Algorithms for constructing discrete approximate Q-optimal experimental designs with active identification of regression models of multifactor systems

In the theory of optimal experiment, there is a group of optimality criteria, for example, such as D-, A-, E-criteria, reflecting the accuracy of estimating model parameters. There is also a group of criteria related to the accuracy of the forecast based on the model, which can be characterized by the variance of estimates of mathematical expectations of responses. For example, using the G-optimality criterion allows you to obtain designs on which the constructed models will minimize the maximum variance of the forecast. Among these is the Q-optimality criterion, which assumes minimizing the average variance of the forecast for the regression model over the planning area. Most of the theoretical and applied research is related to the use of the D-optimality criterion. This is also explained by the fact that the criteria of D- and G-optimality are interconnected. At the same time, it should be noted that minimizing the maximum variance in the general case may not lead to a decrease in the average variance of the forecast area. In this regard, the use of Q-optimal designs in practical regression modeling tasks is relevant. For the widespread introduction into practice of the active identification of regression models of the concept of Q-optimality of experimental designs, an arsenal of effective algorithms for their construction is needed. The paper proposes and describes algorithms for constructing discrete approximate Q-optimal designs. The proposed algorithms are based on the developed approach of consistently increasing the number of points in the designs, as well as procedures for replacing points in the design. The designs obtained by such algorithms are recommended for use in practice when, on average, good prediction accuracy is required for the model over the entire range of input factors.