To address climate change and promote green and low‐carbon development, this study proposes an urban travel carbon footprint optimization method for transportation structures. Considering the environmental friendliness and efficiency of travel and combining carbon incentive policies and regret mechanisms, the travel preference model is constructed using game theory. Through the comprehensive perceived benefit function and multidimensional analysis, the effective reduction of travel carbon footprint is achieved. Taking Beijing as an example, the optimized transportation structure reduces the carbon footprint of travel by 17.17% and the total carbon emissions by 13.04%. Research has shown that to achieve the optimal carbon footprint, the green travel preference weight p ₁ in the multiobjective optimization model needs to be no less than 0.48, which verifies that this method can effectively alleviate the problem of transportation carbon emissions. Although this study has certain limitations in dynamic traffic demand applications, it has good practical application value for travel carbon footprint optimization under static demand conditions and contributes to the sustainable development of urban transportation and the realization of the “dual carbon” goals in China.

High-speed railway corridors operating under dense traffic conditions often face capacity limitations and operational conflicts caused by minimum headway constraints and heterogeneous train services. Differences in running times and stopping patterns between fast and slow trains may lead to overtaking conflicts and inefficient infrastructure utilization. This study investigates a multi-objective timetable optimization problem for high-speed railways under minimum headway constraints. A timetable optimization framework is established for high-speed railways under dense heterogeneous operations. The core mathematical formulation explicitly models timetable variables and basic temporal bounds, including sectional running-time limits, dwell-time bounds, and operating time-window constraints. Additional engineering feasibility requirements, such as minimum headway, station-capacity restrictions, and in-station overtaking feasibility, are enforced through the BS-FGS feasibility-scheduling procedure and the repair-based constraint-handling mechanism in the improved MOPSO stage. A hierarchical solution framework is proposed in which a Binary Search–Feasibility-Guided Greedy Scheduling (BS-FGS) method first evaluates the maximum feasible train number and generates an initial feasible timetable, followed by an improved Multi-Objective Particle Swarm Optimization (MOPSO) algorithm to obtain Pareto-optimal solutions within the feasible region. A case study on the Shanghai–Hangzhou High-Speed Railway corridor shows that system utilization can reach approximately 0.93–0.94 when in-station overtaking is allowed. Robustness simulations further demonstrate that the optimized timetables maintain stable train intervals and exhibit strong disturbance resistance. These results indicate that the proposed framework provides effective support for capacity evaluation and timetable optimization in high-density high-speed railway operations.

Optimizing high-speed railway (HSR) timetables requires coordinated decisions on train stopping patterns and local feasibility constraints, such as headway separation and service ordering, particularly at stations where consecutive trains share infrastructure. As network size and service density increase, station-level interactions can induce strategic behavior among trains competing for overlapping passenger markets. This study introduces a delayed-feedback evolutionary game framework to model interactions between two trains under incomplete information. Here, “delayed feedback” represents the lag in information transmission and periodic strategy updates, rather than operational train delays. We first formulate replicator dynamics for the non-delayed scenario, deriving equilibrium points and local stability conditions. The model is then extended to include delayed feedback in payoff evaluation, and the impact of delay parameters on stability and convergence is analyzed. To account for operational heterogeneity, two station layouts are considered: (i) two tracks per direction, representing small stations with limited overtaking and stop–pass combinations, and (ii) four tracks per direction, representing large stations that allow simultaneous stopping and richer operational patterns. Numerical simulations examine convergence, oscillatory behavior, and parameter sensitivity. Results indicate that delayed feedback significantly influences system dynamics: small delays maintain convergence to evolutionarily stable strategies, whereas larger delays induce persistent oscillations and complex transient trajectories. Station layout further affects stability regions and long-term strategy profiles. This study is based on analytical derivation and numerical simulation rather than sample-based statistical inference; therefore, non-parametric hypothesis testing is not applicable in the present framework. This framework provides a game-theoretic and stability-oriented tool for station-level timetable analysis, offering methodological guidance for timetable design under delayed decision feedback in HSR operations.