# Multi-Objective Optimization Study on Production of AlSi10 Mg Alloy by Laser Powder Bed Fusion
## 3 Results and Discussions
According to these results, the equation of the regression model obtained is as follows:  
Surface roughness = 30.63 \(-\) 0.14738 Laser Power (W) + 204.07 Hatch Distance (mm) \(-\) 0.017719 Scan Speed (mm/s) \(-\) 0.5669 Laser Power (W) * Hatch Distance (mm) + 0.000135 Laser Power (W) * Scan Speed (mm/s) \(-\) 0.07101 Hatch Distance (mm) * Scan Speed (mm/s)  
According to the ANOVA results in Table 5, the activities of the factors did not show a significant and meaningful effect on their binary interactions (\(p\) > 0.05). The regression coefficient for relative density was obtained as R\({}^{2}\) = 0.6449. According to these results, the equation of the regression model obtained is as follows:  
Relative density = 1.017 \(-\) 0.00033 Laser Power (W) + 0.61 Hatch Distance (mm) \(-\) 0.000098 Scan Speed (mm/s) \(-\) 0.00093 Laser Power (W) * Hatch Distance (mm) + 0.000001 Laser Power (W) * Scan Speed (mm/s) \(-\) 0.00045 Hatch Distance (mm) * Scan Speed (mm/s)  
The results obtained with the factorial experimental design were analyzed with the graphs given in Figure 7.  
It is thought that multiple responses, such as surface roughness and relative density, should be optimized simultaneously. Improving both properties simultaneously is important in terms of increasing the overall quality and functional adequacy of the product. In order to achieve this goal, the parameters that optimize both responses were determined using the TOPSIS method. This method analyzes the necessary parameters in an integrated manner to maximize relative density while minimizing surface roughness. It is aimed at improving both important properties of the production process simultaneously. The formulas required in the TOPSIS method were used from the work of [PERSON] et al. [14]. The values calculated in the use of the TOPSIS method are given in Table 6. The weight values for surface roughness and relative density were determined as 0.5 for each. Positive and negative ideal solutions for each response are given in Table 7. When Table 6 is examined, it is seen that the closest value to the ideal solution is 0.9729, and the optimum result is obtained in experiment number 2. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{1}{c}{**Normalized Data**} & \multicolumn{2}{c}{**Weighted Normalized Data**} & \multicolumn{1}{c}{**Si+**} & \multicolumn{1}{c}{**Si-**} & \multicolumn{1}{c}{**Ci +**} & \multicolumn{1}{c}{**Rank**} \\ \hline
**Ra** & **Rd** & **Ra** & **Rd** & & & \\ \hline
0.160028 & 0.358107 & 0.080014 & 0.179054 & 0.009423 & 0.136394 & 0.9354 & 2 \\ \hline
0.141217 & 0.351155 & 0.070609 & 0.175577 & 0.004054 & 0.145631 & **0.9729** & **1** \\ \hline
0.360383 & 0.349025 & 0.180192 & 0.174512 & 0.109703 & 0.036154 & 0.2479 & 4 \\ \hline
0.42758 & 0.357071 & 0.21379 & 0.178535 & 0.143186 & 0.008007 & 0.0530 & 7 \\ \hline
0.325795 & 0.359262 & 0.162897 & 0.179631 & 0.092289 & 0.053979 & 0.3690 & 3 \\ \hline
0.432328 & 0.353081 & 0.216164 & 0.176541 & 0.145588 & 0.005652 & 0.0374 & 8 \\ \hline
0.421714 & 0.358586 & 0.210857 & 0.179293 & 0.140249 & 0.00994 & 0.0662 & 5 \\ \hline
0.413346 & 0.341778 & 0.206673 & 0.170889 & 0.136345 & 0.009491 & 0.0651 & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Values calculated with TOPSIS method. Figure 7: Effects of production parameters on surface roughness and relative density.