## 2 Literature Review
### Multi-Strategy Line Planning  
Scholars have begun to focus on multi-strategy line planning [20; 21; 22]. [PERSON] et al. [23] and [PERSON] et al. [24] took the operator and passenger travel costs as their optimization objectives and the turn-back station and frequency of short-turn buses as their decision variables; then, they established an integrated short turning and deadheading model. Using the first-order conditions, they obtained analytical expressions for the optimal value of frequency. [PERSON] et al. [25] presented an integrated optimization model to determine the optimal service frequency, stopping pattern, and train formation and to minimize the total passenger travel time loss and total operating costs, including the fixed overhead costs and variable operating costs of high-speed railways. A fuzzy mathematical programming method was used to solve the model.  
Most studies predefine the line-planning strategies and remaining timetable structure information in the line-planning stage and timetabling stage, which presents two problems in their practical application.  
The first problem is that there is insufficient research on the comparison and combination of line-planning strategies with the same (different) operational effects when improving the temporal and spatial imbalances of train or (and) station loads alone (simultaneously). For example, according to Table 1, when improving the spatial imbalance of train load (SIT), it is necessary to choose multiple turn-backs or express/local stopping modes. When improving the SIT and the temporal imbalance of train load (TIT) simultaneously, there are 11 possible combination strategies, which are obtained by combining time-varying frequency, multiple turn-backs, and variable train length modes with multiple turn-backs and express/local stopping modes. Only a few studies have compared the optimal solutions of different strategies, e.g., [PERSON] et al. (2016), but their research considered a bus system, so it is necessary to study a more comprehensive and general multi-strategy model for urban rail transit.  
The second problem is that the coordination between the line plan and timetable is poor due to the predefined timetable structure information in the timetabling stage, which means that the line-plan- and timetable-designing processes are handled individually and sequentially. Although this top-down hierarchical approach can decompose the entire problem into subproblems of manageable size, it is not optimal, because the optimal output of a subtask, which serves as the input of a subsequent task, will generally not result in an overall optimal solution ([PERSON] et al., 2017). In addition, the predefined structure will not only lead to a limited efficiency, robustness ([PERSON] et al., 2018), and flexibility of the output solutions (such as no overtaking), but it will also fail to fully consider the passenger path choice behavior, because a passenger's alternative travel paths are affected by each train service level (such as train speed and service time, which depend on timetable structure) and cannot be ignored. This problem must be solved using the integrated optimization of line planning and timetabling.