## 1 Introduction  
In open-pit coal mining operations, the transportation costs associated with traditional fuel trucks constitute approximately 45% to 60% of the total operational expenses. These substantial fuel-related transportation costs significantly hinder the improvement of production efficiency in open-pit mines [1]. To address this issue, some open-pit mines have adopted battery-swapping trucks as a means to reduce transportation costs [2]. Battery-swapping technology, initially gaining traction in the early 2020s, allows electric trucks to replace depleted batteries with fully charged ones, significantly reducing downtime. Currently, thousands of electric-powered trucks with battery-swapping capabilities are in service, with China and several other countries at the forefront of this adoption. This technology is particularly valuable in industries such as mining, where extended range and minimal downtime are crucial. Leading manufacturers, including CATL, BYD, and NIO, produce battery-swapping trucks, which typically offer a range of 150-200 km when fully loaded, with slightly greater distances when unloaded. Battery-swapping stations are strategically located within open-pit mines to minimize the time required for each swap, which averagesbetween 5 and 10 min per truck. Battery swapping differs significantly from conventional refueling, as it eliminates the need for on-site fuel storage and often relies on renewable energy sources, enhancing both safety and environmental sustainability. However, there are considerable differences between the new battery-swapping truck transportation model and the conventional fuel truck model in terms of range, battery-swapping station deployment, and scheduling. Consequently, traditional scheduling strategies for fuel trucks are not applicable to the battery-swapping truck model, potentially leading to inefficiencies and increased transportation costs. Therefore, optimizing the scheduling of battery-swapping trucks within this new transportation framework is critical for reducing operational costs and improving transportation efficiency in open-pit mining operations. Establishing a rational scheduling model is crucial for optimizing the scheduling of battery-swapping trucks [3; 4]. Several researchers have proposed various multi-objective scheduling models based on different scheduling requirements. [PERSON] et al. [5] developed a bi-objective linear mathematical model aimed at reducing the total tardiness of outbound trucks and maximizing the reliability of truck operations. [PERSON] et al. [6] proposed a multi-objective mixed-integer model with the goal of minimizing delays for inbound/outbound trucks and reducing energy consumption during the transfer of PI containers using PI conveyors. [PERSON] et al. [7] considered two conflicting objective functions in a multi-objective mixed-integer mathematical programming problem and constructed a scheduling optimization model by accounting for scheduling costs and time. [PERSON] et al. [8] addressed an optimal decision problem targeting the maximization of output, minimization of ore grade deviation, minimization of tonnage deviation to ore destinations, and minimization of fuel consumption for mining trucks. [PERSON] et al. [9] studied the truck scheduling problem for rail-road transportation while considering the uncertainty in truck arrival times. [PERSON] et al. [10] developed a multi-objective mathematical programming model to minimize non-loading travel distances and achieve the shortest completion time for multi-vessel container loading and unloading tasks. [PERSON] et al. [11] proposed a bi-objective optimization model to minimize truck waiting times in queues for gate allocation and to minimize the energy consumption of forklifts in cross-docking operations. [PERSON] et al. [12] developed a multi-objective linear programming model to minimize early and late departures of outbound trucks in a stochastic environment. [PERSON] et al.