The D-optimality criterion minimizes the determinant of the variance-covariance matrix of the regression coefficients. You specify the model, then Minitab selects design points that optimize the D-optimal criterion from a set of candidate points. The rows of design columns in the worksheet contain the candidate set of design points. The selection process consists of two steps:
Minitab selects design points from the candidate set to obtain the initial design. You can choose which algorithm will be used to select these points in the Methods sub-dialog box. Choices include: sequential selection, random selection, or a combination of sequential and random selection. By default, Minitab selects all points sequentially. Sequential selection means that all of the points in the initial design were added in an order that provided the maximum increase in D-optimality. If you repeat the design selection and the runs that are in the candidate set are in the same order, the algorithm will find the same solution.
Candidate design points may be added with replacement to the final design during the optimization procedure. Therefore, the final design may contain duplicate design points.
In numerical optimization, there is always a danger of finding a local optimum instead of the global optimum. To avoid finding a local optimum, you could perform multiple trials of the optimization procedure starting from different initial designs. Only one trial is possible if you generate the initial design by purely sequential selection or if you specify the initial design with an indicator column.
If you do not want to select a model in advance, a good strategy is to spread the design points uniformly over the design space. In this case, the distance-based method provides one solution for selecting the design points. The distance-based optimality algorithm selects design points from a candidate set, such that the points are spread evenly over the design space.
The algorithm for distance based designs does not use an exchange method. The algorithm also does not replicate points when you select an optimal design.
Minitab selects the candidate point with the largest Euclidean distance from the origin (response surface design) or the point that is closest to a pure component (mixture design) as the starting point. Then, Minitab adds additional design points in a stepwise manner such that each new point is as far as possible from the points already selected for the design.
You must use an indicator column to indicate which points are available to add to the original design. Then, Minitab adds additional design points in a stepwise manner such that each new point is as far as possible from the points already selected for the design.