Multiple time steps optimization for real-time heat transfer model of continuous casting billets

In this paper, the real-time problem of heat transfer model for continuous casting billets has been converted to an optimization problem of multiple time steps. In the optimization problem, the time steps as the optimal variables were constrained by the numerical stability. Furthermore, the objective function was defined by the relative calculation time, and the calculations were subject to the accuracy constraint determined by the maximum absolute temperature difference from the reference grid system. The optimization problem has been solved by particle swarm optimization (PSO) algorithm, by introducing a penalty factor for the accuracy constraint. Results and corresponding analysis show that when the penalty factor is big enough, especially when it tends to positive infinity, the optimized time steps are only determined by the accuracy constraint, independent of the penalty factor and also computers.