## 8 Conclusions  
This paper presents a novel method for the optimization of the stacking sequence in laminated structures. The proposed method is robust and efficient in simple optimization cases as well as in more \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**ANN** & **CL** & **Optimal Lamination Angles** & **Optimal Solution [Hz]** \\
**Type** & **Level** & \(\mathbf{\Lambda^{*}}\) & \(\mathbf{g^{ANN}}\) & \(\mathbf{g^{FEM}}\) \\ \hline \multicolumn{5}{c}{Excitation frequency \(p=90\) Hz} \\ \hline \multirow{3}{*}{ANN\({}_{1234}^{10}\)} & CL0 & \([-76/16.7]\)-\(30/13.3|30.2/-36.5] & 20.50 & 21.87 \\  & CL1 & \([-74.5/15.4]\)\(-31.1/12.9|29.8/-36.4] & 21.73 & 22.24 \\  & CL2 & \([76/-15.1|-27.7/10.5|31.5/-32.2]\) & 21.93 & 22.03 \\ \hline \multicolumn{5}{c}{Excitation frequency \(p=100\) Hz} \\ \hline \multirow{3}{*}{ANN\({}_{1234}^{10}\)} & CL0 & \([-75.1/-45.7|49/53.1|83.7/89.9]\) & 21.30 & 20.91 \\  & CL1 & \([-62.1/-35.2|56.3/64.2|86.1/90]\) & 21.58 & 21.61 \\  & CL2 & \([-69.2/-39.9|52.9/52.3|87.8/89.9]\) & 22.08 & 22.06 \\ \hline \multicolumn{5}{c}{Excitation frequency \(p=110\) Hz} \\ \hline \multirow{3}{*}{ANN\({}_{1234}^{10}\)} & CL0 & \([-84.4/-16.3|59.2/29.2|-84.7/-88]\) & 23.48 & 23.26 \\  & CL1 & \([90/-18.1|-56.8/-33.4|89.5/89.9]\) & 23.39 & 23.41 \\  & CL2 & \([-80.4/-16.3|61.2/31.3|-88.7/89.9]\) & 23.58 & 23.60 \\ \hline \multicolumn{5}{c}{Excitation frequency \(p=120\) Hz} \\ \hline \multirow{3}{*}{ANN\({}_{1234}^{10}\)} & CL0 & \([-89.8/-16.9|67.5/0.925|86.8/-63.2]\) & 24.04 & 23.48 \\  & CL1 & \([87.9/-12.4|78.5/0.92|-79.7/-59.4]\) & 23.97 & 23.28 \\  & CL2 & \([-86.2/-19.7|72.4/27.6|90/-9.59]\) & 22.89 & 23.17 \\ \hline \multicolumn{5}{c}{Excitation frequency \(p=130\) Hz} \\ \hline \multirow{3}{*}{ANN\({}_{1234}^{10}\)} & CL0 & \([85/-13.6|75/0.252|90/11.1]\) & 21.64 & 22.56 \\  & CL1 & \([82/-12.4|-84.5/0.366|-74.8/11.1]\) & 22.14 & 22.28 \\ \cline{1-1}  & CL2 & \([77.2/-15|80.6/12.9|90/14.5]\) & 22.64 & 23.31 \\ \hline \hline \end{tabular} ANN: artificial neural network; CL: curriculum learning.  
\end{table} 
Table 12: Optimization of the distance between natural frequencies and selected excitation frequencies using MODEL2 with four symmetric layers of laminate. Figure 10: Optimization of the distance between natural frequencies and 120 Hz using MODEL2 with four symmetric layers of laminate. complicated problems with more design variables. Complex boundary conditions, the complicated shape of the investigated structures, and the type of variable (continuous or discrete) do not hinder the effective use of the method. Moreover, the procedure can be successfully applied to optimization cases in which it is not possible to derive analytical formulae that combine design variables and optimized quantities. As a result of replacing the finite element method by deep neural networks for the calculation of the optimized structure parameters, the proposed method significantly accelerates the optimization and enables the optimization to be performed in limited time on typical computer hardware. In addition to instantly calculating the objective function, deep neural networks have another important advantage: they facilitate the use of a very large number of patterns describing the optimization space. In the examples described in this paper, the number of available patterns reaches 10,000. In other cases, which are not discussed in this paper, deep networks were trained on 120,000 patterns, and the training time did not exceed 30 min. The main idea presented in this paper, i.e., the curriculum learning of the applied deep networks, opens the door to new applications of the combined GA+ANN optimization procedure. The procedure can start with a very sparse description of the optimization space, and, in the successive iteration steps, the space description acquires a higher level of accuracy around the global minimum.