(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.