## 2 Literature  
DRTs, integrating both of the vehicle routing problem (VRP) and the pickup and delivery problem (PDP) [7; 8], are used to provide door-to-door transportation services wherein vehicles are assigned to visit some locations to pick up or deliver passengers [9; 10; 11]. However, the distinct differences between VRPs, PDPs, and DRTs result in DRTs addressing more issues and having more complexity than VRPs and PDPs. Compared to FRTs, DRTs are more suitable in low population density areas, especially those places with a weak traffic infrastructure [11; 12]. There have been numerous studies on DRTs in recent years, which can be divided into two main categories: analytic approaches and network approaches [13; 14].  
The analytic approach reveals the optimal relation between route spacing, the operating headway, and the stop space in the service area, where the shape geometry of the street and the demand distribution of these places are required. The first analytical approach was proposed by [PERSON] [15] to design the DRT during a peak-period demand in the Calgary (South Corridor) DRT system. Based on this, [PERSON] and [PERSON] further studied the influencing factors of bus-stop spacing on the DRT model [16; 17]. [PERSON] further extended the DRT model with coordinated routes, where the stochastic feeder vehicle arrivals at transfer stations were considered [18]. However, the analytic approach has not been widely used to deal with DRTs, due to the fact that two model inputs, i.e., the shape geometry of the street and the demand distribution of these places, are regarded as the most significant limitations [14].  
The network approaches represent the service that assigns bus routes to visit the pickup locations, where each location is assumed to be concentrated as a node and the links between these nodes represent the segments of bus routes. There are two typical network approaches to the DRT model, i.e., the feeder-bus network design optimization model proposed by [PERSON] and [PERSON] [17] and extended by [PERSON] and [PERSON] [19], [PERSON] and [PERSON] [20], [PERSON], [PERSON], and [PERSON] [14], [PERSON] and [PERSON] [21], and the heuristic feeder route generation algorithm (HFRGA) proposed by [PERSON] and [PERSON] [22], and also extended by [PERSON] and [PERSON] [23; 24; 25]. [PERSON] et al. [26] proposed a two-phase mode to cope with DRT FBNDP. [PERSON] et al. [27] proposed a model to solve the multi-levelcost structure (passengers' cost and operators' cost) of M-to-M DRT. [PERSON] et al. [28] presented a bi-level model to serve the maximum number of passengers in the feeder transit system in the upper level and to obtain the optimal operational cost for transit operators in the lower level. [PERSON] et al. [29] presented a bi-level nonlinear MIP model to optimize the flexible feeder dedicated transit from bus stops to rail stations, and vice versa. [PERSON] et al. [30] constructed a multi-objective MIP model in establishing coordination between rail and bus lines. [PERSON] et al. [31] used a robust MIP model to minimize the sum of the operator cost and its variability, following a weighting process of the cost components. [PERSON] et al. [32] presented a MIP model for DRT that considered passengers' multiple time windows and their satisfaction.  
Although existing studies have successfully studied a variety of DRTs, the two key issues deserve further investigation:  
(1) Few of the studies take the synchronous transfer of rail transit and personalized travel (the subway schedule chosen by passengers) into account. In the case, it implies a neglect of the integrated operation of the feeder bus routing and the schedule considering synchronous transfer between the shuttle and the feeder bus to minimize the total ride-time and wait-time for all passengers.  
(2) DRTs, as extensions of the VRP and PDP, are NP-hard problems, and should be resolved by an efficient algorithm.