## 3 Results and Discussion
### Evaluation of Different Vehicle Types and Parking Areas  
Figure 4 presents the best vehicle placement configurations achieved by each method across different scenarios. In Scenario 1, the ABC method utilized the small remaining space at the end of the parking area by placing a Citroen AMI, while the CSA method attempted to fit a standard vehicle within this space by pushing the cost function tolerance limits. Since ABC, GWO, HHO, PSO, and PPSO placed fewer vehicles, they resulted in a more flexible parking arrangement. In contrast, MDE successfully accommodated 13 vehicles. If the small remaining space at the end of the parking area had been used, a second AMI could have increased the total vehicle count to 14. However, to ensure a standard comparison across all methods, only one AMI and one Crafter were included in each scenario. Scenario 1 demonstrated that the Volkswagen Crafter did not pose significant challenges, while Figure 4 highlights the importance of developing flexible solutions for unmarked parking areas.  
According to Figure 4, in Scenario 2, only ABC, CSA, MDE, HHO, and PPSO produced optimal parking arrangements. GWO and PSO failed to generate any feasible solutions within the maximum iteration limit. HHO managed to place 11 vehicles, performing better than ABC and PPSO in terms of capacity, though its layout was more constrained. ABC and PPSO placed two fewer vehicles compared to the CSA and MDE, resulting in a more flexible layout. The CSA, despite maximizing the number of parked vehicles, utilized the tolerance limits, leading to two adjacent vehicles touching each other. Meanwhile, MDE placed the vehicles in a more balanced manner than the CSA. Additionally, both MDE and the CSA positioned the Citroen AMI in the remaining space at the end of the parking area due to its compact dimensions.  
For Scenario 3, Figure 4 indicates that the Volkswagen Crafter was the most challenging vehicle to park. As its length exceeded the perpendicular width of the parking area, it had to be rotated, making it a more complex optimization problem. In this scenario, MDE achieved the highest vehicle placement count with 10 vehicles, but the Crafter's placement remained highly challenging. ABC, the CSA, and PPSO placed up to 9 vehicles, while GWO, PSO, and HHO placed fewer. Although GWO, the CSA, and ABC placed fewer vehicles, they provided relatively more feasible parking arrangements for the Volkswagen Crafter. As seen in Figure 4, while MDE managed to fit 10 vehicles, it resulted in a more constrained parking scenario for the Crafter. PSO and HHO placed only 7 vehicles but still failed to provide a more spacious arrangement. When comparing different methods, ABC, the CSA, and GWO produced more accessible parking layouts, which facilitated easier entry and exit. Although MDE achieved the highest vehicle capacity, it did so by minimizing the space between Citroen AMI and Volkswagen Crafter, utilizing the cost function's tolerance limits. It is suggested that MDE's performance could be further improved by reducing the tolerance threshold, allowing for a more precise solution. Alternatively, MDE could be adjusted to place fewer vehicles, avoiding excessive space constraints.  
Unmarked parking areas are not limited to roadside parking; they are also commonly used in temporary market areas, concert venues, and large open spaces. The proposed optimization framework can be applied to such large parking areas. In these cases, the parking area can be divided into predefined blocks, enabling the framework presented in this study to be executed simultaneously or separately for each block. Figure 5 provides a conceptual representation of the block-based approach for large parking areas.  
Figure 4: Best parking arrangements achieved by each optimization method (source: author’s own elaboration).