## 3 Results and Discussion  
In this section, the performance of the ABC, CSA, GWO, HHO, MDE, PSO, and PPSO algorithms is evaluated across three different parking optimization scenarios. These scenarios represent increasing levels of complexity based on the rotational freedom of vehicles within the parking area. The evaluation criteria include the maximum number of parked vehicles, computation time, and solution consistency. The findings are based on simulation results conducted using real-world parking areas in Kayseri. Each method and scenario was executed 30 times, and the results illustrate performance across repeated trials. The performance outcomes of the implementations are presented in Tables 2-5. Additionally, a graphical comparison of the results for each method is provided in Figure 3. Table 2 presents the number of runs (out of 30) in which each algorithm achieved its maximum number of successfully placed vehicles. The optimization process for each algorithm begins with a low vehicle count and incrementally increases the number until no valid solution can be found. As such, the values in the table indicate how often an algorithm terminated at a specific vehicle count as its best result. Since some algorithms failed to find feasible solutions in certain runs, the total number of successful results is less than 30. For example, ABC, GWO, HHO, and PPSO achieved valid placements in only a limited number of runs due to the complexity of the scenarios. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Vehicles Count** & **ABC** & **CSA** & **GWO** & **HHO** & **MDE** & **PSO** & **PPSO** \\ \hline \multicolumn{8}{c}{Scenario 1 (Parking Area 1—Without Rotation)} \\ \hline
10 & 6 & 0 & 10 & 13 & 0 & 6 & 12 \\
11 & 22 & 2 & 8 & 4 & 3 & 4 & 4 \\
12 & 2 & 22 & 2 & 0 & 12 & 0 & 4 \\
13 & 0 & 6 & 0 & 0 & 15 & 0 & 0 \\ \hline \multicolumn{8}{c}{Scenario 2 (Parking Area 1—Optimization up to 45 Degrees)} \\ \hline
10 & 3 & 0 & 0 & 6 & 1 & 0 & 3 \\
11 & 0 & 10 & 0 & 1 & 3 & 0 & 0 \\
12 & 0 & 17 & 0 & 0 & 13 & 0 & 0 \\
13 & 0 & 3 & 0 & 0 & 13 & 0 & 0 \\ \hline \multicolumn{8}{c}{Scenario 3 (Parking Area 2—Optimization between 0 and 180 Degrees)} \\ \hline
7 & 1 & 0 & 7 & 3 & 4 & 1 & 13 \\
8 & 21 & 20 & 3 & 0 & 12 & 0 & 2 \\
9 & 8 & 10 & 0 & 0 & 13 & 0 & 1 \\
10 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Frequency table for the maximum number of successfully placed vehicles over 30 runs for each algorithm (source: author’s own elaboration). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Vehicles Count** & **ABC** & **CSA** & **GWO** & **HHO** & **MDE** & **PSO** & **PPSO** \\ \hline \multicolumn{6}{c}{Scenario 1 (Parking Area 1—Without Rotation)} \\ \hline
10 & 6.20 & 7.25 & 37.27 & 128.67 & 3.65 & 1.54 & 16.08 \\
11 & 18.97 & 15.73 & 45.77 & 188.51 & 6.31 & 3.16 & 25.07 \\
12 & 36.19 & 28.42 & 54.32 & Failed & 10.40 & Failed & 69.05 \\
13 & Failed & 36.68 & Failed & Failed & 19.21 & Failed & Failed \\ \hline \multicolumn{6}{c}{Scenario 2 (Parking Area 1—Optimization up to 45 Degrees)} \\ \hline
10 & 14.44 & 10.94 & Failed & 158.64 & 3.00 & Failed & 46.18 \\
11 & Failed & 21.45 & Failed & 260.72 & 4.75 & Failed & Failed \\
12 & Failed & 36.66 & Failed & 9.03 & Failed & Failed \\
13 & Failed & 42.21 & Failed & 13.05 & Failed & Failed \\ \hline \multicolumn{6}{c}{Scenario 3 (Parking Area 2—Optimization between 0 and 180 Degrees)} \\ \hline
7 & 3.00 & 6.26 & 14.66 & 34.22 & 1.94 & 12.66 & 30.92 \\
8 & 6.76 & 13.57 & 29.15 & Failed & 3.42 & Failed & 26.97 \\
9 & 14.91 & 27.88 & Failed & Failed & 5.57 & Failed & 69.63 \\
10 & Failed & Failed & Failed & 9.65 & Failed & Failed \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mean computation time (in seconds) per trial for each vehicle count in placement optimization (source: author’s own elaboration).