# A Discrete Particle Swarm Optimization Algorithm for Dynamic Scheduling of Transmission Tasks
## 3 Methodologies
### Parameter  
The DPSO is controlled by three parameters: inertia-retention factor (IRF), particle-best factor (PBF), and global-best factor (GBF). The three parameters correspond to \(\omega\), \(c_{1}r_{1}\), and \(c_{2}r_{2}\) in Formula (13). Set the sum of the three parameters to 1. Each iteration has a proportion of \(\omega\) to perform inertia retention, a proportion of \(c_{1}r_{1}\) to perform local-best motion, and a proportion of \(c_{2}r_{2}\) to perform global-best motion. In the parameter experiment, we set the change-step size of the parameter to 0.1. The experiment setsthe number of equipment and the number of time periods to be equal. The enumeration algorithm is used to verify the interval between the number of time periods and the number of equipment [4; 7]. The enumeration algorithm cannot be tested due to the computing time periods including more than 8 pieces of equipment. Each task number randomly generates 100 task sequences for testing. The experimental data are shown in Table 2:  
According to the number of equipment and time periods in the 4-7 interval, the enumeration algorithm is used to obtain the optimal values for the comparison tests. The iteration number of the parameter test table is obtained as follows. In order to better compare the change in the iteration number of different parameter groups, the iteration number is evaluated and calculated. The number of each equipment is calculated by dividing the iteration number by the average value of the iteration number obtained by all parameter groups. The cumulative-average proportion is shown in Table 3.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Parameter** & \multicolumn{6}{c}{**Number of Equipment and Time Periods**} & **Total** \\ \hline
**IRF** & **PBF** & **GBF** & **4** & **5** & **6** & **7** & \\ \hline  
\hline \hline \end{tabular}
\end{table}
Table 2: Comparison of the number of successful tests of DPSO parameters.  
It can be seen from Table 3 that the number of iterations in the parameter groups' calculations to obtain all global-best solutions in Table 2 is also small, indicating that the algorithm's success rate and efficiency are unified within the same parameter group.  
It is impossible to enumerate the parts of the algorithm's comparison experiments and to compare whether the evaluation values obtained under different parameters obtained the maximum value for all parameters. The number of iterations of the algorithm is the number of iterations of the greedy algorithm. The formula is as follows:  
\[IterationNumber=\sum_{i=1}^{n}t^{2} \tag{23}\]  
The number of experimental tasks includes the data from the previous 4-7 intervals. According to the computing power of the current experimental environment, the number of equipment and the number of time periods during the experiment is 12. The data can be found in Table 4.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{3}{c}{**Parameter**} & \multicolumn{5}{c}{**Number of Equipment and Time Periods**} & **Average** \\ \hline
**IRF** & **PBF** & **GBF** & **4** & **5** & **6** & **7** & **Weighted** \\ \hline  
\hline \hline \end{tabular}
\end{table}
Table 3: Comparison table of iterations of DPSO.  
groups achieved maximum values, including (0.3,0.1,0.6), (0.5,0.1,0.4), (0.2,0.1,0.7), and (0.4,0.1,0.5).
* The groups (0.3,0.1,0.6) are better in the iterative-weighting calculation in the previous two comparison tables, but the success rate is slightly lower. The groups (0.2,0.2,0.6)' weighted-average number of iterations is minimal. In order to ensure the comprehensiveness of the subsequent multi-algorithm experiments, use 5 groups of parameters to carry out experiments in the subsequent comparison experiments of DPSO. The list is in Table 5.