GA-Optimized Self-Attention LSTM for Multi-Asset Price Forecasting: Incorporating Trading Volume Features for Crude Oil, Gold, and Bitcoin

We propose a GA-optimized self-attention LSTM (SAG-LSTM) for multi-asset price forecasting and evaluate it on daily series of crude oil, gold, and Bitcoin, augmented with trading volumes (01-Apr-2021 to 30-Dec-2024). The model marries LSTM sequence learning with a multi-head self-attention layer and a post-attention gating block; a genetic algorithm tunes key hyperparameters (learning rate, hidden size, epochs). Using a 30-day horizon and standard preprocessing with lagged features, we benchmark SAG-LSTM against SA-LSTM and vanilla LSTM on MSE, RMSE, MAE, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , supplemented by error-trend and residual diagnostics, a forecast coherence score, and inter-asset dynamic/cross-correlation analyses. SAG-LSTM consistently dominates the baselines across assets: out-of-sample <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> rises to 0.90 for oil, 0.94 for gold, and 0.88 for Bitcoin, with visibly flatter error profiles and tighter, near-zero residuals. Inter-asset analyses show time-varying contemporaneous correlations but weak lead–lag effects, clarifying when co-movement is episodic rather than persistent. The largest gains occur in oil, reflecting more structured fundamentals; improvements for gold and Bitcoin are material but tempered by regime shifts and sentiment-driven jumps. Training time is higher due to GA search (≈2,121 s), but inference is fast (≈0.40 s), making the approach suitable for infrequent retraining with near-real-time scoring. Our findings highlight the value of hybrid, optimization-aware deep architectures for medium-horizon forecasting while underscoring the limits of price-volume inputs in sentiment-sensitive markets. These results offer actionable guidance for practitioners and a roadmap for future research and policy.