###### Abstract  
The rapid growth of cities and their populations in recent years has resulted in significant tidal passenger flow characteristics, primarily manifested in the imbalance of passenger numbers in both directions. This imbalance often leads to a shortage of train capacity in one direction and an inefficient use of capacity in the other. To accommodate the tidal passenger flow demand of urban rail transit, this paper proposes a timetable optimization method that combines multiple strategies, aimed at reducing operating costs and enhancing the quality of passenger service. The multi-strategy optimization method primarily involves two key strategies: the unpaired operation strategy and the express/local train operation strategy, both of which can flexibly adapt to time-varying passenger demand. Based on the decision variables of headway, running time between stations, and dwell time, a mixed integer linear programming model (MILP) is established. Taking the Shanghai Suburban Railway airport link line as an example, simulations under different passenger demands are realized to illustrate the effectiveness and correctness of the proposed multi-strategy method and model. The results demonstrate that the multi-strategy optimization method achieves a 38.59% reduction in total costs for both the operator and the passengers, and effectively alleviates train congestion. multi-strategy optimization; unpaired operation; express/local train operation; mixed integer linear programming model (MILP) +
Footnote †: journal: Applied sciences  
cycle running time by adjusting the skip-stop behavior of express trains, and also ensure that passengers waiting on the platform can board the trains smoothly using the all-stop behavior of local trains. Due to urban development, passenger flow in commercial center stations far exceeds that of other stations. The short-turning strategy is adopted to increase the number of trains running in the commercial center section [6; 14; 15]. The above studies are about the imbalance of passenger flow at stations, and it is worth noting that passenger flow imbalances in opposing directions are often caused by the tidal passenger flow phenomenon [16]. However, studies on passenger flow imbalances in opposite directions are minimal. According to passenger travel patterns during morning peak hours, the number of people traveling from the suburbs to the city center is significantly higher than those traveling in the opposite direction. However, during the evening rush hour, many people who work and study near the city center return to their suburban homes, resulting in the tidal passenger flow phenomenon [17]. To cope with the problem, this paper proposes a train unpaired operation strategy (TUOS), i.e., the number of trains running in both directions is not the same. Compared to the traditional train paired operation strategy (T-TPOS) [3; 18; 19], the TUOS improves the matching of passenger numbers and train capacity by flexibly determining the number of trains in both directions. The above discussed is the Line Planning level of the rail transport planning process [20; 21]. As shown in Figure 1, after the Line Planning level, the Timetable Generation level should be entered. In other words, the Timetable Generation level is the confirmation of train departure time, arrival time, headway, and dwell time. Timetable optimization considering rolling stock scheduling is the focus of our current research, which takes into account the quality of passenger service as well as the cost of operating trains [19; 22]. Therefore, this paper selects three processes in the rail transport planning process for research, which are the Line Planning level, Timetable Generation level, and Rolling Stock Scheduling level. Usually, timetable optimization is conducted with the objective of improving passenger service quality and reducing operating costs. Passenger service quality is generally defined as total passenger waiting time [23; 24], total passenger travel time [16; 25], number of stranded passengers [20], etc.