Multi-Strategy Improved Aquila Optimizer Algorithm and Its Application in Railway Freight Volume Prediction

This study proposes a multi-strategy improved Aquila optimizer (MIAO) to address the key limitations of the original Aquila optimizer (AO). First, a phasor operator is introduced to eliminate excessive control parameters in the X2 phase, transforming it into an adaptive parameter-free process. Second, a flow direction operator enhances the X3 phase by improving population diversity and local exploitation. The MIAO algorithm is applied to optimize Long Short-Term Memory (LSTM) hyperparameters, forming the MIAO_LSTM model for monthly railway freight forecasting. Comprehensive evaluations on 15 benchmark functions show MIAO’s superior performance over SOA, PSO, SSA, and AO. Using freight data (2005–2021), MIAO_LSTM achieves lower MAE, MSE, and RMSE compared to traditional LSTM and hybrid models (SSA_LSTM, PSO_LSTM, etc.). Further, Grey Relational Analysis selects high-correlation features (≥0.8) to boost accuracy. The results validate MIAO_LSTM’s effectiveness for practical freight predictions.