Efficient approximation of time consuming models for their use in optimization frameworks

Several widely used model optimization techniques such as, for instance, genetic algorithms, exploit an intelligent test of different input variables configurations. Such variables are fed to an arbitrary model and their effect is evaluated in terms of the output variables, in order to identify their optimal values according to some predetermined criteria. Unfortunately some models concern real world phenomena which involve a high number of input and output variables, whose interactions are complex. Consequently the simulations can be so time consuming that their use within an optimization procedure is unaffordable. In order to overcome this criticality, reducing the simulation time required for running the model within the optimization task, a novel method based on the combination of clustering and interpolation techniques is proposed. This technique is based on the use of a set of pre-run simulations of the original model, which are firstly used to cluster the input space and to assign to each cluster a suitable output value within the output space. Subsequently, in the simulation phase, an ad-hoc interpolation is performed in order to provide the final simulation results. The proposed method has been tested on two complex models related to the steel making industry: the first one concerns the optimization of blast furnace, the other one the operation of a EAF scrap pretreatment plant. The proposed approach has obtained good results in terms of accuracy and time-efficiency.