D-Optimal

Primarily intended to be used as the input matrix for a Least Squares Regression Fit. By identifying the type of regression that will be used, samples are selected to maximize the determinant of the information matrix that is inverted during the Fit’s regression analysis, which in turn improves the numerical efficiency of the DOE.

This optimal determinant is the source of the name D-Optimal. Unlike factorial designs, which also have high information matrix determinants, D-Optimal DOEs can have an arbitrary number of runs. The evaluation points are selected from a candidate pool that uses an advanced combination of factorial and space filling designs.

Usability Characteristics

  • The minimum number of allowable runs is equal to the number of unknown coefficients in the selected regression, which in turn is a function of the number of variables.
  • The iterative search to improve the information matrix determinant can become computationally expensive. The search contains some internal logic to reduce excessive run times, but overall the time will scale with the number of variables, the number of terms in the regression, and the number of runs in the DOE.
  • For linear regression, D-Optimal runs will tend to cluster near the corners and resemble a factorial design pattern. This is expected as edge points will have the largest impact on a linear function. This effect is less pronounced as the order of the regression is improved.
  • Any data in the inclusion matrix is combined with the run data for post-processing. The optimal determinant is calculated using candidate and included points.
  • Supports input variable constraints.

Settings

In the Specifications step, Settings tab, change method settings.
Parameter Default Range Description
Number of Runs Twice the number of runs required for a linear regression. > 0 integer Number of new designs to be evaluated.
Regression Model Linear
  • Linear
  • Squared
  • Cubic
  • Interaction
  • Full Quadratic
  • Full Cubic
 The target regression structure used to build the information matrix. Maybe limited by problem size.
Use Inclusion Matrix Off Off or On Concatenation without duplication between the inclusion and the generated run matrix. The D-Optimal solution considers the locations of the existing inclusion runs when generating its data.