1. Introduction
A batch plan for a steelmaking-continuous casting section (SM-CC) primarily comprises of a charge plan and a cast plan and is located in a transition layer between a contract plan and an operation plan. It should not only rely on a production contract pool after preparing the contract plan but also consider the slab width, production process, delivery time, and other constraints to realize continuous production at a steel plant. In SM-CC, the steelmaking procedure is the starting point of the overall production wherein a charge is considered as the minimum unit of production. Therefore, defining a relevant and accurate charge plan is necessary. A charge plan for SM-CC implies combining and optimizing slabs of different steel grades and specifications to obtain different charges according to the constraints of steelmaking production and to prepare the background for a subsequent cast plan.
Scholars worldwide have conducted extensive research on the development of a charge plan for SM-CC. Quelhadj et al. [
1] first hypothesized that the SM-CC production process could serve as an important link in steel production and that the optimization of a steelmaking charge plan could save costs and increase the benefits in steel enterprises. In addition, the charge plan optimization problem of a steelmaking process was formulated as an integer programming model and solved using the Tabu search algorithm. Yan [
2] proposed a flexible charge plan. Although the number of unselected slabs was reduced therein, the difficulty of solving the model simultaneously increased, and the final results were listed carelessly. Tang et al. [
3,
4] established a charge plan model with a known number of the charge and incomplete contract arrangements considering the preselection of a contract pool and then applied a genetic algorithm to solve it. Huang et al. [
5] formulated a mathematical model to minimize residual materials and the steel-grade replacement costs. In addition, they identified the weight factors of different optimization objectives to promote on-site decision-making and solved the problem using a dynamic programming algorithm. Considering two flows of continuous machine casting and assuming the possibility of producing slabs with different widths, Cheng et al. [
6] developed a charge plan model to minimize the number of casts and the difference in adjacent slab widths of charges. Then, they solved this model using the variable neighborhood search combined with a simulated annealing algorithm.
In existing studies focused on the development of a charge plan, researchers mainly considered two approaches: one corresponded to an establishment method of a model and the other one corresponded to a solution method of a model. Concerning the former, several research works could be mentioned as examples. Ma et al. [
7] compared the task of charge plan formulation with the one-dimensional packing problem. This analogy method allowed fitting a conventional problem with a practical one and the degree of fit between these two problems directly influenced the results of modeling and solving. Ouelhadj et al. [
8] adopted a multi-agent system, and Wang et al. [
9] utilized Petri nets and other intelligent modeling methods. The use of such methods provides certain advantages. It allows the overcoming of the fixed rationale of conventional modeling methods and understanding the essence of a problem. However, in the current related research, certain limitations still exist. The complexity of SM-CC production planning is a limitation associated with a modeling method. In steel mills, the actual information is constantly updated, and various scenarios may occur. Therefore, researchers seek to identify the most effective approaches to address such a complex situation and model a real situation with high accuracy. A similar purpose is pursued in the present study.
Concerning the solving methods of a model, early studies introduced methods such as heuristic methods [
10] and operations research methods [
11]. However, with the development of computer intelligence techniques, researchers have begun utilizing more intelligent algorithms. For example, Lu et al. [
12] and Tang et al. [
13] applied the Tabu search algorithm to solve an optimization problem corresponding to a steelmaking process. Yuan et al. [
14] and Gong [
15] employed a genetic search algorithm to solve a multi-objective production optimization problem in SM-CC under different constraints. Chen [
16] proposed a method combining the immune and genetic algorithms that effectively prevented premature convergence of the genetic algorithm. Liu et al. [
17] summarized numerous research methods that were mainly divided into static and dynamic scheduling; however, they could not be separated from the improvement of solving algorithm. Evidently, intelligent algorithms are deemed more convenient than conventional solution methods as they improve the calculation speed and save manpower as well as material resources. However, defining an appropriate intelligent algorithm is necessary to apply specific changes to adapt a specific model and to address the premature or local optimum problem of an algorithm itself.
Existing research on a charge plan in SM-CC is too extensive to consider in its entirety. However, the global metallurgical industry field determines the status of relatively few foreign researchers. Existing research mainly suggests applying the simulation method to actual steel mills, i.e., they promote the development of intelligent approaches for investigating heavy industry. Based on the aforementioned observations, herein, we first clarify the specific problem of charge plan definition, and subsequently develop a concrete charge plan model and solve it using a proposed improved elitist genetic algorithm (IEGA).
Author Contributions
Modeling, F.Y. and S.W.; algorithm, S.W. and W.S.; testing, S.W.; formal analysis, F.Y.; resources, A.X.; writing—original draft preparation, F.Y. and S.W.; writing—review and editing, F.Y. and S.W. All authors contributed equally to editing and revising of this review. All authors have read and agreed to the published version of the manuscript.
Funding
This research is supported by the National Key Research and Development Program of China (grant no. 2016YFB0601301).
Acknowledgments
We would like to thank all the people, reviewers, and editors for their hard work in getting this article published.
Conflicts of Interest
The authors declare no conflict of interest.
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