## 5 Experimental Result
### Experimental Evaluation  
The average total costs, number of cameras, coverages, and computation times of GA, ULA, and greedy algorithm for 40 experiments are compared in Tables 4-6. Based on the simulation results, it was obvious that the ULA outperforms the GA and greedy algorithm, because the ULA demonstrates a significantly lower average cost and a lower number of cameras. Furthermore, the ULA's average coverage is greater than that of the GA and greedy algorithm for the large-sized, medium-sized, and small-sized problems.  
In the simulation experiment, as the size of the bridges increased, the performance gap--in terms of the computation time and total cost--between the ULA and other algorithms increased significantly. In addition, as the minimum coverage level increased, the GA's computation time and total cost were greater than those of the ULA, though neither algorithm's average computation time changed significantly. In some cases of the greedy algorithm, despite its quick computation time, the total cost increases rapidly as the minimum coverage level increases.  
These simulation results showed that the performance of the GA depended mainly on the quality of the initial population generated by the random algorithm, because the initial solution played an important role in determining the eventual outcome. In addition, the greedy algorithm cannot find a good solution when it fails to find camera placements for covering the remaining surveillance areas effectively. Hence, we concluded that the proposed ULA can achieve a better solution than the GA and greedy algorithm can for the same parameters, computation times, and all problem sizes.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Result types**} & \multicolumn{3}{c}{**Small**} & \multicolumn{3}{c}{**Medium**} & \multicolumn{3}{c}{**Large**} \\ \cline{2-10}  & **Greedy** & **GA** & **ULA** & **Greedy** & **GA** & **ULA** & **Greedy** & **GA** & **ULA** \\ \hline Avg. Computation Time (min) & 0.10 & 6.06 & 3.41 & 0.26 & 8.56 & 5.23 & 0.42 & 10.21 & 6.71 \\ Avg. Number of Cameras & 17.70 & 15.55 & 10.58 & 19.03 & 16.48 & 10.78 & 20.45 & 16.60 & 11.75 \\ Avg. Total Cost (1000 USD) & 145.10 & 150.15 & 101.80 & 155.00 & 155.60 & 102.70 & 165.90 & 156.70 & 112.50 \\ Avg. Coverage (\%) & 91.40 & 90.19 & 90.81 & 91.10 & 90.12 & 90.39 & 91.30 & 90.20 & 90.29 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Results summary (Minimum coverage 90%).  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Result types**} & \multicolumn{3}{c}{**Small**} & \multicolumn{3}{c}{**Medium**} & \multicolumn{3}{c}{**Large**} \\ \cline{2-10}  & **Greedy** & **GA** & **ULA** & **Greedy** & **GA** & **ULA** & **Greedy** & **GA** & **ULA** \\ \hline Avg. Computation Time (min) & 0.07 & 5.81 & 3.40 & 0.17 & 8.09 & 5.20 & 0.29 & 9.88 & 6.66 \\ Avg. Number of Cameras & 12.88 & 9.50 & 8.15 & 14.05 & 9.78 & 8.38 & 14.93 & 11.20 & 9.15 \\ Avg. Total Cost (1000 USD) & 104.20 & 90.95 & 80.00 & 113.00 & 94.05 & 81.65 & 119.70 & 105.90 & 88.70 \\ Avg. Coverage (\%) & 82.50 & 80.63 & 80.98 & 82.10 & 80.64 & 80.97 & 82.00 & 80.57 & 80.56 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Results summary (Minimum coverage 80%).  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Result types**} & \multicolumn{3}{c}{**Small**} & \multicolumn{3}{c}{**Medium**} & \multicolumn{3}{c}{**Large**} \\ \cline{2-10}  & **Greedy** & **GA** & **ULA** & **Greedy** & **GA** & **ULA** & **Greedy** & **GA** & **ULA** \\ \hline Avg. Computation Time (min) & 0.09 & 5.88 & 3.38 & 0.21 & 8.14 & 5.21 & 0.33 & 10.00 & 6.65 \\ Avg. Number of Cameras & 14.75 & 10.50 & 9.00 & 16.20 & 11.10 & 9.18 & 17.1 & 12.55 & 10.30 \\ Avg. Total Cost (1000 USD) & 119.90 & 100.90 & 87.65 & 131.00 & 105.90 & 88.65 & 137.9 & 118.10 & 99.50 \\ Avg. Coverage (\%) & 86.90 & 85.74 & 85.70 & 87.00 & 85.48 & 85.63 & 86.70 & 85.39 & 85.61 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Results summary (Minimum coverage 85%).