## 3 Results and Discussion
### Discussion  
The methods and scenarios examined in this study reveal how optimization performance varies under different conditions. While the study by [PERSON], [PERSON], and [PERSON] [31] used only the ABC algorithm, which provided satisfactory results for the given problem, the CSA and MDE methods achieved significantly better outcomes as the complexity of the problem increased. Across all three scenarios, MDE consistently delivered the best performance both in terms of maximum vehicle placement and computational speed. The CSA followed MDE as the second most successful method overall, demonstrating strong and stable performance, particularly in Scenarios 1 and 2. PPSO also performed better than PSO in all tested scenarios, indicating the advantage of this modern variant. ABC demonstrated stable performance in simpler scenarios and outperformed GWO, HHO, PSO, and PPSO in terms of vehicle placement frequency and success rates. However, HHO was able to surpass ABC in Scenario 2 in terms of maximum vehicle count, despite its longer computation time. The MDE algorithm demonstrated clear superiority over other methods in terms of both computation time and robustness across all scenarios, positioning it as a strong candidate for future research on similar problems. Additionally, MDE and the CSA, which yielded successful results in this study, require minimal parameter tuning, apart from setting the population size and iteration count. One of the key findings of this study is that such complex optimization problems can be solved efficiently and that the choice of method plays a crucial role in both solution time and accuracy, as supported by previous research on machine learning model calibration [53]. Apart from their effectiveness and ease of implementation, the underlying structures of MDE and the CSA also offer practical advantages in terms of computational efficiency. PSO and GWO are semi-parallel algorithms in which individual particle or wolf updates can be computed concurrently, though the update of the leader information requires synchronization. In contrast, MDE's multi-population structure is inherently more suitable for parallel computation, and the CSA offers similar advantages. Considering that MDE achieves superior performance in a short period, its efficiency could be further optimized through advanced parallel programming techniques. Furthermore, the improved performance of PPSO compared to PSO suggests that algorithmic refinements can significantly enhance optimization capabilities. PPSO's phase-based dynamics enabled better convergence behavior, particularly in scenarios where  
Figure 5: Example of block division for optimization in large parking areas (source: author’s own elaboration). precise spatial coordination was required. These findings underscore the value of employing enhanced or hybrid versions of established methods in similar applications. This research makes a significant contribution to the literature by addressing how to maximize the utilization of available space in unmarked parking areas. By utilizing the Janowski, Husrevoglu, and Renigier-Bilozor [31] framework, a comparative analysis of different vehicle types, parking area types, and optimization methods was conducted. As one of the few studies focused on this problem, this work provides a new perspective on vehicle placement optimization. In addition to maximizing capacity, several other factors should be considered to enhance the applicability and reliability of the system. For instance, in sloped environments, placing vehicles perpendicular to the direction of the incline may lead to safety concerns, reduced stability, or maneuvering difficulties. Assigning preferred or constrained rotation angles based on local terrain slope could improve both safety and spatial feasibility. This information could be derived automatically from external geospatial sources such as digital elevation models or three-dimensional point clouds or entered manually if unavailable.