## 3 Results
### Case Study 1: Optimization of a Robotic Machining Cell  
The CNC machining center is designed to manufacture three different types of shafts, each with variations in length and diameter. The RC is composed of one input station, where raw parts are loaded, and three output stations, where the finished products are placed and classified according to the type of shaft produced. The CNC machine includes a circular exclusion zone that the robot cannot reach due to its proximity to the base, which is modeled as a square-shaped area. Table 3 presents the dimensions of each workstation, which will be used as a reference for applying the proposed optimization methodology. The RC is equipped with a six-axis industrial robot (RV8 CRLD-S15 M, Mitsubishi Electric, Tokyo, Japan), specifically designed for handling tasks in confined spaces. This unit supports a payload of up to 8 kg, provides a maximum reach of 931 mm, and features a repeatability of \(\pm\)0.02 mm, making it suitable for precision operations in compact environments. Figure 6 shows the robot installed within the RC, along with the technical specifications required as input for the proposed algorithm. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Stations** & **Length (mm)** & **Width (mm)** \\ \hline CNC & 750 & 600 \\ Station 1 & 350 & 325 \\ Station 2 & 400 & 150 \\ Station 3 & 275 & 225 \\ Station 4 & 260 & 197 \\ Robot base & 300 & 300 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Dimensions of machining stations. Figure 6: RV-8 CRL-D industrial robot installed in the RC with technical specifications used in the optimization model. For this case study, the maximum workspace considered by the algorithm corresponds to the current layout of the RC, since the objective is to optimize this arrangement by reducing the utilized area. The operational environment measures 847.5 mm in width and 1737 mm in length, representing a total area of 1.47 m\({}^{2}\). Based on the input parameters, which include the current spatial arrangement of the workstations and the kinematic capabilities of the robot, the proposed optimization methodology was executed. Figure 7 shows the current configuration of the RC prior to the application of the optimization. The GA evaluated multiple possible configurations within the defined workspace, considering both geometric constraints and efficiency criteria related to the robot's movement. As a result, a new, more compact workstation layout was obtained, allowing the robot to access all stations without excessive trajectories or collisions. The final configuration occupies an area of 750 mm by 1634 mm (equivalent to 1.25 m\({}^{2}\)), representing a 14.97% reduction compared to the original area. Figure 8 shows this optimized layout generated by the GA.  
After determining the optimal spatial configuration of the RC using the GA, the ACO was applied to compute the robot's shortest trajectory between stations. To quantify its  
Figure 8: Optimized layout of the RC after applying for the GA.  
Figure 7: Current configuration of the machining RC, showing the spatial layout of workstations and the maximum workspace considered for optimization. performance, a comparative assessment was conducted across three reference scenarios: (1) the actual cycle time recorded during the current operation of the cell, (2) the cycle time estimated by the Mitsubishi RT TOOLBOX3 PRO simulation software using the new layout, and (3) the optimized cycle time resulting from the execution of the ACO algorithm on the same configuration. Table 4 summarizes the results obtained in each case, providing a quantitative evaluation of the improvements achieved by the ACO in terms of cycle time reduction. This comparison serves to validate the efficiency of the proposed model with respect to conventional simulation-based approaches. The results presented in Table 4 reveal a substantial improvement in the performance of the RC following the application of the proposed optimization methodology.