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

Abstract

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 2k 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.

Keywords

• bias; efficiency; designs; precision; simulation.