## 3 Results
### Case Study 2: Evolutionary Optimization in a Robotic Assembly Cell  
The RC dedicated to the assembly process consists of five workstations arranged around an industrial robot. The central station (Cell #3) is where the assembly takes place, while the remaining stations hold the parts to be assembled. Once the process is completed, the finished product is removed by an external system.  
Table 5 shows the dimensions of each workstation, which serve as reference data for applying the proposed optimization methodology. The total dimensions of the cell are 1305 mm in length and 1180 mm in width, resulting in a total operational area of 1.54 m\({}^{2}\). The exclusion zone of the robot base has a radius of 395 mm.  
This RC is equipped with a Mitsubishi Electric RV-7 FRD industrial robot (Mitsubishi Electric, Tokyo, Japan), a six-axis vertical-type model installed on the floor. This robot  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Trajectory**} & **Current Transfer** & **AG + MRT Transfer** & **AG + ACO Transfer** \\  & **Time (s)** & **Time (s)** & **Time (s)** \\ \hline
1 to CNC & 4.56 & 4.46 & 4.12 \\
2 to CNC & 3.45 & 2.57 & 2.37 \\
3 to CNC & 3.89 & 4.03 & 3.71 \\
4 to CNC & 3.71 & 2.78 & 2.57 \\ Total Time & 15.61 & 13.84 & 12.77 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Cycle time comparison between the current configuration, optimization AG and simulation software, and the ACO result.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Stations**} & **Length (mm)** & **Width (mm)** \\ \hline Assembly 3 & 750 & 400 \\ Station 1 & 350 & 325 \\ Station 2 & 400 & 150 \\ Station 4 & 275 & 225 \\ Station 5 & 260 & 197 \\ Robot base & 395 & 395 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Dimensions of robotic assembly cell.  
provides full coverage around its base, as it has a 240\({}^{\circ}\) operating range in both directions, allowing it to easily access workstations distributed throughout its surroundings. It features a radial reach of 713.4 mm, a maximum operating speed of 11,064 mm/s, and a repeatability of \(\pm\)0.02 mm.  
The technical specifications of the robotic arm, along with an image of the robot installed within the cell, are shown in Figure 9.  
Figure 10 shows the current layout of the RC used for the assembly process. In this configuration, the workstations are arranged in a circular pattern around the robot's base, efficiently leveraging its radial reach to cover the entire operating area.  
Once the GA was executed, a more compact layout was obtained, featuring a linear arrangement that reorganizes the stations into a narrower strip. The new dimensions were 950 mm in width and 1080 mm in length, resulting in a total area of 1.03 m\({}^{2}\), which represents a 33.12% reduction compared to the original design. Figure 11 shows the layout generated by the GA for the assembly RC.  
Figure 10: Current layout of the robotic assembly cell prior to applying the optimization.  
Figure 9: Mitsubishi Electric RV-7 FRD robot installed in the RC with its main technical specifications.  
As in the previous case study, a cycle time comparison was carried out across three scenarios: (1) the current operational time, (2) the estimated time using Mitsubishi RT TOOLBOX3 PRO software with the new layout optimized by the GA, and (3) the optimized time resulting from the application of the ACO algorithm. Table 6 summarizes the results obtained, allowing for a quantitative evaluation of the performance achieved in each case.  
Based on the results obtained, the total transfer time was reduced from 10.70 s in the current configuration to 8.86 s by using the layout generated by the GA and simulated through the Mitsubishi RT TOOLBOX3 PRO software, representing a 17.20% improvement. Subsequently, the implementation of the ACO on the same spatial arrangement further reduced the total time to 8.36 s. Overall, this resulted in a 21.87% reduction in cycle time compared to the original setup.