## 6 Numerical Experiments
### Analysis of Results
The best solution (MAX), average (AVG), and minimum (MIN) run time (T) obtained by all 9 algorithms is around 30 s for the first dataset to the third dataset of the small-sized problem, respectively, as shown in Tables 4-6. 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 small-sized problem, respectively, as shown in Tables 4-6 and Figure 4. For the number of generations obtains 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 small-sized problem, respectively, as shown in Tables 4-6. 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 solutions (MAX) of how many generations were run during the provided time (Ngen) obtained by GA are **3018**, **2959**, and **3021**, 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. 2. The proposed SSO1-SSO7 are the updates of all variables, showing 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 **2197**, **2182**, and **2200**, which exceed the cost limit of 2000 for the first dataset to the third dataset of the small-sized problem, respectively, as shown in Tables 4-6. 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 small-sized problem, respectively, as shown in Tables 4-6. ==ERROR: No output for this page== \begin{table} \
\begin{tabular}{c c c c c c c c c c c} \hline  & & **GA** & **PSO** & **SSO1** & **SSO2** & **SSO3** & **SSO4** & **SSO5** & **SSO6** & **SSO7** \\ \hline  & T & 30.008 & 30.016 & 30.011 & 30.01 & 30.01 & 30.01 & 30.011 & 30.011 & 30.011 \\  & F & 9981 & 9821 & **9983** & **9983** & **9983** & **9983** & **9983** & **9983** & **9983** & **9983** \\ MAX & Best & 2177 & 2 & 2375 & 2712 & 2159 & 2672 & 2457 & 2190 & 2327 \\  & Ngen & **3140** & 1648 & 2752 & 2820 & 2789 & 2771 & 2795 & 2761 & 2790 \\  & Cost & 1768 & **2196** & 1816 & 1815 & 1813 & 1795 & 1776 & 1884 & 1821 \\  & T & 30 & 30 & 30 & 30 & 30 & 30 & 30 & 30 \\  & F & **9978** & 9735 & **9978** & **9978** & **9978** & **9978** & **9978** & **9978** & **9978** \\ MIN & Best & 1 & 1 & 325 & 67 & 206 & 251 & 396 & 511 & 471 \\  & Ngen & 2722 & 1569 & 2632 & 2676 & 2659 & 2667 & 2668 & 2640 & 2673 \\  & Cost & 1622 & 1962 & 1629 & 1636 & 1647 & 1659 & 1623 & 1622 & 1650 \\  & T & 30.00393 & 30.0088 & 30.00623 & 30.00503 & 30.00503 & 30.00587 & 30.00533 & 30.00547 & 30.00433 \\  & F & 9978.3 & 9777 & 9979.067 & 9979.833 & 9978.433 & **9980.6** & 9978.667 & 9979.833 & 9978.567 \\ AVG & Best & 94.83333 & 1.2 & 1303.767 & 1127.133 & 1265.567 & 985.7667 & 1213.833 & 1245.967 & 1179.167 \\  & Ngen & 2913.6 & 1604.933 & 2696.867 & 2751.233 & 2717.533 & 2724.3 & 2725.3 & 2700.033 & 2735 \\  & Cost & 1709.5 & 2104.5 & 1723.033 & 1716.333 & 1724 & 1726.533 & 1719.133 & 1741 & 1730.533 \\  & T & 0.002803 & 0.005242 & 0.00324 & 0.003057 & 0.003206 & 0.003441 & 0.003387 & 0.003421 & 0.003642 \\  & F & **0.915386** & 20.35716 & 20.03306 & 2.290661 & 1.356551 & 2.343001 & 1.604591 & 1.78274 & 1.50134 \\ STD & Best & 398.6142 & 0.406838 & 488.6539 & 623.4962 & 323.6076 & 628.7728 & 458.7228 & 354.8188 & 388.8087 \\  & Ngen & 128.3596 & 23.43286 & 34.89861 & 39.51402 & 32.91235 & 35.7319 & 32.52389 & 35.1553 & 34.02433 \\  & Cost & 49.21715 & 54.57848 & 42.06931 & 49.62225 & 37.42118 & 37.48446 & 38.59939 & 52.92936 & 50.27081 \\ \hline \end{tabular} \end{table}