Model Browser User's Guide

Creating an Optimal Design

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. Optimal designs require linear models.

The Design Editor can average optimality across several linear models. This is a flexible way to design experiments using optimal designs. If you have no idea what model you are going to fit, you would choose a space-filling design. However, if you have some idea what to expect, but are not sure which model to use, you can specify a number of possible models. The Design Editor can average an optimal design across each model.

For example, if you expect a quadratic and cubic for three factors but are unsure about a third, you can specify several alternative polynomials. You can change the weighting of each model as you want (for example, 0.5 each for two models you think equally likely). This weighting is then taken into account in the optimization process in the Design Editor. See Global Model Class: Multiple Linear Models.

1. Click the  button in the toolbar or select File -> New. A new node appears in the design tree. It is named according to the model for which you are designing, for example, Linear Model Design.
2. Select the node in the tree by clicking. An empty Design Table appears if you have not yet chosen a design. Otherwise, if this is a new child node the display remains the same, because child nodes inherit all the parent design's properties.
3. Set up any constraints at this point. See Applying Constraints.
4. Choose an Optimal design by clicking the  button in the toolbar, or choose Design -> Optimal.

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 three tabs that contain the settings for three main aspects of the design:

• Start Point tab: Starting point and number of points in the design
• Candidate Set tab: Candidate set of points from which the design points are chosen
• Algorithm tab: Options for the algorithm that is used to generate the points

Setting Up a Space Filling Design

Optimal Design: Start Point Tab