## 4 Case and Discussion
### Result Analysis  
With the above simulation parameters, a single objective optimization is performed based on the two objective functions of the DES mathematical model described in Section 1 to obtain the minimum values \(\min(J_{1})=0.0294\) and \(\min(J_{2})=11\),584.32. Table 3 demonstrates the comparison of the two objective function values under optimization with a single objective, method 1, method 2, and the SSO method. Figure 5 shows the optimization results under three different methods and the stepper search process of the SSO method. Figure 6 shows the differences of the optimization scheduling results between three different methods from four perspectives: distributed power, new energy generation power stations, energy storage system and grid node voltage. Table 3 presents the following: (1) Optimizing with a single objective guarantees that the results obtained will be optimal for that metric, but the other metric will be so far from the optimal position that it will not be possible to balance the two optimization objectives, and the results obtained will be very poor. (2) Compared to single-objective optimization, the optimization result obtained by using method 1 and 3 increases only by 0.0248 and 0.0637 in the \(J_{2}/\min(J_{2})\) direction but decreases by 25.9617 and 59.2115 in the \(J_{1}/\min(J_{1})\) direction, respectively. It means that the optimization result is better than the single-objective optimization approach in terms of the whole system but still exhibits poorer performance in the \(J_{1}/\min(J_{1})\) direction. (3) Compared to method 1, although method 2  
Figure 5: The distribution of optimization results \((J_{1}/\min(J_{1})\,|\,J_{2}/\min(J_{2})\,|\,)\) from the different methods at the pareto front. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \(\min J_{1}\) & \(\min J_{2}\) & **Method 1** & **Method 2** & **Method 3** & **SSO Method** \\ \hline \(J_{1}/\min(J_{1})\,|\) & 1 & 140.7114 & 114.7497 & 1.5586 & 81.4999 & 1.5141 \\ \(J_{2}/\min(J_{2})\,|\) & 7.7836 & 1 & 1.0248 & 2.3756 & 1.0637 & 2.4047 \\ Computing time & 18.44 s & 18.67 s & 21.94 s & 26.22 s & 3907.16 s & 280.44 s \\ \hline \end{tabular}
\end{table} 
Table 3: \(J_{1}\) and \(J_{2}\) values under different methods. and the SSO method decrease by 1.3508 and 1.3799, respectively, in the \(J_{2}/\min(J_{2})\) direction, they increase by 113.1911 and 113.2356, respectively, in the \(J_{1}/\min(J_{1})\) direction, improving approximately 80 times. It means that the scheduling strategies based on these two methods will be more conducive to the overall performance of the system. (4) Compared to method 2, the SSO method decreases by 0.0291 in the \(J_{2}/\min(J_{2})\) direction and increases by 0.0445 in the \(J_{1}/\min(J_{1})\) direction. Although this numerical change is small, it achieves approximately 1.5 times the benefit, which means that the SSO method is slightly better than method 2. (5) In terms of solving time, the proposed method is superior to method 3 and reduces the solution time by more than 10 times, but it is inferior to other methods. The reason for the above results is that the proposed method and method 3 have iterative processes, and there are more iterations required in method 3. Figure 6: _Cont._  
Figure 5 shows the distribution characteristics of different methods on the pareto front and the stepper search process of the SSO method in the coordinate system composed of \((J_{1}/\mid\min(J_{1})\mid,\,J_{2}/\mid\min(J_{2})\mid)\). From the figure, it can be observed that (1) the two optimization objectives show significant contradiction, that is, as the value of one optimization objective decreases, the value of the other optimization objective increases. (2) In the coordinate system composed of \((J_{1}/\mid\min(J_{1})\mid,\,J_{2}/\mid\min(J_{2})\mid)\), the pareto front shows two parts with significant slope differences, namely, the AB section and BC section.