## 4 Results  
The distribution of the lift-to-drag ratio over the design space is illustrated in Figure 9. The lift-to-drag ratio of Baseline model 1 (at \((\omega_{1},\,\omega_{2})=(1,0)\)) is measured as 3.885, while that of Baseline model 2 (at \((\omega_{1},\,\omega_{2})=(0,1)\)) is approximately 5.926. Although Baseline model 3, whose the weights are \((\omega_{1},\,\omega_{2})=(0,0)\), shows the highest lift-to-drag ratio among the baseline models, its loading capacity is so low that it fails to satisfy the constraints presented in Equation (11), indicating that this type of aircraft design cannot be an optimal shape. In the design space, the high lift-to-drag ratio region is found around the left top corners. From this observation, an optimal solution can be found close to this region if the constraints related to the aircraft loading capacity are satisfied at the region. In addition, when the change in the BWB aircraft's performance is analyzed as a function of the design  
Figure 8: The illustration of the design space with 19 initial design points. The bold black lines show the design space of the optimization problem, while the black dotted points are the 19 design points in the design of experiment. parameters, a moderate inverse proportion between the lift-to-drag ratio and \(\omega_{1}\) is observed, as shown by Figure 10. When this distribution is modeled using a linear regression analysis, the regression model (\(L/D=-2.018\omega_{1}+5.960\)) is obtained, here with an R-squared value \(R^{2}=0.822\). However, unlike \(\omega_{1}\), no apparent association of \(\omega_{2}\) with the lift-to-drag ratio is found. When an ANN-based surrogate model is constructed, the ANN-related parameters, such as number of neurons, number of hidden layers, and value of the regularization constant, are important factors that affect the predication accuracy of the surrogate model. To find the proper values of these parameters, numerical investigations are performed by varying these parameters' values; here, the change in the ANN's prediction accuracy is analyzed. For the ANN-related parameters, three parameters (number of neurons, number of hidden layers, and value of regularization constant) are chosen, and the effects of these parameters on the prediction accuracy are investigated. If the number of neurons, number of hidden layers, and regularization constant are defined as \(N\), \(M\), and \(\lambda\), respectively, numerical studies are conducted at 5 \(N\)s (8, 16, 32, 64, and 128), 4 \(M\)s (1, 2, 3, and 4), and 4 \(\lambda\)s (0.1, 0.01, 0.001, and 0.0001), totaling 80 cases. When \(M\) is greater than 1 (meaning that multiple hidden layers are used in constructing the ANN), the number of neurons at each hidden layer is defined as being equal so as to reduce the complexity of the analysis (see Figure 11). Based on the numerical investigations, the proper values of the ANN-related parameters are determined based on the following steps: First, the effect of \(\lambda\) is studied with the 80 numerical cases, and the best value of \(\lambda\) is determined. Then, by fixing the value of \(\lambda\), the influences of \(M\) are identified, and its best value is decided. After this,  
Figure 10: Correlation between \(L/D\) and \(\omega_{1}\). The black dots show the lift-to-drag ratio of the 19 design points at the design of experiment and four test data sets. The red line shows the linear regression model computed with data from the 23 simulations. The R-squared value of this regression model is \(R^{2}=0.822\), representing a moderate correlation between \(\omega_{1}\) and \(L/D\). Figure 9: Distribution of the lift-to-drag ratio in the design space. the best value of \(N\) is searched for while fixing the values of \(\lambda\) and \(M\) to their best values. The prediction error of the constructed ANN \(\epsilon\) is evaluated by using the \(L_{2}\) norm.