Pareto multi-objective optimization of tandem cold rolling settings for reductions and inter stand tensions using NSGA-II.

In this paper, multi-objective optimization of tandem cold rolling settings for reductions and inter-stand tensions using NSGA-II and Pareto-optimal front are investigated. In this multi-objective optimization, the total power consumption and uniform power distribution are suggested as objective functions, and reduction thicknesses in each stand and inter stand tensions were selected as problem decision variables. Analytical formulations are introduced to determine the rolling forces and power based on the Stone approach. Then, the main variables of the optimization problem, objective functions, linear and nonlinear constraints, are defined. Moreover, some empirical constraints are introduced regarding the practical limitations of cold rolling equipment and the mechanical properties of the material. At first, considering the conditions of a practical tandem rolling line, single-objective optimization is performed separately, and finally, NSGA-II was used for multi-objective optimization. Compared to the initial setting of the rolling line, the obtained single objective schedules have better performance. Moreover, the multi-objective results based on the Pareto-optimal front are investigated, and an optimized setting for rolling schedule has been suggested. Using this proposed schedule the total power consumption is reduced by more than 11% comparing to the initial setting and more uniform power distribution has been obtained in rolling stands. The normalized reductions calculated from this investigation are compared with numerical and experimental results found in the literature and the similarity was observed in the pattern of thickness reduction distribution.