An Effective Subgradient Method for Scheduling a Steelmaking-Continuous Casting Process

Abstract

The steelmaking-continuous-casting (SCC) process, which includes steelmaking, refining and continuous casting, is one of the major bottlenecks of iron and steel production. Efficient and effective scheduling of this process is essential to improve the productivity and reduce the production costs of the entire production system. We present a time-index formulation for this scheduling problem and a Lagrangian relaxation (LR) approach based on the relaxation of the machine capacity constraints. The relaxed problem is solved using an efficient polynomial dynamic programming algorithm. The corresponding Lagrangian dual (LD) problem is solved using a deflected conditional subgradient level method. Unlike the conventional subgradient algorithms for the LD problem, our method guarantees convergence using the Brannlund's level control strategy to replace the strict convergence condition that the optimum of the dual problem is known a priori. Furthermore, our method enhances the efficiency by introducing a deflected conditional subgradient to weaken the zigzagging phenomena that slows the convergence of conventional subgradient algorithms. The computational results demonstrate that the approaches can quickly obtain high-quality solutions and are notably promising for the SCC scheduling. Note to Practitioners-Efficient and effective SCC schedule is vital for the manufacturing system of iron and steel production.Unfortunately, the scheduling is extremely difficult because of its combinatorial nature and practical complex constraints such as job grouping constraints, precedence constraints, different transport time, and setup times. To obtain high-quality solutions within an acceptable computational time, we can use a problem-oriented approach, which can be the LR. However, there are two deficiencies in this approach: its empirical termination criteria, such as maximal iteration number or running time, which make it difficult to find a golden rule for various problems, and the inefficiency, which is caused by the so-called zigzagging phenomena. To overcome these deficiencies, this paper develops an effective subgradient method for SCC scheduling based on the machine capacity relaxation. This method gives an objective termination criterion based on the convergence condition of the method, and improves the efficiency based on a new search direction or a new subgradient. Then, the work shows how this method can be applied to solve an SCC scheduling problem. The computational results confirm their effectiveness and efficiency. The approaches can also be applied to other similar production scheduling problems.

Rescheduling optimization of steelmaking-continuous casting process based on the Lagrangian heuristic algorithm

“…The enhanced strategies improve not only the practicality of the LR approach but also the exactness of evaluation of the quality of the solution, and these strategies can instruct the production of SCC schedule effectively. The global convergence of the proposed algorithm can be proved by means of the previously reported methods [10,19,21] and the characterization of the deflected-conditional subgradient.…”

“…Finally, in order to avoid the confliction of the decoupled constraints, a feasible solution is obtained from the relaxed solution by the use of the different heuristic-based algorithm. The combination of SG or SSG with FDP or BDP under the LR frame has been used in different SCC scheduling problem, such as static scheduling problems [7,15,16,22,23] or dynamic scheduling problems with different objectives and under different conditions [19,31,37]. As for the rescheduling problems with LR algorithm, Xiong et al [36] proposed a dynamic scheduling algorithm with constant processing times in the rescheduling problems without considering the processing time and the other disturbance factors.…”

“…Some studies [6,11,13] have proposed various search-direction methods to improve the efficiency of the subgradient algorithm, whereas some others [5,10,17,29] have proposed various step-size methods to replace the strict convergence condition. Mao et al [19] integrated these two types of methods into a new subgradient algorithm, called the deflected-conditional subgradient level algorithm (DCSLA), which not only improves the efficiency of the subgradient algorithm but also guarantees global convergence. The present study also adopted the DCSLA to solve the LD problem [18].…”

A Dynamic Analytics Method Based on Multistage Modeling for a BOF Steelmaking Process

“…HE iron and steel industry is a major backbone of many fundamental production processes worldwide. It provides the basic raw materials for civil infrastructure, such as that for construction, machinery, automobiles, shipbuilding, railroads, and for other modern manufacturing industries [1][2][3][4]. Usually, iron and steel production processes consist of ironmaking, steelmaking-continuous casting, hot rolling, and cold rolling.…”

An effective multi-objective discrete grey wolf optimizer for a real-world scheduling problem in welding production

“…Thus, welding scheduling problem (WSP) plays an important role in promoting an enterprise to be a manufacturing giant. However, studies on the WSP are relatively scarce in comparison with other real-world scheduling problems such as steelmaking scheduling issues [2][3][4][5][6][7][8][9] . The main reasons for few researches on the real-world WSP may be the following aspects.…”