## 4 Discussion  
In the field of building energy optimization, multi-objective optimization methods have been widely applied to climate control systems in various energy-intensive buildings. Current research primarily focuses on minimizing energy consumption and operational costs while ensuring indoor thermal comfort. With the continuous refinement of energy pricing mechanisms, the integration of demand response strategies has become a research hotspot. In particular, under time-of-use electricity pricing, increasing attention has been paid to the adaptability of optimization models and their capability for precise scheduling. Moreover, an increasing number of optimization studies targeting different types of buildings--such as office buildings, hospitals, residential complexes, and sports  
Figure 10: Comparison of electricity cost and other costs under fixed-rate and time-of-use pricing for typical summer, transition season, and winter days. Figure 9: Optimized scheduling results of a typical day in winter: (**a**) single-objective optimization (F1); (**b**) single-objective optimization (F2); and (**c**) multi-objective optimization. venues--have emerged, providing valuable theoretical foundations and technical references for this study. This work systematically compared the performance differences in three typical multi-objective optimization algorithms--NSGA-II, MOEA/D, and MOBBO--in the climate control scheduling of ice sports venues. The results show that MOEA/D demonstrates outstanding computational efficiency, making it suitable for scenarios with high time constraints; however, it has certain limitations in solution diversity and convergence. Although the MOBBO algorithm exhibits good search balance and solution coverage, performing well in complex and non-convex problems, its high computational cost limits its practical application. In contrast, NSGA-II delivers the best performance in solution quality, combining strong global search capability with excellent solution diversity, effectively approaching the optimal Pareto front. It is particularly well-suited for scheduling problems that require high solution quality and optimization performance. Considering solution quality, algorithm stability, and practical application needs, NSGA-II was ultimately selected as the core algorithm for climate control optimization in ice sports venues, as it achieved high-quality optimization results and demonstrated the robustness and applicability of the optimization framework. The multi-objective optimization model can better meet the comprehensive requirements of the climate control system for the operating economy as well as spectator comfort than single-objective optimization. Compared with the model optimized solely for users' comfort, the multi-objective optimization model improves economic performance under typical summer, transitional, and winter conditions by 26.5%, 14.9%, and 15.1%, respectively. In contrast, compared with the cost-optimal model, it reduces spectators' discomfort under the same three typical conditions by 10.0%, 39.3%, and 28.9%, respectively. Furthermore, with the integration of demand response strategies under time-of-use electricity pricing, operational costs are effectively reduced through reasonable load shifting. Operational costs can be significantly reduced by 25.3%, 24.4%, and 18.7% in summer, transitional, and winter conditions, respectively. These results not only verify the optimization capability of the NSGA-II-TOPSIS model but also demonstrate its practical application potential in energy-intensive venues like ice sports arenas, providing a replicable optimization approach and methodological framework for energy scheduling and management in similar settings. The optimization results of this work exhibit strong consistency with several existing studies. [PERSON] et al. proposed a BIM-GLSSVM-NSGA-II framework to optimize both building energy consumption and indoor thermal comfort, which shares similar objectives with this study [PERSON] et al. (2020).