A hybrid enhanced Gray Wolf-deep learning framework for multi-step crude oil price forecasting

Crude oil price forecasting requires models that are accurate, reproducible, and protected against temporal leakage. This study proposes a hybrid Enhanced Adaptive Gray Wolf Optimizer and deep ensemble framework for three-step-ahead Brent and WTI forecasting. The framework combines BiGRU, BiLSTM, and TCN learners with sentiment-derived information, uses time-ordered preprocessing, and optimizes both architectural hyperparameters and convex ensemble weights through walk-forward validation. The three algorithmic additions of E-AGWO serve distinct roles: an exponential control schedule provides a gradual, non-collapsing contraction of the search radius, a binomial crossover operator preserves component-wise diversity, and a Lévy-flight refresh operator introduces rare long moves accepted by a greedy rule. The revised experimental design includes statistical testing of forecasting losses, execution-time reporting, and accuracy-cost analysis. Compared with the best individual learner, the optimized ensemble reduces test RMSE by 21.6% on Brent and by 6.3% on WTI. These gains indicate that the main empirical benefit is not a claim of universal dominance, but a stable improvement obtained by adapting the ensemble weights to market-specific model strengths. Data and code are available on GitHub.