A modified augmented lagrange multiplier method for production scheduling within steelmaking plants

Abstract

Within the current steelmaking and continuous-casting (SCC) production, the growing differentiation in the production processes stemming from the product diversification, brings about great difficulties in solving the SCC scheduling problem, and decreases pitifully the possibility of ascertaining the duality gap which is the essential criterion for performance evaluation of algorithms. Hence, this paper proposes a modified Augmented Lagrange multiplier method (m-ALM) in which the machine capacity constraint is relaxed to objective function and the original SCC problem is subsequently decomposed into several tractable subproblems by separating the charges in a cast. Particularly, a strongly convex punish component is appended to the objective function to achieve a better iteration-complexity bound than that by the commonly used Lagrangian relaxation approaches (LR). Additionally, a new fine-adjusting strategy is designed to construct a continuous penalty function as the updating direction vector of lagrangian multiplier to achieve the global convergence and boundedness of the decomposed subproblems within the iteration process. Theoretical derivations prove the global optimality of the proposed algorithm and numerical experiments indicate that the m-ALM outperforms LR in terms of solution quality within a significantly shorter CPU time.