## 1 Introduction  
The university course scheduling problem (UCSP) is a complex optimization issue in the field of education, aiming to reasonably allocate course times and teaching resources to students and faculty [1]. The UCSP is classified as a typical NP-complete problem [2], meaning that finding the optimal solution requires significant computational resources. The constraint set of the UCSP is usually divided into hard constraints and soft constraints. Hard constraints are conditions that must be strictly followed during the schedulingprocess, and violating these constraints renders the schedule infeasible. These include the school's curriculum planning policies, the equipment and facilities of the available classrooms, and the availability of teachers and students. Soft constraints, on the other hand, are conditions that are preferable to satisfy but can be violated at the cost of reducing the quality of the schedule. These include teacher preferences for timetable arrangements, student expectations for offered courses, and the unique management requirements of each institution [3]. Therefore, creating a satisfactory schedule is not a simple task, as it requires balancing multiple constraints. In recent years, many scholars have used heuristic algorithms to solve scheduling problems [4; 5], including the UCSP. Some commonly used heuristic methods include particle swarm optimization (PSO) [6; 7; 8], Simulated Annealing (SA) [9; 10; 11], and Tabu Search (TS) [12; 13; 14; 15]. Among these, [PERSON] et al. [16] designed PSOSS and introduced a forced exchange operation, which significantly optimized PSO. [PERSON] [17] incorporates a local search mechanism into PSO, which enhances the solution refinement, but the method heavily depends on the quality of the initial population and lacks robustness in highly constrained scheduling environments. [PERSON] and [PERSON] [18] propose a hybrid ant colony system (ACS-SA) that combines Simulated Annealing and particle swarm optimization. While this hybrid approach enhances the exploration and exploitation, SA is highly sensitive to parameters such as the initial temperature and cooling rate. Improper parameter settings may result in slow convergence or premature convergence to a local optimum, reducing the scheduling efficiency. [PERSON] [19] applies DCM and Vertex Graph Coloring (VGC) to significantly improve the computational efficiency. However, this method primarily focuses on satisfying hard constraints and has a limited ability to handle soft constraints, making it less suitable for scheduling scenarios that require greater flexibility. Genetic algorithms also demonstrate significant effectiveness in solving scheduling problems. [PERSON] et al. [20] propose a QIGA based on Q-learning, and [PERSON] et al. [21] develop LSWT-GA. [PERSON], [PERSON], [PERSON], and [PERSON] [22] propose a heuristic algorithm for the UCSP that combines a GA, a GCP, and enhanced Tabu Search. Some researchers have used exact algorithms by formulating the UCSP as a linear programming problem and solving it using integer linear programming (ILP). [PERSON] and [PERSON] [23] developed a MILP model that incorporated teachers' teaching loads and preferences for different categories of teachers. [PERSON] et al. [24] propose an enhanced branch-and-check algorithm based on Benders decomposition. However, decomposition-based methods often require well-structured problem formulations, and their efficiency deteriorates in real-world scheduling scenarios with complex and dynamic constraints. Constraint-based approaches have also been explored. Some researchers have employed the epsilon-constraint method to address distributed scheduling issues [25; 26], while others have integrated mixed-integer programming (MIP) with Constraint Programming (CP) in hybrid models [27; 28; 29; 30]. Although these methods have made some progress in addressing the UCSP, limitations still remain.