A FIG-IWOA-BiGRU Model for Bus Passenger Flow Fluctuation Trend and Spatial Prediction

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.