Example 24.5: Optimal Design Using a Small Candidate Set

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 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

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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