<p>Accurate copper price forecasting is crucial and challenging due to the uncertainty and complex fluctuations caused by various factors of financial markets. In this area, the single-factor point prediction methods have made significant contributions but do not fully consider the influence of multiple factors and the robustness of the predictions. This study develops a novel hybrid interval prediction framework that combines multi-objective optimization with quantile deep learning for copper price prediction. The framework holistically evaluates the fluctuation range by assessing the distribution of copper prices and incorporates multiple variables chosen through diverse feature selection methods, which are crucial for accurate copper price prediction. The proposed framework encompasses two sub-stages: (1) initial interval prediction and quantile deep learning models of copper price; (2) multi-objective optimization procedure. In the first phase, four probabilistic forecasting algorithms are employed to sharpen prediction accuracy and provide a comprehensive picture of the interpretation of the outcome parameters by evaluating the distribution. The subsequent phase delves deeper to enhance prediction precision. Four multi-objective optimization algorithms are harnessed to refine the predictions, aiming to boost their reliability and resolution. The experiment findings underscore the superior predicted capabilities of the Quantile Regression Long Short-Term Memory (QRLSTM) model when optimized using the Multi-Objective Salp Swarm Algorithm (MOSSA), achieving a Prediction Interval Coverage Probability of 94.5205%, a Prediction Interval Normalized Average Width of 0.0066, and an Average Interval Score of -373.9687 at 95% confidence levels. The probabilistic forecasting framework developed in this research is reliable and comprehensive, considering many factors influencing the copper price.</p>