Creating Optimal Designs

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Introducing Optimal Designs Start Point Tab Candidate Set Tab Algorithm Tab

Introducing Optimal Designs

Choose an optimal design by clicking the   button in the toolbar, or choose Design > Optimal.

Optimal designs are best for cases with high system knowledge, where previous studies have given confidence on the best type of model to be fitted, and the constraints of the system are well understood.

The optimal designs in the Design Editor are formed using the following process:

• An initial starting design is chosen at random from a set of defined candidate points.

• m additional points are added to the design, either optimally or at random. These points are chosen from the candidate set.

• m points are deleted from the design, either optimally or at random.

• If the resulting design is better than the original, it is kept.

This process is repeated until either (a) the maximum number of iterations is exceeded or (b) a certain number of iterations has occurred without an appreciable change in the optimality value for the design.

The Optimal Design dialog consists of several tabs that contain the settings for three main aspects of the design:

• Starting point and number of points in the design

• Candidate set of points from which the design points are chosen

• Options for the algorithm that is used to generate the points

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Start Point Tab

The Start Point tab allows you to define the composition of the initial design: how many points to keep from the current design and how many extra to choose from the candidate set.

1. Leave the optimality criteria at the default to create a V-Optimal design.

2. Increase the total number of points to 30 by clicking the Optional additional points up/down buttons or by typing directly into the edit box. You can edit the additional points and/or the total number of points.

   

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Candidate Set Tab

The Candidate Set tab allows you to set up a candidate set of potential test points. This typically ranges from a few hundred points to several hundred thousand.

1. Choose Grid for this example. Note that you could choose different schemes for different factors.

2. This tab also has buttons for creating plots of the candidate sets. Try them to preview the grid.

3. Notice that you can see 1-D, 2-D, 3-D, and 4-D displays (the fourth factor is color, but this example only uses three factors) at the same time as they appear in separate windows (see example following). Look at a display window while changing the number of levels for the different factors. See the effects of changing the number of levels on different factors, then return them all to the default of 21 levels.

   

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Algorithm Tab

1. Leave the algorithm settings at the defaults and click OK to start optimizing the design.

   When you click the OK button on the Optimal Design dialog, the Optimizing Design dialog appears, containing a graph. This dialog shows the progress of the optimization and has two buttons: Accept and Cancel. Accept stops the optimization early and takes the current design from it. Cancel stops the optimization and reverts to the original design.

   

2. Click Accept when iterations are not producing noticeable improvements; that is, the graph becomes very flat.

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Getting Started with the Design Editor

Viewing Design Displays

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