## 3 Results
### Case Study 3: Optimal Redesign of a Robotic Screwing Cell  
This RC is designed to perform a screwing operation across six workstations, which are arranged within a front-facing fixture area. Table 7 presents the dimensions of each workstation. The system uses a four-axis SCARA robot, (RH-6 CRH6020-D, Mitsubishi Electric, Tokyo, Japan), which operates exclusively within the front area where the fixture is located. As a result, no rear exclusion zone is considered in this configuration. Figure 12 shows the general specifications of the robot used in this cell.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Trajectory**} & **Current Transfer** & **AG + MRT** & **AG + ACO** \\  & **Time (s)** & **Transfer Time (s)** & **Transfer Time (s)** \\ \hline
1 to 3 & 2.78 & 2.50 & 2.33 \\
2 to 3 & 2.61 & 2.02 & 1.93 \\
4 to 3 & 2.90 & 2.45 & 2.30 \\
5 to 3 & 2.41 & 1.89 & 1.80 \\ Total Time & 10.70 & 8.86 & 8.36 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Cycle time comparison in the assembly cell: current configuration, simulation-based estimate, and ACO result.  
Figure 11: Optimized layout of the assembly RC obtained using the GA.  
Figure 13 shows the current layout of the RC dedicated to the screwing process. The operational area measures 352 mm in width and 403 mm in length, resulting in a total area of 0.142 m\({}^{2}\).  
Figure 14 shows the resulting configuration after applying the GA to the screwing RC. In this new layout, the workstations were redistributed to achieve a more compact and efficient arrangement. The resulting dimensions are 345 mm by 345 mm, which corresponds to a total area of 0.12 m\({}^{2}\), resulting in a 15.49% reduction in occupied area.  
\begin{table}
\begin{tabular}{c c c} \hline
**Stations** & **Length (mm)** & **Width (mm)** \\ \hline Station 1 & 175 & 80 \\ Station 2 & 170 & 85 \\ Station 3 & 140 & 120 \\ Station 4 & 195 & 180 \\ Station 5 & 170 & 34 \\ Station 6 & 120 & 60 \\ \hline \end{tabular}
\end{table}
Table 7: Dimensions of robotic screwing cell.  
Figure 12: Mitsubishi Electric RH-6 CRH6020-D robot installed in the robotic screwing cell with its main technical specifications.  
Figure 13: Current layout of the RC used for the screwing process.  
In the first two case studies (machining and assembly), the working order of the stations was predefined. Therefore, the optimization focused solely on improving the spatial distribution of the workstations and the robot's trajectory. In contrast, in the third case (screwing), there was no predetermined sequence for visiting the workstations. This allowed the algorithm to freely modify the execution order, adding an additional layer of optimization by reorganizing both the station layout and the operation sequence to minimize the total cycle time. Table 8 presents the results obtained after applying the ACO to the optimized configuration of the screwing RC.  
In the current configuration, the total transfer time is 11.63 s. By applying the GA to redesign the layout and estimate the times using Mitsubishi RT TOOLBOX3 PRO software (GA + MRT), the total time was reduced to 9.60 s, representing a 17.45% improvement over the original configuration. An additional improvement was achieved by applying the ACO algorithm to the layout, reaching a total time of 9.26 s. This represents a total cycle time reduction of 20.38% compared to the original setup.  
It is important to note that the new execution order of the stations contributed to shortening trajectories and generating a more logical flow within the fixture area, something that was not possible in the previous case studies where the station order was predefined.