## 3 Results
### Selecting a Solution on the Pareto Front  
To assist stakeholders in selecting the most appropriate solution from the Pareto front, the following strategies were applied to the final population:  
* Solution closest to the ideal point: This solution offers the best trade-off between minimal area utilization, improved worker well-being, and the shortest walking distance. This method focuses on achieving optimal outcomes across all objectives while maintaining balance between the objectives [28].
* Solution furthest from the nadir point: This solution, although having the largest area utilization, was furthest from the nadir point. It maintained acceptable worker well-being and minimized walking distance. This solution may be preferable when prioritizing the avoidance of poor outcomes across objectives [28].
* Best solution along the ideal nadir vector: The solution selected is the one that lies closest to the ideal point along this vector, which signifies a strong compromise between competing objectives. This solution provides stakeholders with a balanced approach, where the trade-offs between objectives are well-managed, making it a suitable option when neither extreme (ideal or nadir) is perfectly attainable [28].  
Figure 5 illustrates generation 15, showcasing the Pareto front along with all solutions of the solution search space. The gray points represent all the solutions tested by the NSGA-II algorithm, while the green points highlight the Pareto front solutions. The mesh binding these points visually represents the trade-offs among objectives.  
Figure 5: Three-dimensional representation of generation 15, showing the Pareto front, ideal point, nadir point, ideal nadir vector, and tested solutions. The ideal point (blue) and nadir point (purple) are marked, with the ideal nadir vector presented in red. Solution 2466 (orange), which is furthest from the nadir, and Solution 2808 (yellow), which is closest to the ideal point and ideal nadir vector, are also highlighted.  
The calculated nadir point is marked in purple, while the ideal point is indicated in blue. The solution furthest from the nadir point is shown in orange, and the solution closest to the ideal point is in red. The solution closest to the ideal nadir vector is marked in yellow. This visualization helps stakeholders identify which solutions optimize multiple objectives and which ones offer more robust, risk-averse trade-offs.  
The solution closest to the ideal point, which was also the solution closest to the ideal nadir vector (solution 2808), and the solution furthest from the nadir point (solution 2466), were both further evaluated for system performance using additional metrics (Figure 6). However, it is important to note that this alignment between the solution closest to the ideal point and the one closest to the ideal nadir vector is not guaranteed in every case and may vary depending on the nature of the Pareto front in different optimization runs.  
System Performance Measures  
As shown in Figure 6, the system performance metrics for both solutions are evaluated based on Green time, Yellow time, and Red time:  
* Solution 2466 exhibits the longest Green time at 23%, meaning it allocates slightly more time to value-adding tasks than Solution 2808, which has 21% Green time;
* Solution 2808 shows a slightly longer Red time (59%) compared with Solution 2466 (55%). Minimizing Red time is crucial as it corresponds to wasted time in the layout, particularly walking distance;
* Solution 2466 exhibits longer Yellow time (22%) compared with solution 2808 (20%).  
Since solution 2808 has a slightly longer distance walked (37.80 m) compared with solution 2466 (36.3 m), it is expected the Red time is longer for solution 2808.