## 6 Numerical Experiments
### Analysis of Results
The best solution (MAX), average (AVG), and minimum (MIN) for the run time (T) obtained by all 9 algorithms are around 30 s for the first dataset to the third dataset of the middle-sized problem, respectively, as shown in Tables 7-9. 2. If it is compared more accurately, the best solution (MAX) for the run time (T) obtained by PSO shows the worst performance because it has the longest time for the first dataset to the third dataset of the middle-sized problem, respectively, as shown in Tables 7-9 and Figure 6.  
For the number of generations to obtain the optimal solution (Best):  
1. The average (AVG) number of generations to obtain the optimal solution (Best) obtained by PSO is around 1 for the first dataset to the third dataset of the middle-sized problem, respectively, as shown in Tables 7-9. In the same run time, the PSO converges faster but the solution is not better, which indicates it is trapped in the local solution and cannot escape. For how many generations were run during the provided time (Ngen):  
1. The best solution (MAX) for how many generations were run during the provided time (Ngen) obtained by GA are **3084**, **2909**, and **2974**, 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. 2. The proposed SSO1-SSO7 represent the update of all variables, meaning that the average run time of each generation is long. In the future, it will be changed to the update of some variables. For the total cost (Cost):  
1. The best solution (MAX) values of the total cost (Cost) obtained by PSO are **2165**, **2189**, and **2172**, which exceed the cost limit of 2000 for the first dataset to the third dataset of the middle-sized problem, respectively, as shown in Tables 7-9. 2. The total cost obtained by GA and the proposed SSO1-SSO7 comply with the cost limit of 2000 for the first dataset to the third dataset of the middle-sized problem, respectively, as shown in Tables 7-9. Finally, for the larger-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 10-12 and Figures 7 and 8 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 larger-sized problem as shown in Table 10 and Figure 7a. 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 of the larger-sized problem as shown in Table 11 and Figure 7b. 3. The best solution (MAX) of the fitness function value (F) obtained by SSO2-SSO7 is **9983**, which is the best among all algorithms for the third dataset of the larger-sized problem as shown in Table 12 and Figure 7c. 4. The average (AVG) fitness function values (F) obtained by SSO4, SSO4, and SSO2 are **9980.6**, **9980.233**, and **9980.1**, which are the best among all algorithms for the first dataset to the third dataset of the larger-sized problem, respectively, as shown in Tables 10-12. 5. The minimum (MIN) fitness function value (F) obtained by GA and SSO1-7 is **9978**, which is the best among all algorithms for the first dataset and the third dataset of the larger-sized problem, as shown in Tables 10 and 12. For the run time (T):  
1. The best solution (MAX), average (AVG), and minimum (MIN) of the run time (T) obtained by all 9 algorithms are around 30 s for the first dataset to the third dataset of the larger-sized problem, respectively, as shown in Tables 10-12. 2.