Global method for a class of operation optimization problem in steel rolling systems

Many steel products are produced in hot or cold rolling lines with multiple stands. The steel material becomes thinner after being rolled at each stand. Steady-state parameters for controlling the rolling line need to be set so as to satisfy the final product specifications and minimize the total energy consumption. This paper develops a generalized geometric programming model for this setting problem and proposes a global method for solving it. The model can be expressed with a linear objective function and a set of constraints including nonconvex ones. Through constructing lower bounds of some components, the constraints can be converted to convex ones approximately. A sequential approximation method is proposed in a gradually reduced interval to improve accuracy and efficiency. However, the resulting convex programming model in each iteration is still complicated. To reduce the power, it is transformed into a second-order cone programming (SOCP) model and solved using alternating direction method of multipliers (ADMM). The effectiveness of the global method is tested using real data from a hot-rolling line with seven stands. The results demonstrate that the proposed global method solves the problem effectively and reduces the energy consumption.