## 3 Artificial Neural Networks and Optimization
#### Artificial Neural Network Application
The reason for choosing MSE besides the R-value is to prevent over-fitting and increase accuracy. Thus, in this study, the hold-out technique is employed to evaluate the learning algorithm of the present neural network model. The present neural network model offers an ANN model with higher prediction ability. The pseudocode of the optimum ANN model is presented in Algorithm 1. ```
1-Input: Design Variables [DBW,DBH,DBD,BMT,PP,LP], Targets [TM, SEA, PF]
2-MSE_init = 100,000;
3-training_types = [\"trainlm\",\"trainscg\"];
4 for learning_rate = 0.01:0.01:1
5 for trainFcns = 1:2
6 create neural network = feedforward
7 train network
8 test network
9 ifR_Test > 0.965 and MSE < MSE_init
10 MSE_init=MSE
11 save network
12 else
13 end if
14 end if
15
16 end if \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Energy (k))** & **Total Mass (kg)** & **Force (kN)** \\ \hline Type & Feed-forward & Feed-forward & Feed-forward \\ Training function & Scaled Conjugate & Levenberg– & Levenberg– \\  & Gradient & Marquardt & Marquardt \\ Learning rate & 0.11 & 0.34 & 0.92 \\ Number of hidden layer & 1 & 1 & 1 \\ Number of neuron & 9 & 4 & 10 \\ Number of epochs & 41 & 15 & 7 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Artificial neural network (ANN) parameters. Figure 18: The R-value curves of the best artificial neural network (ANN) structures of Specific Energy Absorption. The smallest R-values for Specific Energy Absorption and Total Mass are 0.97171 and 0.98207, respectively, so they have a high correlation. Although the smallest R-value for Peak Force is 0.93451 in validation, as it is a high nonlinear problem with the heat input and flow curves used for the material discretization difficulties in the analysis, it offers a sufficient validation. Figure 19: The R-value curves of the best artificial neural network (ANN) structures of Total Mass. In this research, optimization of the hybrid DED semi cross part is carried out with a genetic optimization algorithm. GA is one of the evolutionary optimization methods that work using mechanisms similar to evolutionary mechanisms observed in nature [37]. Under the constraints which are defined for the DOE RSM approach, the genetic algorithm estimates the input parameters as shown in Table 12. As a next step, these input parameters, obtained via genetic algorithm, were evaluated following the steps in a DED process simulation, mapping DED results into structural analysis, three point bending simulation, and comparison of the results. Results were calculated with validated CAE analysis as defined in Table 13. It is observed that the ANN + GA approach presents acceptable results, with over 80% correlation for each outputs investigated in this research. Table 14 points out that, under the same constraints and conditions, the ANN + GA approach gives the better results for energy and total mass estimation. Besides this, the performance of DOE RSM on the prediction of the peak force is more reliable than the ANN + GA approach results. ## 4 Conclusions

The objective of this research was to introduce an approach for the integration of the two structures to improve the properties of the final part, such as the specific energy absorption, considering the optimum peak force and total mass constraints for the DED hybrid product. A computationally efficient approach is developed for constructing a DOE RSM and neural network based surrogate model for problems where both inputs and outputs are high-dimensional and nonlinear, using a small training data set. The proposed approach helps to fill the existing gap for development of the DED hybrid product, which includes the contributing and controllable design and process parameters. ANN + GA optimization approach is presented to increase the prediction for the specific energy absorption value of the semi cross hybrid DED part considering peak force and total mass constraints with a small data set to decrease the computation time and production costs.