in a high order bias in some factors, which is caused by the accumulation of -1 or +1 signals. The objective of this study is to propose new designs generated by the simulate annealing technique, which respects the main A-optimal and D-optimal optimality criteria as random execution orders that minimize order bias. With this approach, 2⁴ and 2⁵ factorials were generated and compared with the designs in standard order. It was concluded that the simulated annealing technique is a viable method to generate optimal designs with the same efficiency as the usual designs. For the generation of A-optimal and D-optimal designs with new execution orders that minimize the effect of order bias in relation to standard order designs. Regarding efficiency, the generated designs were precise in the variance of the estimates of the model parameters, similar to the original designs.