## 1 Introduction  
Demand-responsive feeder transit services (DRTs), assigning buses to cover all pickup locations to transport passengers to the rail station, can provide a door-to-door type of service for the first/last mile access to link residential areas and a major fixed-route transit network [1, 2]. Compared to fixed-route feeder transit services (FRTs), DRTs can catch each passenger's personalized desires in low-density residential areas by using a cell phone app to place a travel order involving pickup or drop-off locations, windows of time service, and the predetermined subway schedule to provide a lower operating cost and a higher service level [3]. Therefore, DRTs have attracted the widespread attention of domestic and foreign scholars.  
The passengers' travel orders are the input to the design process of the DRT model. In general, they are willing to choose their own subway schedule, except for the pickup or drop off locations, the boarding time window, etc. Obviously, the passengers' personalized subway schedules affect the route-building process. However, the DRT model has not been integrated with personalized travel [4].  
Therefore, it is necessary to reveal the impact of the subway schedule chosen by passengers on the design process of the feeder bus route in order to trade off operation cost and service level.  
Another major motivation of this paper is to address DRTs with the synchronous coordination of rail transit. Few studies have examined this problem, but many examined the synchronous transfer between the shuttle and the feeder bus [5; 6]. Without the loss of generality, it is only relevant to the wait-time for passengers taking the subway beforehand, being an important part of total travel time, and it has an impact on the design process of the feeder bus route to the change in ride-time. Obviously, the synchronous transfer between the shuttle and the feeder bus may reduce the total travel time for all passengers. Hence, it is very important to find the optimal relation between the feeder bus routing and the synchronous coordination of rail transit in order to trade off wait-time and ride-time.  
The main contribution of this paper is to present an efficient optimization framework for DRTs with personalized travel orders using a cell phone app and synchronous coordination of rail transit to improve the service level. This study will pay attention to the following critical research tasks: (1) coordinating the process of designing the feeder transit routing and the schedule, considering the synchronous transfer between the shuttle and the feeder bus; (2) based on the division of the problem into several sub-problems, developing a distributed genetic algorithm to efficiently find meta-optimal solutions to the proposed mode; and, finally, (3) a numeric case study is used to illustrate the application and feasibility of the proposed methodology.  
The remainder of this paper is organized as follows: The related studies of DRTs are introduced in Section 2. Section 3 describes the problem of the proposed methodology and formulates the mathematic model of the DRT. Section 4 presents a distributed genetic algorithm for resolving the model. Sections 5 and 6 display and discuss a case study to illustrate the proposed methodology, as well as remarks and possible future work.