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 Details of the OPTEX Procedure

## Example 24.5: Optimal Design Using a Small Candidate Set

 See OPTEX4 in the SAS/QC Sample Library

This example is a continuation of Example 24.4.

A well-chosen initial design can speed up the search procedure, as illustrated in Example 24.2. 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 af|egr|sa@2 af*af egr*egr sa*sa;
generate n=50 method=sequential;
output out=b;
proc freq;
table af egr sa / nocum;
run;
```

Output 24.5.1: Factor Level Frequencies for Sequential Design

 The FREQ Procedure

 af 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 24.5.1, 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 24.5.2):

```   proc plan;
factors af=4 ordered egr=4 ordered sa=4 ordered
/ noprint;
output out=a af  nvals=(  15,  16,  17,   18)
egr nvals=(.020,.377,.566,1.117)
sa  nvals=(  10,  28,  34,   52);
proc optex seed=61552;
model af|egr|sa@2 af*af egr*egr sa*sa;
generate n=50 method=detmax;
run;
```

Output 24.5.2: Optimal Design Using a Smaller Candidate Set

 The OPTEX Procedure

 Design Number D-Efficiency A-Efficiency G-Efficiency Average PredictionStandard 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

Once again, the resulting design is almost as good as the best one derived by a straightforward search (> 99.9% relative D-efficiency and > 98.5% relative A-efficiency) and takes much less time to find. Moreover, designs with fewer factor levels can be much easier to implement.

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

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