## 1 Introduction
introduced the carbon emission objective in the route optimization model, which improves vehicle operating efficiency while reducing environmental costs [11]. (2) Constraints  
Existing studies have considered single or multiple constraints such as station, vehicle capacity, and time window constraints. The station types include both fixed and variable stations. In the studies of fixed station constraints, [PERSON] et al. established a DRT scheduling model considering dynamic stations, the model in which the vehicle operation must pass through fixed stations, and passengers traveling on and off these fixed stations do not need to make reservations in advance. The model can reduce the number of car trips and reduce passenger costs at an unexpectedly high demand level [12]. [PERSON] et al. also researched DRT with fixed stations to introduce uncertainty into route scheduling to reduce vehicle detour costs [13]. Among the studies on variable station constraints, [PERSON] et al. researched flexible DRT, in which passengers do not have to go to stations to obtain services, which can effectively reduce passenger costs [14; 15]. [PERSON] et al. constructed a flexible bus VRP scheduling model, solved it using a heuristic algorithm, and verified the effectiveness and robustness of the model and the algorithm with a case [16]. Vehicle capacity constraint is the limitation of an individual vehicle's capacity on the scheduling method. In the study of vehicle capacity constraint, [PERSON] et al. designed a high-degree-of-freedom responsive bus system and proposed an optimization method for vehicle routes, scheduling, and service areas, and constructed the model with vehicle capacity constraints [17]. [PERSON] et al. considered two factors, capacity constraints and the time window, and transformed the problem into a joint optimization problem of fleet size allocation and vehicle routing with a full-service process time window and capacity constraints to solve it [18]. The time window is the duration from the earliest to the latest departure time that passengers can catch up with after making a reservation. [PERSON] et al. introduced a passenger incentive preference policy to reduce the ineffective distance and time of the vehicle by incentivizing passengers to make passengers arrive at their designated locations on time [19]. [PERSON] et al. investigated the DRT path optimization and vehicle scheduling problem with a time window, vehicle operation time, departure time, and other constraints,constructed an optimization model, and solved it by using a dual genetic algorithm [20]. [PERSON] et al. added time window constraints and considered vehicle punctuality constraints, passenger travel deviation, and passenger real-time demands in the model, which can meet passenger travel demands and improve passenger travel satisfaction [21]. The algorithms for solving the DRT scheduling problem include two categories: exact algorithms and heuristic algorithms. The exact algorithms refer to a class of algorithms that spend a limited amount of computation time to obtain the optimal optimization problem solution through precise mathematical and logical operations. The exact algorithms include branch-and-bound [22; 23; 24], cut-plane [25; 26], and dynamic programming [27; 28]. When the size of the problem is small, the exact algorithm can be solved effectively within an acceptable time. However, when the size and complexity of the solution increase, the computation time required will show an exponential growth trend. Compared to exact algorithms, heuristic algorithms can achieve better results for more complex problems. Therefore, since the 1990s, many scholars have focused on researching the application of heuristic algorithms to solve vehicle scheduling problems. The commonly used heuristic algorithms include the tabu search algorithm (TSA), simulated annealing algorithm (SAA), ant colony optimization (ACO), genetic algorithm (GA), and so on. [PERSON] et al.