## 4 Experimental Results and Analysis
### Experimental Results  
The experimental results are shown in following Tables 21-25, where method represents different algorithms, aver.t is the average running time for each algorithm to perform 10 repeated experiments and its unit is seconds, best is the best fitness value obtained by the algorithm in 10 repeated experiments, worst is the worst fitness value, mean is the average fitness value of ten repeated experiments, and, finally, std represents its standard deviation. For the spring (autumn) experimental data, the experimental results of each algorithm are shown in Table 21 and Figure 10. The results showed that SSO-DE had the best performance in terms of average running time. SSO-DE also outperformed other algorithms in terms of best fitness value and average fitness value, although the performance of SSO-DE in the worst fitness value was slightly lower than that of ABC-DE. Overall, SSO-DE performed the best in the spring (autumn) experimental data set. \begin{table}
\begin{tabular}{c c c c c} \hline
**Algorithm** & **Parameter** & **Spring (Autumn)** & **Summer** & **Winter** \\ \hline \multirow{8}{*}{SSO-DE} & Number of particles & 150 & 150 & 150 \\ \cline{2-5}  & Initial solution & Randomly generated & Randomly generated & Randomly generated \\ \cline{2-5}  & \(c_{g}\) & 0.55 & 0.5 & 0.45 \\ \cline{2-5}  & \(c_{p}\) & 0.35 & 0.4 & 0.4 \\ \cline{2-5}  & \(c_{w}\) & 0.05 & 0.05 & 0.1 \\ \cline{2-5}  & \(\gamma\) & 0.9 & 0.9 & 0.9 \\ \cline{2-5}  & \(F\) & \(0.15+0.0005\times N_{gen}\) & 0.15 + 0.0005 \(\times N_{gen}\) & 0.15 + 0.0005 \(\times N_{gen}\) \\ \hline \multirow{8}{*}{PSO-DE} & Number of particles & 150 & 150 & 150 \\ \cline{2-5}  & Initial solution & Randomly generated & Randomly generated & Randomly generated \\ \cline{2-5}  & \(C_{1}\) & 2 & 2 & 2 \\ \cline{2-5}  & \(C_{2}\) & 2 & 2 & 2 \\ \cline{2-5}  & \(w\) & Random number from & Random number from & Random number from \\ \cline{2-5}  & \(0.1\) to 0.25 & 0.1 to 0.25 & 0.1 to 0.25 \\ \cline{2-5}  & \(Vmax_{AC}(t)\) & \(C_{load}(t)\) & \(C_{load}(t)\) & \(C_{load}(t)\) \\ \cline{2-5}  & \(Vmax_{ES}(t)\) & \(P_{load}(t)\) & \(P_{load}(t)\) & \(P_{load}(t)\) \\ \cline{2-5}  & \(Vmax_{GT}(t)\) & \(P_{load}(t)\) & \(P_{load}(t)\) & \(P_{load}(t)\) \\ \cline{2-5}  & \(Vmax_{HS}(t)\) & 0.5 \(\times Q_{load}(t)\) & 0.5 \(\times Q_{load}(t)\) & 0.5 \(\times\ Q_{load}(t)\) \\ \cline{2-5}  & \(Y\) & 0.9 & 0.9 & 0.9 \\ \cline{2-5}  & \(F\) & \(0.15+0.0005\times N_{gen}\) & 0.15 + 0.0005 \(\times N_{gen}\) & 0.15 + 0.0005 \(\times N_{gen}\) \\ \hline \multirow{8}{*}{iSSO-DE} & Number of particles & 150 & 150 & 150 \\ \cline{2-5}  & Initial solution & Randomly generated & Randomly generated & Randomly generated \\ \cline{2-5}  & \(c_{r}\) & 0.4 & 0.4 & 0.4 \\ \cline{2-5}  & \(c_{g}\) & 0.3 & 0.3 & 0.3 \\ \cline{2-5}  & \(Y\) & 0.9 & 0.9 & 0.9 \\ \cline{2-5}  & \(F\) & \(0.15+0.0005\times N_{gen}\) & 0.15 + 0.0005 \(\times N_{gen}\) & 0.15 + 0.0005 \(\times N_{gen}\) \\ \hline \multirow{8}{*}{ABC-DE} & SN & 150 & 150 & 150 \\ \cline{2-5}  & Initial solution & Randomly generated & Randomly generated & Randomly generated \\ \cline{2-5}  & limit & 20 & 20 & 20 \\ \cline{2-5}  & \(Y\) & 0.9 & 0.9 & 0.9 \\ \cline{2-5}  & \(F\) & \(0.15+0.0005\times N_{gen}\) & 0.15 + 0.0005 \(\times N_{gen}\) & 0.15 + 0.0005 \(\times N_{gen}\) \\ \hline \end{tabular}
\end{table} 
Table 16: Parameter configuration of each algorithm. \begin{table}
\begin{tabular}{c c c c} \hline  & **Spring (Autumn)** & **Summer** & **Winter** \\ \hline \multirow{4}{*}{SSO} & \(c_{g}=0.55\) & \(c_{g}=0.5\) & \(c_{g}=0.45\) \\  & \(c_{p}=0.35\) & \(c_{p}=0.4\) & \(c_{p}=0.4\) \\  & \(c_{w}=0.05\) & \(c_{w}=0.05\) & \(c_{w}=0.1\) \\ \hline \multirow{4}{*}{DE} & \(Y=100\%\) & \multirow{4}{*}{\(Y=100\%\)} \\  & & \(F=0.1+0.0005\times N_{gen}\) & \\ \cline{2-5}  & & \(CR=0,0.1,0.4,0.7,1\) \\ \hline \end{tabular}
\end{table} 
Table 17: Parameter settings for SSO-DE.