New Perspective to Continuous Casting of Steel with a Hybrid Evolutionary Multiobjective Algorithm

In this article, we present a new perspective in solving computationally demanding problems such as the optimal control of the continuous casting of steel. We consider a multiobjective formulation of the optimal control of the surface temperature of the steel strand with five objectives, where constraint violations are minimized as objectives because no feasible solutions exist otherwise. A hybrid evolutionary multiobjective algorithm (HNSGA-II) is used to overcome discrepancies of evolutionary multiobjective optimization algorithms such as slow convergence and lack of convergence proof to the Pareto front. HNSGA-II uses NSGA-II as an underlying evolutionary multiobjective algorithm and an achievement scalarization function to scalarize objective functions for local search, which improves the population and speeds up the convergence. This is important because most evolutionary multiobjective algorithms are known to have difficulties with five objective functions. The algorithm is used to generate a set of Pareto solutions showing different trade-offs. However, it is difficult to generate Pareto solutions showing all the different trade-offs with a finite small population size. Hence, we use the preference information related to constraint violations in the weights of the achievement scalarization function to generate solutions with different trade-offs in preferable regions of the Pareto front. In addition, we use clustering and present typical solutions of different clusters so that the most preferred solution to be implemented can easily be identified. We demonstrate the approach and compare the results to previous studies.