Model and method for evaluating the weighting coefficients of an ensemble machine learning model in the task of forecasting railway freight rates

This article examines the effectiveness of a developed ensemble machine learning model for forecasting rail freight rates. Russian Railways data for a three-year period, comprising approximately 50 million freight shipment records, serves as the empirical base. This dataset ensures a representative sample and accounts for industry-specific data diversity. An ensemble model is developed using the Random Forest, XGBoost, LightGBM, and CatBoost algorithms, with a meta-level implemented as a multivariate linear regression. The ordinary least squares method and Tikhonov regularization are used to calculate the weighting coefficients. This approach stabilizes the solution and reduces the impact of correlated outputs from the base models. Results of computational experiments have shown that combining heterogeneous models into an ensemble improves forecasting accuracy compared to individual algorithms. The average absolute error decreased by 7–13 %, and the average absolute percentage error by 6–12 %, while the determination coefficient increased to 0.942. Additionally, the ensemble's stability was assessed using a sliding window method, which allowed us to determine forecasting horizons that maintain stable results. An extended analysis of the ensemble's behavior with varying input features showed that the model is robust to moderate data distortions and maintains high calculation reproducibility. The obtained results confirm the practical significance of the proposed approach for transport analytics, transportation planning, and the development of economically sound pricing policies.

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