## 5 Discussion  
This study demonstrates the superior comprehensive performance of the ESS-NSGA-III algorithm in solving four-dimensional multi-objective optimization problems through comparative analyses with NSGA-III and NSGA-II. Simulation results reveal that ESS-NSGA-III outperforms conventional algorithms in spread, HV, and IGD metrics (Tables 4 and 5). Specifically, ESS-NSGA-III achieves a 4.12% improvement in HV and a 5.79% reduction in IGD compared to NSGA-II, indicating enhanced convergence and diversity in the obtained solution sets, which align more closely with the true Pareto front (Table 5 and Figure 5). When compared to NSGA-III, ESS-NSGA-III reduces spread and IGD by 8.15% and 3.66%, respectively, validating that the proposed SDE and DCD mechanisms effectively enhance solution distribution uniformity (Table 5 and Figure 5). These findings align with the distance dominance relationship reported in [26], yet our improvements exhibit greater efficacy in four-dimensional objective spaces.  
Figure 8: Energy consumption–distance curves for the three strategies.  
Figure 7: Speed profiles for the three strategies.  
Figure 9: Power–distance curves for the three strategies.  
Practical applications demonstrate that ESS-NSGA-III achieves balanced optimization, excelling in energy efficiency while maintaining high punctuality, comfort, and safety (Table 6). These results corroborate the energy-saving control strategies for trains proposed in [27] but extend the flexibility of multi-objective trade-offs through the Pareto optimization framework. Comparisons of operational strategies reveal that moderately extending running time significantly improves comprehensive performance (Figure 6 and Table 8). This improvement is operationally realized through three key measures: shortening traction duration, lowering cruising speed, and optimizing downhill coasting phases (Figures 7-9). While this aligns with the time-energy trade-off theory in [13], our study further quantifies the marginal benefits of comfort and safety enhancements. The Pareto-optimal solutions derived from ESS-NSGA-III enable the extraction of optimal driving strategies, offering actionable guidance for operators. This methodology supports eco-driving practices for catenary maintenance vehicles, demonstrating practical relevance in railway operations.  
However, this study has several limitations that warrant further investigation. First, the simulation experiments assume a static operational environment and do not incorporate dynamic factors (e.g., weather variations), which may limit the algorithm's generalizability in complex dynamic scenarios. Second, while the case studies focus on operational optimization for a specific section, the applicability of the algorithm across diverse railway lines requires additional validation. Finally, the research considers single-vehicle operations and neglects collaborative optimization in multi-vehicle cooperative scenarios.  
Future research should prioritize the following directions. First, dynamic environmental factors should be integrated into the optimization framework, and online adaptive algorithms (e.g., deep reinforcement learning) could be developed to improve computational efficiency and enhance robustness in time-varying scenarios. Second, simulation validations across different railway lines should be conducted to evaluate the algorithm's effectiveness under heterogeneous operational conditions. Lastly, the model should be extended to accommodate multi-vehicle cooperative operations, thereby broadening the algorithm's applicability in intelligent transportation systems.