# Continuous Space Wireless Communication Tower Placement by Hybrid Simulated Annealing
## 5 Experimental Analysis
### Exploration and Exploitation Capacities
If the hybrid SA finds a solution that does not cover any user in any of the three regions, then we know that the hybrid SA did not explore all the promising regions and, therefore, its exploration capacity is of concern. If the hybrid SA finds a solution that covers at least one user in each of the regions but does not cover all or the majority of the users in the regions, then we know the hybrid SA explores all the promising regions but cannot exploit well in the regions. If the hybrid SA can find the optimal or a near-optimal solutionfor the test problem, then it indicates that both the exploration capacity and the exploitation capacity of the hybrid SA are fine. Using the aforementioned test problem generation ideas, we developed a program and used it to randomly generate two classes of test problems. In one class of test problems, the number of wireless communication towers was fixed at 10, but the number of users in the test problems ranged from 100 to 1000 with increments of 100. In the other class of test  
Figure 6: The process of generating a wireless communication tower placement problem with known promising regions and an optimal solution. In the figure, ‘\(\times\)’ represents the location of a wireless communication tower, and ‘\(\circ\)’ stands for the location of a user, and a large broken line circle shows the coverage of a wireless communication tower. problems, the number of users was fixed to 500, but the number of wireless communication towers varied from 10 to 100 with increments of 10. Parameter \(d_{max}\) was set to 70 in all test problems. The reasons for generating the two classes is that the size of a test problem depends on both the number of wireless communication towers and the number of users and we are interested in how the computation time of the hybrid SA increases when the number of wireless communication towers increases and how the computation increases when the number of users grows in addition to the exploration and exploitation capacities of the hybrid SA. For each of the parameter configurations, we randomly generated 30 different instances in order to make sure that the experimental results were statistically significant, and for each of the instances, we used the hybrid SA algorithm to solve it. The ratio of the number of users covered by the wireless communication towers in the solution generated by the hybrid SA and the total number of users, namely, _coverage rate_, was recorded. The coverage rate indicates both the exploration capacity and the exploitation capacity of a search algorithm. Table 1 shows the statistics of the experimental results for the two classes of test problems. The top 10 rows in the table show the statistics of the experimental results for the first class of test problems, and the bottom 10 rows show the statistics for the experimental results of the second class of test problems. Each row shows the statistics of 30 runs for 30 different test problems with the same configuration. The total number of test problems was 600. It can be seen from Table 1 that, among the 600 tests, the hybrid SA found an optimal solution for the test problem and that, in the worst scenario, the hybrid SA still found a solution with a coverage ratio of 0.96. Thus, it can be concluded that both the exploration capacity and the exploitation capacity of the hybrid SA are excellent, as the hybrid SA explored all the promising search areas for each of the test problems and found almost all the users in each of the promising regions. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Index**} & \multirow{2}{*}{**Towers (\#)**} & \multirow{2}{*}{**Users (\#)**} & **Ave** & **Best** & **Worst** & **Standard** \\  & & & **Coverage** & **Coverage** & **Coverage** & **Coverage** & **Deviation** \\  & & & **Rate** & **Rate** & **Rate** & **Rate** \\ \hline
1 & 10 & 100 & 0.997 & 1.00 & 0.97 & 0.0084 \\
2 & 10 & 200 & 0.997 & 1.00 & 0.98 & 0.0061 \\
3 & 10 & 30