## 2 Literature Review
### Research Gaps  
However, if these methods are applied directly, there may be some limitations. First, most of them do not allow for overtaking, which limits the express travel service of medium- and long-distance passengers, so they cannot fully reflect the advantages of multi-train services. Second, research that allows for overtaking aims at minimizing passenger travel time, such as [13; 51], ignoring the cost of urban rail transit systems. Although this omission can ensure passenger service efficiency, it cannot account for the interests of the operator and may lead to some unrealistic decision schemes, such as an excessive train service frequency or overtaking stations. Third, although some studies have considered costs, they mainly focused on minimizing the operation costs and energy consumption, but such cost analysis is not comprehensive, because the decision schemes for providing multi-trainservices will have an impact on the cost of each stage of the system life cycle (LC), e.g., building overtaking stations in the construction or operation stage and maintaining vehicles in the operation stage. Fourth, research on optimizing the stopping pattern often assumes that the train sequence includes express trains and local trains, which means that the proportion of express trains and local trains is balanced, as in [PERSON] et al. [7]. This assumption is not easy to adapt to practical traffic flows with uneven temporal and spatial distributions, and it ignores the influence of the numbers and service times (or service orders) of trains of different service levels on passenger travel choices.  
This study aimed to address the research gap described above. The objective was to propose the integrated optimization of multi-strategy line planning and periodic even-headway timetabling for an urban rail line, aiming to obtain a set of Pareto optimal solutions with the minimum system life cycle cost (LCC) and total passenger travel time perception (TTTP) under the given OD passenger flow. This study extends previous research in the following ways:  
(1) In this paper, the integrated optimization of line planning and timetabling is described as a space-time network design problem of urban rail transit from a new perspective, which systematically describes timetable structure information and passenger path choice behavior. An equilibrium space-time network design model is proposed to solve this problem, which requires little predefined timetable structure information because it simultaneously optimizes the train service frequency, operation zone, stopping pattern, train formation, and train order, and allows for overtaking to ensure the efficiency and flexibility of the timetable.  
(2) This study considers a more comprehensive heterogeneity of passengers, including not only the commonly used perception of in-vehicle time with congestion, but also the perception of travel fatigue related to path time. Using the user equilibrium model to describe passenger path choice behavior is more realistic than the assumption of first-in-first-out (FIFO) or prorate assignment, because this method allows passengers to freely choose their transfer station between different train services.  
(3) This study considers a more comprehensive system cost by analyzing the cost impact of multi-train services at each stage of the LC of an urban rail transit system, such as the total costs of an overtaking station, train operation, maintenance, and staff, which is more in line with the actual management needs of operators.