See OPTEX4 in the SAS/QC Sample LibraryThis example is a continuation of Example 14.2.
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; run;
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 14.4.1 and Output 14.4.2) 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 14.4.1: Efficiencies for the 25-Point Design to Be Augmented
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 14.4.2: Efficiencies for the Augmented 50-Point Design
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 |