The passenger demand of urban rail transit (URT) lines often present asymmetric tidal time-varying characteristics. To match the demand fluctuation, the train operational plan (TOP) generally has asymmetric bi-directional frequency/headway setting and imbalanced circulation, leading to high operation cost. This paper incorporates circulation balance into TOP optimization to balance the bi-directional arrival, departure, circulation, and resource utilization, and reduce the overall operation cost. Based on time-varying section demand and predetermined service level, bi-directional stepped maximum headway functions are collaboratively constructed, and then the circulation process is described by the trip flow circulation network that is formulated as a cost-oriented integer linear programming model. Using the optimized frequency setting, the final TOP is obtained by a two-stage approach to successively solve the schedule and rolling stock circulations at terminals. The case study based on an URT line in Shenzhen indicates that the proposed approach can not only ensure the required service level for travel demand, but also improve the efficiency of circulation and utilization, and effectively reduce the overall operation cost. The proposed approach provides an effective technique to keep balanced, stable and sustainable operation for URT lines.

Daily line planning in the operation stage should satisfy the fluctuating travel demand on different days and ensure the operation stability. In this paper, we propose an approach of daily line planning optimization for high-speed railway (HSR) lines to trade off the system costs and operation stability. The line plan is optimized by adjusting the reference line plan based on the baseline plan. A bi-level programming model is constructed based on Stackelberg game theory to describe the interaction and conflicts between railway companies and passengers. We propose the thought of “trigger decision, space-time coupling and joint iteration” to solve the model under the framework of the Simulated Annealing Algorithm (SAA). The case study on the Beijing–Shanghai HSR Line demonstrates that the adjusted line plan can not only optimize the system costs but also ensure the operation stability. It can provide sufficient transit capacity to satisfy the travel requirements of passengers and present the obvious advantage of operation cost reduction.

Stop planning is aimed to provide proper services for passenger demand, but diverse stop patterns lead to differences in stop density and travel speeds, impacting the utilization of line capacity. This paper incorporates capacity utilization into stop planning in the strategic line planning stage to trade off the matching between supply and demand and the stop distribution balance among trains. A bi-level programming model is established to formulate the Stackelberg game relation between supply and demand, where the stop distribution imbalance and the passenger travel inefficiency are measured. An adaptive hybrid solving algorithm combined with Genetic Algorithm and Simulated Annealing Algorithm is proposed, with several adaptive operations according to the problem characteristics and optimization degree to improve searching efficiency. A case study on the local network of Beijing–Shanghai High-speed Railway Line demonstrates that the proposed approach can not only mitigate the stop distribution imbalance, but also improve the travel efficiency of passengers, indicating that it can benefit the simultaneous improvement of capacity utilization and service level.

Optimizing passenger train line planning is a complex task that involves balancing operational costs and passenger service quality. This study investigates the adjustment and optimization of train line plans to better align with passenger demand and operational constraints, while minimizing systematic costs. These costs include train operation expenses (e.g., line usage fees and station service fees), passenger travel costs, and hidden costs such as imbalances in station stops. Line usage fees refer to charges for using railway tracks, whereas station service fees cover services provided at train stations. The optimization process employs a Simulated Annealing Algorithm to adjust train compositions, capacity configurations, and stop patterns to better match passenger demand. The results indicate a 13.89% reduction in the objective function value, reflecting improved overall efficiency. Notably, most costs are reduced, including train operating costs and passenger travel costs. However, ticketing service fees—which are calculated as a percentage of passenger fare revenue—increased slightly due to additional backtracking in passenger travel paths, which raised the total fare collected. Overall, the optimization improves the operational performance of the train network, enhancing both efficiency and service quality.

Railway passenger flow forecasting plays a critical role in operational efficiency and resource allocation for transportation systems. However, existing deep learning approaches suffer significant performance degradation when facing rare but high-impact events, primarily due to sample scarcity and their inability to distinguish between routine patterns and disruption regimes. To address these challenges, this study introduces EA-ARIMA-Informer, an adaptive forecasting framework that integrates entropy-augmented ARIMA with Informer through an entropy-guided regime-switching mechanism. The passenger flow series is characterized through a multi-dimensional entropy space comprising four complementary measures: Sample Entropy quantifies local regularity and predictability, Permutation Entropy captures the complexity of ordinal dynamics, Transfer Entropy measures causal information flow from external events (holidays, weather) to passenger demand, and the Conditional Entropy Growth Factor (CEGF)—a novel metric introduced herein—detects regime transitions by tracking the rate of uncertainty change between consecutive time windows. These entropy indicators serve dual roles as feature inputs for representation learning and as state identifiers for segmenting the time series into stable and fluctuating regimes with distinct predictability properties. An adaptive dual-path architecture is then designed accordingly: EA-ARIMA handles low-entropy stable regimes where linear seasonality dominates, while EA-Informer processes high-entropy fluctuating regimes requiring nonlinear residual modeling, with CEGF-guided gating dynamically controlling component weights. Unlike conventional black-box gating mechanisms, this entropy-based switching provides physically interpretable signals that explain when and why different model components dominate the forecast. The framework is validated on a large-scale dataset covering nearly 300 Chinese cities over three years (2017–2019), encompassing normal operations, holiday peaks, and extreme weather disruptions. Experimental results demonstrate that EA-ARIMA-Informer achieves a MAPE of 4.39% for large-scale cities and 7.82% for data-scarce small cities (Tier-3), substantially outperforming standalone ARIMA, XGBoost, and Informer, which yield 15.95%, 13.75%, and 12.87%, respectively, for Tier-3 cities. Ablation studies confirm that both entropy-based feature augmentation and CEGF-guided regime switching contribute significantly to these performance gains, establishing a new paradigm for interpretable and adaptive forecasting in complex transportation systems.