# Multi-Objective Optimization Study on Production of AlSi10 Mg Alloy by Laser Powder Bed Fusion
## 2 Materials and Methods
### TOPSIS Method: Best Option Approach in Decision-Making Processes  
TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) is an effective method widely used in multi-criteria decision-making processes. This method aims to optimize conflicting performance criteria such as density and surface roughness simultaneously. In the fields of material manufacturing and processing, evaluating these two criteria together is critical for obtaining high-quality and high-performance products.  
The application of the TOPSIS method follows specific steps:  
1. Creating a Decision Matrix: A decision matrix is formed that includes the density and surface roughness values of the alternatives (different production methods or parameter settings). This matrix reflects the measurements of both criteria for each alternative.
2. Normalization: The decision matrix is normalized to eliminate the impact of different scales. This process helps make the alternatives comparable.
3. Weighting: Weights are assigned to the density and surface roughness criteria based on their importance. For example, in some applications, if surface roughness is more critical, a higher weight may be assigned to this criterion.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Experiment** & \multirow{2}{*}{**Laser Power**} & **Hatch** & \multirow{2}{*}{**Scan Speed**} & **Surface** & **Relative** \\
**No.** & & & **Distance** & & **Roughness** & **Density** \\ \hline
1 & 275 & 0.08 & 800 & 5.010667 & 0.991244 \\
2 & 275 & 0.14 & 800 & 4.421667 & 0.972 \\
3 & 200 & 0.08 & 800 & 11.284 & 0.966104 \\
4 & 200 & 0.14 & 800 & 13.388 & 0.988376 \\
5 & 275 & 0.14 & 1400 & 10.201 & 0.994442 \\
6 & 200 & 0.08 & 1400 & 13.53667 & 0.977332 \\
7 & 275 & 0.08 & 1400 & 13.20433 & 0.992571 \\
8 & 200 & 0.14 & 1400 & 12.94233 & 0.946044 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Full factorial experimental design and performance values.  
Figure 3: Weighing the sample in liquid.  
4. Identifying Ideal and Negative Ideal Solutions: From the normalized data, alternatives with the best (ideal) and worst (negative ideal) performance values are identified. The ideal solution represents the highest density and lowest surface roughness, while the negative ideal solution represents the opposite characteristics.
5. Distance Calculation: The distances of each alternative from the ideal and negative ideal solutions are calculated, determining how close the alternatives are to the best solution.
6. Relative Proximity Value: Using the calculated distances, the relative proximity of each alternative to the ideal solution is assessed. This step ensures that both density and surface roughness are considered together.
7. Ranking: Based on the obtained relative proximity values, the alternatives are ranked, and the one with the highest proximity is identified as the most suitable option in terms of density and surface roughness.  
In conclusion, the TOPSIS method provides a comprehensive evaluation by simultaneously optimizing important criteria such as density and surface roughness. This approach systematically streamlines complex decision-making processes, facilitating effective and objective results [14; 15].