To address the issues of slow convergence and large errors in existing metaheuristic algorithms when optimizing neural network-based subway passenger flow prediction, we propose the following improvements. First, we replace the random initialization method of the population in the SSA with Circle mapping to enhance its diversity and quality. Second, we introduce a hybrid mechanism combining dimensional small-hole imaging backward learning and Cauchy mutation, which improves the diversity of the individual sparrow selection of optimal positions and helps overcome the algorithm’s tendency to become trapped in local optima and premature convergence. Finally, we enhance the individual sparrow position update process by integrating a cosine strategy with an inertia weight adjustment, which improves the algorithm’s global search ability, effectively balancing global search and local exploitation, and reducing the risk of local optima and insufficient convergence precision. Based on the analysis of the correlation between different types of subway station passenger flows and weather factors, the ISSA is used to optimize the hyperparameters of the CNN-LSTM model to construct a subway passenger flow prediction model based on ISSA-CNN-LSTM. Simulation experiments were conducted using card swipe data from Harbin Metro Line 1. The results show that the ISSA provides a more accurate optimization with the average values and standard deviations of the 12 benchmark test function simulations being closer to the optimal values. The ISSA-CNN-LSTM model outperforms the SSA-CNN-LSTM, PSO-ELMAN, GA-BP, CNN-LSTM, and LSTM models in terms of error evaluation metrics such as MAE, RMSE, and MAPE, with improvements ranging from 189.8% to 374.6%, 190.9% to 389.5%, and 3.3% to 6.7%, respectively. Moreover, the ISSA-CNN-LSTM model exhibits the smallest variation in prediction errors across different types of subway stations. The ISSA demonstrates superior parameter optimization accuracy and convergence speed compared to the SSA. The ISSA-CNN-LSTM model is suitable for the precise prediction of passenger flow at different types of subway stations, providing theoretical and data support for subway station passenger density and trend forecasting, passenger organization and management, risk emergency response, and the improvement of service quality and operational safety.

To address the challenges of characterizing subway passenger flow fluctuations and overcoming the slow convergence and significant errors of existing intelligent optimization algorithms in tuning deep learning parameters for flow prediction, this study proposes a novel subway passenger flow fluctuation interval prediction model based on a Symmetry-Enhanced FIG-ICPO-XGBoost model. The core innovation is an Improved Cheetah Optimization Algorithm (ICPO), which incorporates enhancements including Circle mapping for population initialization, a hybrid strategy of dimension-by-dimension pinhole imaging opposition-based learning and Cauchy mutation to escape local optima, and adaptive variable spiral search with inertia weight to balance exploration and exploitation. The construction of this methodology embodies the concept of symmetry in algorithm design. For instance, Circle mapping achieves uniformity and ergodicity in the initial distribution of the population within the solution space, reflecting the symmetric principle of spatial coverage. Dimension-by-dimension pinhole imaging opposition-based learning generates opposite solutions through the principle of mirror symmetry, effectively expanding the search space. The adaptive variable spiral search strategy dynamically adjusts the spiral shape, simulating the symmetric relationship of dynamic balance between exploration and exploitation. Utilizing fuzzy-granulated passenger flow data (LOW, R, UP) from Harbin, the ICPO was employed to optimize XGBoost hyperparameters. Experimental results demonstrate the superior performance of the ICPO on 12 benchmark functions. The ICPO-XGBoost model achieves mean MAE, RMSE, and MAPE values of 10,291, 10,612, and 5.8%, respectively, for the predictions of the LOW, R, and UP datasets. Compared to existing models such as CPO-XGBoost, PSO-BiLSTM, GA-BP, and CNN-LSTM, these values represent improvements ranging from 4541 to 13,161 for MAE, 5258 to 14,613 for RMSE, and 2.6% to 7.2% for MAPE. The proposed model provides a reliable theoretical and data-driven foundation for optimizing subway train schedules and station passenger flow management.

To capture bus passenger flow fluctuations and address the problems of slow convergence and high error in machine learning parameter optimization, this paper develops an improved Whale Optimization Algorithm (IWOA) integrated with a Bidirectional Gated Recurrent Unit (BiGRU). First, a Logistic–Tent chaotic mapping is introduced to generate a diverse and high-quality initial population. Second, a hybrid mechanism combining elite opposition-based learning and Cauchy mutation enhances population diversity and reduces premature convergence. Third, a cosine-based adaptive convergence factor and inertia weight strategy improve the balance between global exploration and local exploitation. Based on the correlation analysis between bus passenger flow and weather condition data in Harbin, and combined with the fluctuation characteristics of bus passenger flow, the data were divided into windows with a 7-day weekly cycle and processed by fuzzy information granulation to obtain three groups of fuzzy granulated window data, namely LOW, R, and UP, representing the fluctuation trend and spatial characteristics of bus passenger flow. The IWOA was employed to optimize and solve parameters such as the hidden layer weights and bias vectors of the BiGRU, thereby constructing a bus passenger flow fluctuation trend and spatial prediction model based on FIG-IWOA-BiGRU. Simulation experiments with 21 benchmark functions and real bus data verified its effectiveness. Results show that IWOA significantly improves optimization accuracy and convergence speed. For bus passenger flow forecasting, the average MAE, RMSE, and MAPE of LOW, R, and UP data are 2915, 3075, and 8.1%, representing improvements over existing classical models. The findings provide reliable decision support for bus scheduling and passenger travel planning.

