## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & \begin{tabular}{c} **Maximum** \\ **Vehicles Count** \\ \end{tabular} & \
\begin{tabular}{c} **Mean Solution** \\ **Time (Second)** \\ \end{tabular} &
\begin{tabular}{c} **Mean Cumulative** \\ **Maximization Time (Second)** \\ \end{tabular} \\ \hline \hline \multicolumn{6}{c}{Scenario 1 (Parking Area 1—Without Rotation)} \\ \hline ABC & 12 & 36.19 & 59.08 \\ CSA & 13 & 36.68 & 86.03 \\ GWO & 12 & 54.32 & 127.93 \\ HHO & 11 & 188.51 & 350.69 \\ MDE & 13 & 19.21 & 40.68 \\ PSO & 11 & 3.16 & 4.58 \\ PPSO & 12 & 69.06 & 101.19 \\ \hline \multicolumn{6}{c}{Scenario 2 (Parking Area 1—Optimization up to 45 Degrees)} \\ \hline ABC & 10 & 14.44 & 14.44 \\ CSA & 13 & 42.21 & 85.63 \\ GWO & Failed & Failed & Failed \\ HHO & 11 & 260.72 & 260.72 \\ MDE & 13 & 13.05 & 29.82 \\ PSO & Failed & Failed & Failed \\ PPSO & 10 & 46.18 & 46.18 \\ \hline \multicolumn{6}{c}{Scenario 3 (Parking Area 2—Optimization between 0 and 180 Degrees)} \\ \hline ABC & 9 & 14.91 & 23.55 \\ CSA & 9 & 27.88 & 50.1 \\ GWO & 8 & 29.15 & 41.08 \\ HHO & 7 & 34.22 & 34.22 \\ MDE & 10 & 9.65 & 19.92 \\ PSO & 7 & 12.66 & 12.66 \\ PPSO & 9 & 69.63 & 69.63 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Maximum number of successfully placed vehicles, mean solution time, and cumulative maximization time (source: author’s own elaboration). Figure 3: Performance comparison of optimization methods (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{8}{c}{Scenario 1 (Parking Area 1—Without rotation)} \\ \hline
12 or 13 & 7\% & 93\% & 7\% & 0\% & 90\% & 0\% & 13\% \\
13 & 0\% & 20\% & 0\% & 0\% & 50\% & 0\% & 0\% \\
12 & 7\% & 93\% & 7\% & 0\% & 90\% & 0\% & 13\% \\
11 & 80\% & 100\% & 33\% & 13\% & 100\% & 13\% & 27\% \\
10 & 100\% & 100\% & 60\% & 57\% & 100\% & 33\% & 67\% \\ \hline \multicolumn{8}{c}{Scenario 2 (Parking Area 1—Optimization up to 45 Degrees)} \\ \hline
12 or 13 & 0\% & 67\% & 0\% & 0\% & 87\% & 0\% & 0\% \\
13 & 0\% & 10\% & 0\% & 0\% & 43\% & 0\% & 0\% \\
12 & 0\% & 67\% & 0\% & 0\% & 87\% & 0\% & 0\% \\
11 & 0\% & 100\% & 0\% & 3\% & 97\% & 0\% & 0\% \\
10 & 10\% & 100\% & 0\% & 23\% & 100\% & 0\% & 10\% \\ \hline \multicolumn{8}{c}{Scenario 3 (Parking Area 2—Optimization between 0 and 180 Degrees)} \\ \hline
10 & 0\% & 0\% & 0\% & 0\% & 3\% & 0\% & 0\% \\
9 & 27\% & 33\% & 0\% & 0\% & 47\% & 0\% & 3\% \\
8 & 97\% & 100\% & 10\% & 0\% & 87\% & 0\% & 10\% \\
7 & 100\% & 100\% & 23\% & 10\% & 100\% & 3\% & 53\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Success rate distribution over 30 runs (source: author’s own elaboration). In Tables 3 and 4, the mean solution time refers to the average computation time required by each algorithm to successfully place a specific number of vehicles over 30 independent runs. The mean cumulative maximization time represents the average total time taken by the algorithm throughout the incremental optimization process, in which the number of vehicles is gradually increased until no feasible solution can be found. This metric provides insight into the overall computational cost of reaching the optimal placement result.