## 1 Introduction
Since predictive control strategies help match supply and demand, save energy, and reduce energy costs, this study considers dynamic electricity information, weather variation information, and audience presence information. This approach contributes to reasonably formulating the operational scheme for the climate control system in the spectator stands. In the field of equipment system operation research, studies can be classified into single-objective and multi-objective approaches based on the number of optimization goals. In single-objective research, [PERSON] studied a CCHP system coupled with a thermal energy storage tank, aiming to minimize the overall cost of fuel consumption, electricity purchase, electricity sale revenue, and system operation [18]. [PERSON] investigated intermittently heated radiant floor heating systems and proposed predictive control strategies, resulting in 10-12% energy savings during cold winter months compared to conventional control approaches [19]. [PERSON] studied the energy-saving effects of predictive Integrated Room Automation (IRA), which maximizes the use of low-energy-cost actuators to maintain comfort within the desired range while minimizing energy consumption [20]. [PERSON] proposed a co-optimization framework for minimizing energy costs and investigated the climate control of buildings utilizing a shared set of heat pumps through economic model predictive control [21]. [PERSON] aimed to minimize electricity costs and discussed equipment start-stop strategies under both real-time and fixed pricing schemes. The results showed that shifting the operation of climate control equipment to periods of low electricity prices can lead to significant cost savings [9]. In summary, the majority of studies focus primarily on reducing energy consumption and minimizing energy costs as separate objectives. In the multi-objective optimization research, [PERSON] aimed to achieve two objectives: minimizing energy consumption and stabilizing indoor temperature. To accomplish these goals, he proposed a model predictive control-based optimal temperature controller for air conditioning and mechanical ventilation systems in buildings [10]. [PERSON] et al. also investigated a similar solar-driven MED system, aiming to maximize net profit and enhance unit production economy through system configuration optimization [22]. The thermal and humidity conditions in ice sports venues are complex, yet relatively little consideration has been given to the development of equipment operation strategies. Current research primarily focuses on operational strategies for ice sports venues from a single-objective perspective, without considering them from a multi-objective approach [9]. Given that the stands accommodate a substantial number of spectators, ensuring occupant comfort has become a primary objective. Additionally, cost and comfort are mutually constraining goals. Therefore, this study takes spectator comfort and energy cost as its objectives to achieve efficient and economical system operation. Furthermore, in the current research on climate control systems for ice sports venues, most studies focus on minimizing electrical energy costs, typically by optimizing the switching states of the climate control system equipment. However, these studies often overlook other important factors such as equipment startup and shutdown costs, operation and maintenance costs, and environmental impact costs. Therefore, while some progress has been made in optimizing energy costs, these studies fail to comprehensively reflect the overall benefits of the system. The core of multi-objective optimization methods lies in providing a moderate number of Pareto solution sets of good quality within a limited computational time to support the solution of complex decision problems. Evolutionary algorithms have been widely used in the field of multi-objective optimization due to their superior search capability and low computational burden [23].