## 6 Numerical Experiments
### Analysis of Results  
The descriptive statistics including the maximum (denoted by MAX), i.e., the best solution, minimum (denoted by MIN), average (denoted by AVG), and standard deviation (denoted by STD) of the run time (denoted by T, in seconds), fitness function value (denoted by F), number of generations to obtain the optimal solution (denoted by Best), how many generations were run during the provided time (denoted by Ngen), and total cost (denoted by Cost) were employed for the nine algorithms including GA, PSO, and the proposed bi-tuning SSO including seven SSO variates (denoted by SSO1 to SSO7) and the best solutions compared among the nine algorithms are shown in bold. Hence, the following Tables 4-6 indicate the experimental results obtained by all algorithms for the first dataset to the third dataset of the small-sized problem, Tables 7-9 indicate the experimental results obtained by all algorithms for the first dataset to the third dataset of the middle-sized problem, and Tables 10-12 indicate the experimental results obtained by all algorithms for the first dataset to the third dataset of the larger-sized problem. For a more abundant and detailed analysis of the experimental results, the statistical boxplots of the displayed images were adopted to show the performance including the maximum, interquartile range (75 th percentile, median, and 25 th percentile), and minimum and are shown in Figures 3-8. Figures 3 and 4 indicate the sensor coverage (fitness function value) and run time for all algorithms for the small-sized problem, Figures 5 and 6 indicate the sensor coverage (fitness function value) and run time for all algorithms for the middle-sized problem, and Figures 7 and 8 indicate the sensor coverage (fitness function value) and run time for all algorithms for the larger-sized problem, respectively. Here, for the small-sized problem, the experimental results in terms of the fitness function of sensor coverage (F), the run time (T), the number of generations to obtain the optimal solution (Best), how many generations were run during the provided time (Ngen), and total cost (Cost) obtained by the GA, PSO, and the proposed bi-tuning SSO (SSO1-SSO7) are shown in Tables 4-6 and Figures 3 and 4 and were analyzed as follows: For the fitness function value (F): 1. The best solution (MAX) of the fitness function value (F) obtained by SSO1-SSO6 is **9983**, which is the best among all algorithms for the first dataset of the small-sized problem as shown in Table 4 and Figure 3a. 2. The best solution (MAX) of the fitness function value (F) obtained by GA is **9989**, which is the best among all algorithms for the second dataset of the small-sized problem as shown in Table 5 and Figure 3b. 3. The best solution (MAX) of the fitness function value (F) obtained by SSO1-2 and SSO4-7 is **9983**, which is the best among all algorithms for the third dataset of the small-sized problem as shown in Table 6 and Figure 3c. 4. The average (AVG) of the fitness function value (F) was obtained by SSO4, GA. The AVG values in each database are **9979.83333**, **9981.4**, and **9979.36667**, which are the best among all algorithms for the first dataset to the third dataset of the small-sized problem, respectively, as shown in Tables 4-6. 5. The minimum (MIN) fitness function value (F) obtained by GA, SSO1-5, and SSO7 is **9978**, which is the best among all algorithms for the first dataset of the small-sized problem, as shown in Table 4.
6. The minimum (MIN) fitness function value (F) obtained by GA, SSO1-2, and SSO4-7 is **9978**, which is the best among all algorithms for the second dataset to the third dataset of the small-sized problem, as shown in Tables 5 and 6. 7. The standard deviation (STD) values of the fitness function value (F) obtained by GA, SSO3, and GA are **0**, **1.055364**, and **0**, which are the best among all algorithms for the first dataset to the third dataset of the small-sized problem, respectively, as shown in Tables 4-6. For the run time (T):
1.