Lagrangian framework fusion with deep learning for steelmaking-continuous casting scheduling

Steelmaking–continuous casting (SCC) production scheduling is a critical step for optimising charge combinations, enhancing process compactness, and reducing energy consumption, thereby influencing the production efficiency and economic benefits of steel enterprises. However, the small batch sizes and extensive product variety inherent in modern steelmaking substantially increase scheduling complexity, making it difficult to rapidly generate feasible production plans. Therefore, we incorporate deep learning (DL) into the surrogate Lagrangian relaxation (SLR) framework to accelerate the acquisition of scheduling schemes by replacing the costly process of accurately solving subproblems with predicting ‘good-enough’ subproblem solutions. First, we propose a novel pointer network (GDPN) that integrates gated recurrent unit (GRU) with dot-product attention (DPA) to predict subproblem solutions in the Lagrange decomposition-coordination process. Subsequently, a dual-phase masking (DM) mechanism is developed during both the training and inference of GDPN to enforce the feasibility of the surrogate subproblem constraints caused by the continuous casting process in SCC. Finally, extensive numerical experiments and an industrial study with different scales demonstrate the effectiveness of the proposed DM-GDPN-SLR method.