## 4 Discussion  
The results obtained in this study validate the effectiveness of the proposed methodology based on evolutionary algorithms for the simultaneous redesign of the workspace and the kinematic flow in industrial RC. The methodology was applied to three representative case studies, and in all three scenarios, a significant improvement was observed in key performance indicators such as occupied area and total cycle time. One of the main strengths of the approach lies in its ability to address a multi-objective optimization problem through a sequential approximation strategy; GA reconfigures the spatial arrangement of workstations by minimizing the occupied area, while ACO optimizes the robot's trajectory over the resulting layout by minimizing transfer time. This decomposition makes it possible to efficiently address a complex combinatorial problem with nontrivial geometric and kinematic constraints. In industrial environments, where physical redesign is both costly and disruptive, this computational strategy offers a scalable, viable, and low-cost solution. From an operational perspective, the methodology proved sufficiently robust across different topological configurations of RC, successfully adapting to circular, linear, and matrix-like layouts. Moreover, the incorporation of geometric constraints, such as exclusion zones and robot reach limitations, was effectively managed through parametric modeling of the workspace, confirming its applicability in contexts with strict spatial restrictions. Furthermore, the optimized trajectories were validated and benchmarked using Mitsubishi RT TOOLBOX3 PRO, a widely adopted industrial simulation platform. This step confirmed that the proposed solutions are not only theoretically feasible but also executable under real-world constraints, reinforcing the operational relevance of the methodology. In practical terms, the incorporation of geometric and kinematic constraints, such as robot reach limits, exclusion zones, and layout boundaries, was critical to ensure the feasibility of the proposed solutions. These boundary conditions, derived from the physical configuration and operational requirements of each cell, shaped the design space explored by the algorithms. Their integration into the optimization framework not only guaran \begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Case Study**} & \multirow{2}{*}{**Area Reduction (\%)**} & **Transfer Time** & **Transfer Time** \\  & & **Reduction with** & **Reduction with** \\  & & **GA + MRT (\%)** & **GA + ACO (\%)** \\ \hline Case Study 1 & 14.97 & 11.34 & 18.19 \\ Case Study 2 & 33.12 & 17.20 & 21.87 \\ Case Study 3 & 15.49 & 17.44 & 20.38 \\ Average & 21.19 & 15.33 & 20.15 \\ \hline \end{tabular}
\end{table} 
Table 9: Quantitative comparison of the three case studies: area and cycle time reduction. teed collision-free configurations but also enhanced the applicability of the method to real-world scenarios. However, some inherent limitations of the current approach were identified. First, the model assumes deterministic and static operating conditions, excluding potential disruptions typical of flexible manufacturing environments, such as variable cycle times or dynamic changes in task sequencing. The integration of robust or stochastic optimization models could significantly broaden the applicability of the proposed framework. Second, the computational cost associated with the evolutionary search process, particularly in scenarios involving many stations or possible routes, can become substantial. While computational times were acceptable for the case studies presented, future applications in large-scale cells or systems involving multiple concurrent robots may require the adoption of acceleration techniques such as GPU-based parallelization, pruning heuristics, or hybrid methods incorporating machine learning. Another critical aspect is the complexity involved in tuning the parameters of evolutionary algorithms. The performance of such algorithms is highly sensitive to the choice of parameters.