A Learning-based Lagrangian Relaxation Algorithm for Integrated Scheduling of Oxygen Allocation and Steelmaking-Continuous Casting in Steel Enterprise

Effective energy management is crucial for reducing production costs in industrial settings. This is particularly evident in the steel industry, where the steelmaking and continuous casting scheduling processes consume substantial amounts of energy. The intermittent nature of steelmaking leads to significant fluctuations in energy supply and demand, resulting in energy waste. Neglecting the scheduling of energy supply during the production process fails to effectively reduce the overall production costs. To address this issue, we propose a mixed-integer linear programming (MILP) model that integrates steelmaking-continuous casting scheduling with oxygen supply scheduling. Given complex constraints on the model and combinatorial characteristics, we employ the Lagrangian relaxation algorithm to solve it. To enhance the algorithm’s efficiency, we introduce a reinforcement learning approach to dynamically update the step size coefficients of the Lagrangian multipliers. Through numerical experiments, we first validate the model’s ability to reduce production costs and subsequently examine the impact of various reinforcement learning strategies on algorithm performance. The results indicate that the proposed model effectively reduces production costs and the algorithm improvement strategy significantly improves performance.