###### Abstract
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Indictors**} & \multirow{2}{*}{\begin{tabular}{c} **Time-** \\ **Varying** \\ **Frequency** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Multiple** \\ **Turn-Backs** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Express/Local** \\ **Stopping** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Variable** \\ **Train** \\ **Lengths** \\ \end{tabular} } \\ \hline Temporal imbalance of train load & \(-\) & & & \(-\) \\ Spatial imbalance of train load & & \(-\) & \(-\) \\ Imbalance of station load & & \(-\) & \(-\) & \\ Operator cost & \(\pm\) & \(-\) & \(\pm\) & \(-\) \\ Total waiting time & \(-\) & \(\pm\) & \(+\) & \\ Total passenger & & & \(-\) & \\ In-vehicle time & & & \(-\) & \\ Total passenger & & & \(+\) & \(-\) \\ Transfer time & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Effects of line-planning strategies (\(-/+\) indicates decrease/increase). Figure 1: Morning peak timetable of Seibu-Shinjuku line in Japan on weekdays. Considering the complexity of the integrated optimization of the entire train planning process, existing research generally optimizes these processes individually in stages by decomposing them into controllable subproblems and predefining the timetable structure information of other stages, such as the stopping pattern and train length in the line-planning stage and the departure time, train orders, and overtaking stations in the timetabling stage. Optimizing the entire problem sequentially is always inferior to integrated optimization, because the optimal output of a subtask will generally not result in an overall optimal solution [8]. With improvements in the performance of computer hardware and optimization methods, scholars have begun to deal with some sequential processes of the entire problem, such as the integrated optimization of line planning and timetabling [9; 10]. These studies usually have a limited flexibility in the timetable structure (i.e., they have some predefined timetable structure information). The optimal results are theoretically different from the flexible timetable structure (i.e., without predefined timetable structure information) because this information directly affects the calculation of the detailed timetable solution described by the specific department and arrival times. Passengers have a variety of travel paths under diversified train services because there are multiple paths between the same origin-destination (OD) pair in the passenger travel space-time network. Passengers will choose these paths differently because the travel times, which include waiting time, on-board time, transfer time, and train congestion, differ; thus, analyzing passenger path choice behavior is essential. The heterogeneity of passengers' travel demands, such as travel congestion and fatigue, is an important reason for path choice behavior. Passengers will choose follow-up trains according to daily travel experiences and timetables to avoid discomfort caused by in-vehicle crowding [11] and fatigue caused by long journeys, especially for standing passengers [12]. However, in studies on the optimization of line planning for providing train services at different speeds [7; 13], travel fatigue is rarely considered, which makes the original intention of designing fast trains (i.e., reducing travel time) unable to be fully reflected. This study aimed to address the above research gap. The objective was to propose an integrated line-planning and timetabling optimization model, which can fully consider passenger path choice behavior to implement a new timetable, with multi-strategy line planning for an urban rail line. The remainder of this paper is organized as follows. Section 2 reviews the relevant state-of-the-art literature. The overall problem statement is presented in Section 3. In Section 4, a bi-objective equilibrium space-time network design model (ESTNDM) is formulated, and Section 5 describes the solution algorithms for the model.