## 4 Results
### Analysis and Discussion
A more evenly distributed  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**The Number of Controllable Loads**} \\ \hline
**Algorithms** & **3** & **4** & **5** & **6** & **+/-/** \\ \hline AGEMOEA & \(4.6273\times 10^{-1}\) & \(4.2289\times 10^{-1}\) & \(4.0552\times 10^{-1}\) & \(3.0880\times 10^{-1}\) & 0/2/2 \\  & \((2.49\times 10^{-2})\) & \((2.64\times 10^{-2})\) & \((6.18\times 10^{-2})\) & \((7.74\times 10^{-2})\) & \\ ANSGA-III & \(4.3520\times 10^{-1}\) & \(4.0843\times 10^{-1}\) & \(3.6078\times 10^{-1}\) & \(3.0284\times 10^{-1}\) & 0/3/1 \\  & \((2.81\times 10^{-2})\) & \((1.30\times 10^{-2})\) & \((4.98\times 10^{-2})\) & \((5.56\times 10^{-2})\) & \\ ARMOEA & \(4.2165\times 10^{-1}\) & \(4.2218\times 10^{-1}\) & \(4.0862\times 10^{-1}\) & NaN & 0/2/1 \\  & \((9.96\times 10^{-2})\) & \((1.83\times 10^{-2})\) & \((6.00\times 10^{-2})\) & \((\)NaN\()\()\) & \\ CCMO & \(4.4546\times 10^{-1}\) & \(4.0787\times 10^{-1}\) & \(3.9540\times 10^{-1}\) & \(3.2897\times 10^{-1}\) & 0/4/0 \\  & \((1.32\times 10^{-2})\) & \((1.12\times 10^{-2})\) & \((2.67\times 10^{-2})\) & \((3.15\times 10^{-2})\) & \\ CTAEA & NaN & \(1.5567\times 10^{-1}\) & NaN & NaN & 0/0/1 \\  & \((\)NaN\()\) & \((0.00\times 10)\) & \((\)NaN\()\) & \((\)NaN\()\) & \\ DCNSGA-III & \(3.3743\times 10^{-1}\) & \(3.2180\times 10^{-1}\) & \(3.7492\times 10^{-1}\) & NaN & 0/2/1 \\  & \((6.28\times 10^{-2})\) & \((2.38\times 10^{-2})\) & \((2.79\times 10^{-2})\) & \((\)NaN\()\()\) & \\ NSGA-II & \(4.6170\times 10^{-1}\) & \(3.8818\times 10^{-1}\) & \(3.7344\times 10^{-1}\) & \(2.2796\times 10^{-1}\) & 0/2/2 \\  & \((1.69\times 10^{-2})\) & \((8.70\times 10^{-2})\) & \((1.17\times 10^{-1})\) & \((1.51\times 10^{-1})\) & \\ NSGA-III & \(4.4267\times 10^{-1}\) & \(3.8955\times  
Pareto front that covers a wider range of objective values indicates better diversity. This means that more choices can be provided to decision-makers. The results from Figure 2 demonstrate that the NSGA-II-MC algorithm proposed in this paper exhibits significant advantages over the traditional NSGA-II algorithm, showcasing improved convergence and diversity. It is worth noting that in the scenario with three controllable loads, the algorithm proposed in this paper shows a relatively smaller advantage. However, as the complexity of the management decision problem increases, i.e., with an increasing number of loads to be scheduled, the traditional NSGA-II algorithm struggles to reliably optimize the problem. In contrast, the NSGA-II-MC algorithm designed in this paper demonstrates superior performance. In the scenario with six controllable loads, there is a noticeable gap between NSGA-II-MC and NSGA-II. As the problem scale increases and constraint complexity grows, the advantages of the NSGA-II-MC algorithm become more pronounced. This validates the effectiveness and reliability of the multi-objective optimization approach proposed in this paper. Figure 3 presents the management strategies under different objective preferences with three controllable loads, where (a-d) represent the strategies under various objective  
Figure 2: Comparison of the Pareto Fronts between the NSGA-II-MC Algorithm and Traditional Algorithms in Different Scenarios. preferences. Objective one is the total cost, and objective two is the dependence on the main grid. The management strategy charts display the power generation, load power, charging and discharging states of energy storage batteries, regulation states of controllable loads, and the shedding of switchable loads at different times.