With the rise of the sharing economy, shared bicycles have become an important component of urban transportation. This paper explores the nonlinear dual oligopoly system for the Cournot model in the bike-sharing market; both operators have maximized profits as their competitive goals. The analysis of pivotal factors influencing passenger preferences, including pricing discounts and comfort levels, is meticulously depicted by a bifurcation diagram. A new chaotic attractor—the shared bicycle attractor—is discovered. The research results indicate that larger discounts and adjustment speeds can cause the system to be in a chaotic state, which is not conducive to the long-term development of operators, although discounts can indeed attract more passengers to a certain extent. On the other hand, the increase in the marginal cost of comfort loss can also make it difficult for enterprises to operate, which requires continuous technological innovation to improve the comfort of cycling.

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.

To enhance the safety operation management of the subway and ascertain the level of the subway department's emergency response capability, a cloud diagnostic model is proposed. This model, grounded in the 4R crisis management theory and the subway's unique characteristics, constructs a comprehensive diagnostic system. The DEMATEL-ANP model is employed to identify the interactive coupling relationship between various indicators in the diagnostic system, and the diagnostic level is judiciously divided. The cloud model is then utilized to holistically diagnose the subway's emergency handling capacity, thereby pinpointing the specific areas for improvement in subway emergency capacity and bolstering the safety and reliability of subway operation. To circumvent the emergence of imaginary numbers in the digital features of the cloud model, the MBCT-SR algorithm is implemented to enhance the cloud model, and the PSCM algorithm is applied to optimize the precision of cloud similarity discrimination. Using the Nanjing Metro Line 2 as a case study, the analysis reveals that the first-level indicators A and B of the object under diagnosis are underperforming. This necessitates a targeted enhancement of both organizational management of subway emergency personnel and capabilities for monitoring and early warning. Ultimately, the comprehensive diagnostic outcome was classified as a ‘good’ level, which is consistent with the actual situation, verifying the effectiveness and practical application value of the diagnostic model.

This paper investigates the competition between two types of bike-sharing services, particularly at bus stops, subway stations, and residential areas. Two types of shared bicycle travel choice models are constructed. A shared bicycle operator attracts users by implementing discount incentives, and the comfort levels of riding the two types of shared bicycles are different. The equilibrium fares, potential user demand, and operator profits under joint profit maximization, price competition, and potential user demand competition scenarios are derived, and the competitive results under the three scenarios are compared. The results show that, in the potential user demand competition, the difference in potential demand between the two operators is largest; in the joint profit maximization scenario involving shared bicycle operators, the difference in potential user demand is smallest. In all competitive scenarios, higher operating costs and costs in lowering comfort loss for the shared bicycle operators will increase fares; the substitution level between the two types of shared bicycles has a positive impact on potential user demand, and the higher the substitution level, the better the effect of discounts in attracting users.