## 7 Conclusions  
This study analyzed the integrated optimization problem of line planning and timetabling in urban rail transit and its essence, which showed that this problem can be described as an ESTNDP of urban rail transit from a new perspective, that is, adjusting the topology (the existence of vertices and links) and link attributes (time and capacity) of the passenger travel space-time network by line plan information (i.e., train service frequency, operation zone, stopping pattern, and train formation) and timetable information (e.g., train order and overtaking events at each station) to optimize the performance index of the system. Figure 23: Comparison of normalized Pareto fronts of line plans under different passenger flow conditions. An instantiation of the bi-objective ESTNDM based on user equilibrium was proposed for the ESTNDP to solve the optimal line planning and train order to minimize the LCC of the urban rail transit system and the TTTP. To be more practical, the heterogeneity of passenger demands not only includes a congestion penalty, which is common, but also a travel fatigue penalty, which is important for commuters, especially long-distance ones. In this model, the timetable can provide multi-train services, which are allowed to overtake, and passenger path choice behavior conforms to [PERSON]'s first principle and is described by a variational inequality model based on path flow. An algorithm was constructed using the NSGA-II combined with the SAGP to solve the model. The algorithm included three modules, which were used to solve the equilibrium passenger flow under \(\mathcal{J}_{1}\left|\boldsymbol{\Psi}^{(i)}\right.\), the Pareto front \(P_{i}\) of \(\boldsymbol{\Psi}^{(i)}\), and the Pareto front \(P\) of the original problem, respectively. The feasibility of the model and algorithm proposed in this paper was tested for the case of the Beijing Subway Line L. This paper compared and analyzed the solution effects of the ESTNDM for different train types, line-planning strategies, and passenger flow scenarios. The results showed that more types of trains is not better, and the reasonable value must be calculated and compared according to the actual line. The line plan considering all strategies had the best optimization effect due to the least predefined timetable structure information. There are combination effects between some line-planning strategies, and the decision maker can adopt different combinations of strategies according to the specific conditions of the actual line. When it is difficult to change the number of vehicles, it is recommended to adopt the combination line planning strategy of optimizing the operation zone and stopping pattern, such as in models 6, 7, 14, and 15. When the line conditions do not support the construction of overtaking stations, the combination line-planning strategy of optimizing the service frequency and operation zone is acceptable, such as in models 12, 13, 14, and 15. When the line conditions do not support the construction of overtaking stations and turn-back stations, a line plan with multiple train formations can be considered, such as in models 1, 3, 5, 9, 7, 11, 13, and 15. In addition, multiple strategies are more suitable for the scenario of a high imbalance in trains and station loads, which also verifies the rationality of providing multi-train services in the morning peak in Japan. There are some deficiencies in this study, and our future work will consider these deficiencies and focus on the following:  
(1) The random arrival of passenger flow was not considered. This study assumed that all passengers are regular passengers, i.e., they often use the urban rail transit system, and that the OD flow is fixed. However, in the real world, there are still some irregular passengers who do not often use the urban rail transit system; these passengers generally do not pay much attention to the train timetable, and their arrival time is highly random.