## 6 Numerical Experiments
### Analysis of Results

Table 10: The experimental results obtained by all algorithms for the first dataset of the larger-sized problem. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & **GA** & **PSO** & **SSO1** & **SSO2** & **SSO3** & **SSO4** & **SSO5** & **SSO6** & **SSO7** \\ \hline  & T & 30.015 & 30.032 & 30.019 & 30.012 & 30.019 & 30.014 & 30.018 & 30.019 & 30.017 \\  & F & 9978 & 9845 & 9981 & **9983** & **9983** & **9983** & **9983** & **9983** & **9983** & **9983** \\ MAX & Best & 209 & 2 & 2041 & 2733 & 2158 & 2574 & 2596 & 2391 & 1907 \\  & Ngen & **2959** & 1640 & 2756 & 2817 & 2775 & 2783 & 2812 & 2772 & 2783 \\  & Cost & 1686 & **2191** & 1840 & 1818 & 1833 & 1841 & 1847 & 1792 & 1808 \\  & T & 30 & 30 & 30 & 30 & 30 & 30.001 & 30 & 30 \\  & F & **9978** & 9745 & **9978** & **9978** & **9978** & **9978** & **9978** & **9978** & **9978** \\ MIN & Best & 1 & 0 & 677 & 538 & 350 & 148 & 764 & 510 & 554 \\  & Ngen & 1548 & 873 & 1477 & 1502 & 1489 & 1491 & 1498 & 1477 & 1494 \\  & Cost & 1666 & 1828 & 1648 & 1636 & 1613 & 1634 & 1641 & 1620 & 1592 \\  & T & 30.0052 & 30.00927 & 30.00637 & 30.00527 & 30.00647 & 30.00663 & 30.0062 & 30.00567 & 30.00687 \\  & F & 9978 & 9789.267 & 9978.3 & **9980.1** & 9978.267 & 9979.6 & 9978.433 & 9978.767 & 9978.4 \\ AVG & Best & 19.23333 & 11.3333 & 1155.067 & 1212.367 & 1178.033 & 872.4667 & 1164.867 & 1213 & 1255 \\  & Ngen & 2657.467 & 1491.2 & 2468.967 & 2549.4 & 2519.267 & 2527.5 & 2531.967 & 2503.5 & 2530.467 \\  & Cost & 1683.067 & 2069.567 & 1736.867 & 1720.667 & 1725.4 & 1741.1 & 1739.233 & 1721.7 & 1716.3 \\  & T & 0.004318 & 0.007674 & 0.005 & 0.003723 & 0.004455 & 0.004165 & 0.004021 & 0.005435 & 0.00471 \\  & F & **0** & 27.33185 & 0.915386 & 2.354013 & 0.980265 & 2.23761 & 1.356551 & 1.654322 & 1.132589 \\ STD & Best & 56.19896 & 0.434172 & 312.2639 & 595.2987 & 366.6347 & 719.0704 & 364.0858 & 368.7952 & 273.7001 \\  & Ngen & 525.0898 & 280.644 & 479.5429 & 473.2856 & 466.1362 & 470.4982 & 468.2634 & 463.8382 & 467.6395 \\  & Cost & 4.15172 & 87.34619 & 44.09921 & 40.41111 & 49.08304 & 40.95948 & 47.64718 & 44.49963 & 53.89079 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: The experimental results obtained by all algorithms for the third dataset of the larger-sized problem. Figure 3: Boxplot of the sensor coverage (fitness function value) among all algorithms for the small-sized problem. (**a**) The first dataset. (**b**) The second dataset. (**c**) The third dataset. Secondly, for the middle-sized problem, the experimental results in terms of the fitness function value (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 7-9 and Figures 5 and 6 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-SSO7 is **9983**, which is the best among all algorithms for the first dataset of the middle-sized problem as shown in Table 7 and Figure 5a. 2. The best solution (MAX) of the fitness function value (F) obtained by GA and SSO1-SSO7 is **9983**, which is the best among all algorithms for the second dataset to the third dataset of the middle-sized problem as shown in Tables 8 and 9 and Figure 5b,c. 3. The average (AVG) fitness function values (F) obtained by SSO2, SSO4, and SSO4 are **9979.767**, **9979.9**, and **9980.633**, which are the best among all algorithms for the first dataset to the third dataset of the middle-sized problem, respectively, as shown in Tables 7-9. Figure 4: Boxplot of the run time among all algorithms for the small-sized problem. (**a**) The first dataset. (**b**) The second dataset. (**c**) The third dataset. For the run time (T):  
1.