(g) Y7 (h) Y8
Figure 4. Y values for 139 simulations. The blue circles indicate the
Bayesian optimization results, the gray triangles indicate the random
search results, the asterisks indicate the Bayesian optimization results
that achieved the target ranges of Y, and the red lines indicate the
target ranges.
Bayesian optimization depends on the initial samples because it starts
with a small number. Therefore, we changed the random value of D-optimal
design, and performed Bayesian optimization again. The result is shown
in Figure 5. In 83 simulations (D-optimal design took 50, and Bayesian
optimization took 33), we succeeded in searching for X values that
achieved target ranges of Y. These X were the same as those before the
random values were changed, indicating that the results of process
design based on ADoE and Bayesian optimization were stable. A comparison
of the results before and after changing the random values shows similar
behavior, but the target was achieved faster after the change. The
number of simulations decreased because there was a sample that could
easily achieve the target in the initial samples. From the results shown
in Figure 5, the reproducibility of the proposed method was confirmed.
We changed the candidates of X to one million samples and compared the
results of the proposed method. Tables (4, 5) list the Y and X results,
respectively. In the second set of results, 77 simulations (50 for
D-optimal design, and 27 for Bayesian optimization) succeeded in
searching for X that achieved the target ranges of Y. Similarly, we
succeeded in the third set of results with 105 simulations (50 for
D-optimal design, and 55 for Bayesian optimization). In Table 4, values
of Y converged to relatively similar solutions. However, in Table 5, the
values of X were dissimilar. In actuality, the final X values will be
selected on the basis of cost comparisons or chemical engineering
knowledge.