This paper studies a steelmaking-continuous casting scheduling problem with different processing routes. We model this problem as a mixed-integer nonlinear programming problem. Next, Lagrangian relaxation approach is introduced to solve this problem by relaxing the coupling constraints. Due to the nonseparability in Lagrangian functions, we design an improved concave–convex procedure to decompose the Lagrangian relaxation problem into three tractable subproblems and analyse the convergence of the improved concave–convex procedure under some assumptions. Furthermore, we present an effective surrogate subgradient algorithm with global convergence to solve the Lagrangian dual problem. Lastly, computational experiments on the practical production data show the effectiveness of the proposed surrogate subgradient method for solving this steelmaking-continuous casting scheduling problem.

本文研究了不同工艺路线的炼钢-连铸调度问题。我们将此问题建模为混合整数非线性规划问题。接下来，引入拉格朗日松弛方法通过放松耦合约束来解决这个问题。由于拉格朗日函数的不可分离性，我们设计了一种改进的凹凸过程，将拉格朗日松弛问题分解为三个易处理的子问题，并分析了改进的凹凸过程在一些假设下的收敛性。此外，我们提出了一种有效的具有全局收敛性的代理次梯度算法来解决拉格朗日对偶问题。最后，