The OPTEX Procedure

## Example 10.4 Optimal Design Using an Augmented Best Design

[See OPTEX4 in the SAS/QC Sample Library]This example is a continuation of Example 10.2.

You can specify a set of points that you want to be included in the final design found by the OPTEX procedure by using the AUGMENT= option in the GENERATE statement to specify a data set that contains a design to be augmented.

In this case, you can try to speed up the search for a 50-run design by first finding an optimal 25-run design and then augmenting that design with another 25 runs, as shown in the following statements:

```proc optex data=a seed=36926;
model AFR|EGR|SA@2 AFR*AFR EGR*EGR SA*SA;
generate n=25 method=detmax;
output out=b;
```
```proc optex data=a seed=37034;
model AFR|EGR|SA@2 AFR*AFR EGR*EGR SA*SA;
generate n=50 method=detmax augment=b;
run;
```

The result (see Output 10.4.1 and Output 10.4.2) is a design with almost 100% D-efficiency and A-efficiency relative to the best design found by the first attempt. However, this approach is not much faster than the original approach, since the run time for the DETMAX algorithm is essentially linear in the size of the design (see the section Memory and Run-Time Considerations.

Output 10.4.1 Efficiencies for the 25-Point Design to Be Augmented
The OPTEX Procedure

Design Number D-Efficiency A-Efficiency G-Efficiency Average Prediction
Standard Error
1 46.2975 26.0374 91.1822 0.5849
2 46.2171 25.9733 86.4608 0.5859
3 46.1720 25.9378 88.3293 0.5860
4 46.1374 25.9128 86.1895 0.5866
5 46.0808 22.6647 86.1502 0.6169
6 46.0620 24.7326 89.7179 0.6012
7 45.9992 25.4549 90.3330 0.5946
8 45.9630 24.7610 88.2701 0.5991
9 45.9627 25.5310 88.5737 0.5894
10 45.7994 24.5645 87.7544 0.6005

Output 10.4.2 Efficiencies for the Augmented 50-Point Design
The OPTEX Procedure

Design Number D-Efficiency A-Efficiency G-Efficiency Average Prediction
Standard Error
1 46.4957 25.0858 94.8160 0.4195
2 46.4773 25.0696 95.0646 0.4195
3 46.4684 24.5519 96.1259 0.4234
4 46.4676 24.5002 95.6830 0.4238
5 46.4587 25.0709 94.6650 0.4196
6 46.4555 24.8087 95.7768 0.4209
7 46.4471 24.5460 95.0073 0.4240
8 46.4373 25.0740 94.4640 0.4194
9 46.3899 25.0007 95.2162 0.4201
10 46.3662 24.4013 94.9539 0.4242

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