 The OPTEX Procedure

## Example 10.3 Using an Initial Design to Search an Optimal Design

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

You can customize the runs used to initialize the search in the OPTEX procedure. For example, you can use the INITDESIGN=SEQUENTIAL option to use an initial design chosen by the sequential search. Or you can place specific points in a data set and use the INITDESIGN=SAS-data-set option. In both cases, the search time can be significantly reduced, since the search only has to be done once. This example illustrates both of these options.

The previous example compared the results of the DETMAX and sequential search algorithms. You can use the design chosen by the sequential search as the starting point for the DETMAX algorithm. The following statements specify the DETMAX search method, replacing the default initialization method with the sequential search:

```proc optex data=a seed=33805;
model AFR|EGR|SA@2 AFR*AFR EGR*EGR SA*SA;
generate n=50 method=detmax initdesign=sequential;
run;
```

The results, which are displayed in Output 10.3.1, show an improvement over the sequential design itself (Output 10.2.2) but not over the DETMAX algorithm with the default initialization method (Output 10.2.1). Evidently the sequential design represents a local optimum that is not the global optimum, which is a common phenomenon in combinatorial optimization problems such as this one.

Output 10.3.1 Initializing with a Sequential Design
The OPTEX Procedure

Design Number D-Efficiency A-Efficiency G-Efficiency Average Prediction
Standard Error
1 46.4333 25.0321 95.1371 0.4199

Prior knowledge of the design problem at hand might also provide a specific set of factor combinations to use as the initial design. For example, many D-optimal designs are composed of replications of the optimal saturated design—that is, the optimal design with exactly as many points as there are parameters to be estimated. In this case, there are 10 parameters in the model. Thus, you can find the optimal saturated design in 10 points, replicate it five times, and use the resulting design as an initial design, as follows:

```proc optex data=a seed=33805;
model AFR|EGR|SA@2 AFR*AFR EGR*EGR SA*SA;
generate n=saturated method=detmax;
output out=b;
```
```data c; set b; drop i;
do i=1 to 5; output; end;

proc optex data=a seed=33805;
model AFR|EGR|SA@2 AFR*AFR EGR*EGR SA*SA;
generate n=50 method=detmax initdesign=c;
run;
```

The results are displayed in Output 10.3.2 and Output 10.3.3. The resulting design is 99.9% D-efficient and 98.4% A-efficient relative to the best design found by the straight-forward approach (Output 10.2.1), and it takes considerably less time to produce.

Output 10.3.2 Efficiencies for the Unreplicated Saturated Design
The OPTEX Procedure

Design Number D-Efficiency A-Efficiency G-Efficiency Average Prediction
Standard Error
1 41.6990 24.8480 67.6907 0.9508
2 41.4931 22.2840 70.8532 0.9841
3 40.9248 20.7672 62.2177 1.0247
4 40.7447 21.6253 52.7537 1.0503
5 39.9563 20.1557 46.4244 1.0868
6 39.9287 19.5856 45.9023 1.0841
7 39.9287 19.5856 45.9023 1.0841
8 38.9078 13.5976 37.7964 1.2559
9 38.9078 13.5976 37.7964 1.2559
10 37.6832 12.5540 45.3315 1.3036

Output 10.3.3 Initializing with a Data Set
The OPTEX Procedure

Design Number D-Efficiency A-Efficiency G-Efficiency Average Prediction
Standard Error
1 46.4388 24.4951 96.0717 0.4242 Previous Page | Next Page | Top of Page