This paper focuses on enhancing the accuracy and efficiency of bus travel speed prediction by improving the optimization process for deep learning model parameters. Existing intelligent optimization algorithms often suffer from slow convergence and substantial errors when tuning parameters for such predictive tasks. To mitigate these shortcomings, this study presents a new predictive framework that synergizes an Improved Atom Search Optimization (IASO) algorithm with a Bidirectional Gated Recurrent Unit (BiGRU) network. The EASO algorithm is developed through three principal modifications: (1) population initialization using a Logistic-Tent composite chaotic map to enhance diversity and initial quality; (2) incorporation of a hybrid operator merging refraction opposition-based learning and Cauchy mutation to broaden the search around promising solutions and alleviate issues of local stagnation and early convergence; and (3) implementation of an adaptive variable spiral search to recalibrate the position update rule, thereby improving the trade-off between extensive exploration and intensive exploitation. Based on the analysis of bus travel speed determinants, the IASO algorithm is applied to optimize the hyperparameters of the BiGRU network, culminating in the proposed IASO-BiGRU predictive model. Validation tests indicate that the devised IASO algorithm shows improved performance in certain aspects compared to several contemporary intelligent optimization techniques in terms of solution accuracy and convergence efficiency. Under the specific experimental conditions of this study, the IASO-BiGRU model achieves MAE, RMSE, and MAPE values of 1.62, 1.80, and 6.70%, respectively, corresponding to an improvement of 1.91–7.56% compared to the baseline models tested. These findings offer valuable data support and a decision-making foundation for bus operation scheduling and passenger travel planning.

The three‐dimensional macroscopic fundamental diagram (3D‐MFD) provides a novel approach to characterize the complex interactions between cars and buses in multimodal urban networks, offering particular value for designing efficient bimodal perimeter control strategies. In this study, a perimeter control strategy for cars is implemented by regulating the transfer flow rate at subregion boundaries, while bus numbers are dynamically adjusted through optimized dispatch frequencies. A multimodal traffic system state equation integrating both car and bus dynamics is constructed. Building on operational state factors for both modes, a passenger mode choice model based on the Logit model is established. With the dual objectives of maximizing the overall passenger arrival rate and minimizing total network energy consumption, an integrated multimodal traffic control framework (I‐MPC) is developed using model predictive control (MPC). The comparative analysis against the no boundary control (NBC) method, the MPC‐based boundary control method for private cars (C‐MPC), and the bus scheduling optimization method (B‐MPC) demonstrates that the proposed I‐MPC method achieves outstanding performance across multiple key metrics, including passenger arrival efficiency, network energy consumption, and average bus occupancy rate, thereby enabling the optimized allocation and efficient utilization of traffic resources. Moreover, the method maintains reasonable bus occupancy levels while significantly enhancing passenger comfort and reducing overall system energy consumption.

This study proposes a novel GPS-based methodology for Macroscopic Fundamental Diagram (MFD) estimation to overcome limitations of fixed detectors and inaccurate penetration rate assumptions. The approach dynamically identifies stop-line positions using spatiotemporal floating car data, calculates maximum queue lengths per signal cycle by combining floating car positions with estimated arriving vehicle lengths, and establishes a speed-based nonlinear model to determine queuing vehicle counts. A dynamic scaling coefficient derived from maximum queue lengths enables assumption-free estimation of total regional vehicles when applied to the floating car population. Validation using Chengdu data demonstrates significant improvements: unary cubic curves achieve optimal fitting for MFD relationships (R ² up to 0.9157); the HMM-CRF hybrid map-matching algorithm reduces average position error by 29% and intersection mismatch rate by approximately 40%; simulation results show queue length estimation accuracy of RMSE 22.8m and MAPE 18.5%, while MFD estimation error for maximum network flow drops from −17.5% to −3.5%, representing an 80% relative accuracy improvement. The proposed methodology provides robust technical support for urban road network assessment and management by enabling high-precision acquisition of MFDs from floating car data, effectively addressing critical challenges in macroscopic traffic modeling and monitoring. This advancement presents potential value for perimeter control applications and other MFD-based traffic management strategies.