## 4 Results
### Analysis and Discussion
In the low-grid-dependence mode shown in (a), there is no need for grid power supply during this period, and the electricity demand shortfall is compensated by using diesel generators; in the low-operational cost-mode shown in (d), cost savings are achieved by supplying power through the main grid during this period. Due to the high cost of generation, diesel generators serve as a supplementary energy source at different times to address the issue of insufficient power from the energy storage batteries and renewable energy sources to meet electricity demand. Figure 5 illustrates the management strategies under different objective preferences with five controllable loads, where (a-d) represent the strategies under various objective preferences. Compared to the scenarios with three and four controllable loads discussed above, the utilization rate of energy storage batteries significantly increases in this scenario due to the higher number of load demands, requiring frequent adjustments among various power supply resources. In the period from 22:00 to 24:00, with the same total load demand, the low-grid-dependence mode shown in (a) fulfills the system's electricity needs using diesel generators, while scenarios (b-d), depending on their respective management modes and preferences for grid dependence, supply electricity demands from the main grid in varying proportions, demonstrating the algorithm's rationality. Figure 4: Management strategies under different objective preferences with four controllable loads. Figure 6 presents the management strategies under different objective preferences with six controllable loads. In scenarios with multiple controllable loads, the complexity of the system increases, leading inevitably to higher overall operational costs and greater dependence on the main grid. From the scenario operation diagrams, it can be observed that the addition of controllable loads creates a peak electricity demand period from 19:00 to 20:00. In the low-grid-dependence management mode (a), the algorithm exclusively uses diesel generators for power supply, resulting in high operational costs of USD 42,990.4. In contrast, management mode (d), which utilizes electricity from the main grid, can effectively reduce system costs. Figure 5: Management strategies under different objective preferences with five controllable loads. In addition, Figure 7 shows the comparative results of management strategies under four controllable loads scenarios between the NSGA-II-MC and NSGA-II algorithms. This experiment selected the solutions at the bottom of the Pareto front, i.e., the scenarios with the lowest dependency on the main grid. However, it can be seen from the results that the traditional NSGA-II algorithm struggles to meet this preference, still relying heavily on the main grid for power supply, whereas the NSGA-II-MC algorithm tends towards using diesel generators, better satisfying user preferences. Figure 6: Management strategies under different objective preferences with six controllable loads. Figure 8 presents the comparison of management strategies between the NSGA-II-MC and NSGA-II algorithms under scenarios with six controllable loads. Comparing the objective values of the two solutions reveals that, in the complex management scenario of six controllable loads, the NSGA-II algorithm struggles to achieve effective optimization, with operational costs reaching USD 51,054.4. Meanwhile, the management strategy derived from the NSGA-II-MC algorithm can achieve a reduction of more than USD 16,000 in operational costs with only about 200 increases in dependency level, demonstrating a clear advantage in algorithm convergence. Figure 7: Comparison of NSGA-II-MC and NSGA-II management strategies (four controllable loads). The results above indicate that the multi-objective optimization method proposed in this paper can intelligently generate management strategies for resilient microgrids with different objective preferences.