## 1 Introduction
### Literature Review
#### 1.1.1 Demand-Responsive Transport  
The core of the demand-responsive transportation system is the reservation processing model, which is essentially a joint optimization of demand and flexible planning. In recent years, demand-responsive transportation has become a hot issue internationally. Some relevant research has been carried out in many fields, such as urban public transportation, the most typical of which is defined as the Dial-A-Ride Problem (DARP). The system for solving this problem based on cars or small buses has been introduced in some European countries in recent years, initially aiming to serve people who travel in remote areas or at night time with low demand.  
For the static DARP, [PERSON] [2] was the first to propose a dynamic programming strategy to address the single-vehicle problem. [PERSON] and [PERSON] [3] solved a multi-vehicle problem with consideration of route duration, vehicle capacity, and the maximum passenger ride times, which were addressed using a tabu search algorithm. [PERSON] and [PERSON] [4] not only considered the heterogeneity of users and vehicles in the modeling, but also studied the algorithm design. A hybrid algorithm was developed to solve the DARP, which combined a large neighborhood search and column-generation method. With the objective of maximizing corporate profits, [PERSON], et al. [5] formulated a mixed integer programming model to solve the DARP. [PERSON], et al. [6] considered the DARP, aiming to maximize the passenger occupancy rate. On the basis of the static problem, many scholars have considered dynamic path planning in problems where a new user request is used as the event that triggers the update schedule. The vehicle paths as well as the service recipients are continuously updated to ensure that users are served as much as possible [7; 8]. Many scholars have also considered the stochastic in DARP. [PERSON] and [PERSON] [9] considered user requires service only as a given probability to design the vehicle routes. [PERSON], et al. [10] proposed a stochastic model, taking the blocking probability, the acceptance rate, and the average sojourn time into account to solve a single-vehicle DAR in a transport system. [PERSON], et al. [11] extended two pairs of metaheuristic methods for dealing with stochastic, time-varying drive speeds for the situation of the dynamic DARP. Given the stochastic service and travel times, [PERSON], et al. [12] established a stochastic model applied to the path planning for the Home Health Aides service. Then, five approaches were adopted, respectively, to find solutions to the problem. [PERSON], et al. [13] built a multiple graph to depict the stochastic DARP, which was formulated by a two-stage recourse model. Authors used an iterative sampling-based method to address the proposed stochastic model, embedded with a heuristic search algorithm. These studies provide a good theoretical basis for developing demand-responsive transportation systems, but most studied a small-scale vehicle routing problem. Compared with the routing problem on the road networks, there is an obvious difference in the theory of the high-speed railway networks and the demand-responsive service, and there are some obstacles to its application to the railway system.