A Temperature-Aware Artificial Hummingbird Algorithm with Application to Multi-Step Combined Forecasting

The Artificial Hummingbird Algorithm (AHA) is a recent swarm intelligence optimizer with a simple structure and few control parameters. However, it still faces limitations in search regulation, population diversity maintenance, and late-stage exploitation when solving complex continuous optimization problems. To address these issues, this paper proposes a Temperature-Aware Artificial Hummingbird Algorithm (TAHA), which integrates temperature-driven stage regulation, adaptive Lévy flight, and a competition–teaching mechanism into a unified enhancement framework. Experiments on the CEC2014 benchmark suite show that TAHA achieves the best Friedman mean rank (3.07) among the compared algorithms and demonstrates competitive solution accuracy and stability. To further examine its applicability to structured optimization tasks, TAHA is applied to horizon-wise dynamic weight learning in multi-step combined forecasting. A dual-model fusion framework based on XGBoost and an improved N-BEATS is constructed, where the horizon-specific combination weights are optimized by TAHA. Results on the GEFCom2014-E, CAISO-2023, and SENI datasets show that the proposed framework achieves MAPEs of 1.5864%, 2.9161%, and 3.3108%, respectively, and obtains the lowest errors among the compared methods on all three datasets. Overall, the results indicate that TAHA is a competitive optimizer for continuous optimization and a useful tool for dynamic weight learning in multi-step combined forecasting.