The OPTEX Procedure

## Example 10.5 Optimal Design Using a Small Candidate Set

[See OPTEX4 in the SAS/QC Sample Library]This example is a continuation of Example 10.4.

A well-chosen initial design can speed up the search procedure, as illustrated in Example 10.2. Another way to speed up the search is to reduce the candidate set. The following statements generate the optimal design with a fast, sequential search and then use the FREQ procedure to examine the frequency of different factor levels in the final design:

```proc optex data=a seed=33805 noprint;
model AFR|EGR|SA@2 AFR*AFR EGR*EGR SA*SA;
generate n=50 method=sequential;
output out=b;
proc freq;
table AFR EGR SA / nocum;
run;
```

Output 10.5.1 Factor-Level Frequencies for Sequential Design
The FREQ Procedure

AFR Frequency Percent
15 19 38.00
16 6 12.00
17 6 12.00
18 19 38.00

EGR Frequency Percent
0.02 20 40.00
0.566 9 18.00
1.117 21 42.00

SA Frequency Percent
10 19 38.00
28 6 12.00
34 5 10.00
52 20 40.00

From Output 10.5.1, it is evident that most of the factor values lie in the middle or at the extremes of their respective ranges. This suggests looking for an optimal design with a candidate set that includes only those points in which the factors have values in the middle or at the extremes of their respective ranges. The following statements illustrate this approach (see Output 10.5.2):

```proc plan;
factors AFR=4 ordered EGR=4 ordered SA=4 ordered
/ noprint;
output out=a AFR nvals=(15, 16, 17, 18)
EGR nvals=(0.020, 0.377, 0.566, 1.117)
SA  nvals=(10, 28, 34, 52);
proc optex seed=61552;
model AFR|EGR|SA@2 AFR*AFR EGR*EGR SA*SA;
generate n=50 method=detmax;
run;
```

Output 10.5.2 Optimal Design Using a Smaller Candidate Set
The OPTEX Procedure

Design Number D-Efficiency A-Efficiency G-Efficiency Average Prediction
Standard Error
1 46.5151 24.9003 96.7226 0.4442
2 46.4997 24.5549 96.1157 0.4478
3 46.4920 24.5530 95.9941 0.4480
4 46.4657 24.8653 95.5627 0.4446
5 46.4547 24.5071 96.0385 0.4481
6 46.4333 25.0321 95.1371 0.4448
7 46.4333 25.0321 95.1371 0.4448
8 46.4333 25.0321 95.1371 0.4448
9 46.3916 24.3617 95.0041 0.4489
10 46.3379 24.8695 94.3115 0.4458

The resulting design is about as good as the best one obtained from a complete candidate set ( relative D-efficiency and marginally higher relative A-efficiency) and takes much less time to find.

See the section Handling Many Variables for another example of reducing the candidate set for the optimal design search.

 Previous Page | Next Page | Top of Page