Abstract
In the hot rolling mill, a cold slab is reheated in reheating furnace and then rolled into thin coils through hot rolling process. Traditional research on hot rolling mill generally takes the two processes as two separate single-objective scheduling problems, though they are closely connected and their optimization objectives are conflicting with each other. In this paper, the integrated scheduling of the reheating furnace and hot rolling is investigated in the view of multiobjective optimization. A mixed-integer programming model with two objectives is formulated for this problem, and a multiobjective differential evolution (MODE) algorithm is developed to solve this model. To make it easy for algorithm design, a hot rolling schedule (i.e., a sequence of slabs) is used to represent a solution and for a given solution, a heuristic with consideration of energy consumption minimization is presented to obtain the schedule of reheating furnace. To achieve the balance of exploration and exploitation, a novel mutation operator with adaptive leader selection, a crossover operator with feasibility consideration, and a guided multiobjective local search are designed. Computational results based on simulated data illustrate that the integrated scheduling is superior to the traditional two-phase scheduling method used in practice and literature. Further results illustrate that the proposed MODE algorithm is effective and superior to some other multiobjective evolutionary algorithms.
Highlights
Iron and steel industry is one of the pillar industries for the national economy, and the typical production process in an iron and steel enterprise can be divided into three parts (Figure 1): primary steel making, hot rolling, and finishing making
To make NSGA-II applicable in our problem, the following modifications are made: first, the NSGA-II adopts the encoding and decoding method described in Section 4.2.1; second, the PMX crossover is used to generate new offsprings and the random insertion move is taken as the mutation operator; third, since the new offsprings generated by the crossover and mutation operator may be infeasible, a feasibility restoring method based on swap moves is used to guarantee feasibility; fourth, the guided multiobjective local search in Section 4.2.4 is used at each generation to improve a nondominated solution randomly selected from the current population
The graphical results of the Pareto fronts obtained by NSGA-II, multiobjective iterated local search (MOILS), and DMODE for each problem group are illustrated in Figure 11
Summary
Iron and steel industry is one of the pillar industries for the national economy, and the typical production process in an iron and steel enterprise can be divided into three parts (Figure 1): primary steel making, hot rolling (or rough making), and finishing making. Some of the hot rolled coils can be directly sold as products, but most of them will be sent to the finishing making section for further complex processing. A slab cannot leave the furnace even if it has reached its maximum heating time, if there are other slabs before it or the hot rolling line is processing another slab. When such scenario occurs, this slab will be overheated, which results in both energy waste and harm to rolling quality. After pulled out from the reheating furnace, the heated slab further enters the hot rolling process that consists of rough rolling and finishing rolling procedures.
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