Optimal control of cooling process in continuous casting of steel using a visualization-based multi-criteria approach

This paper is devoted to the application of a new visualization-based multi-criteria approach in an optimal control problem related to the cooling process in the continuous casting of steel. The purpose is to develop such a control that results in steel of the best possible quality, that is, minimizes the defects in the final product. Since the constraints describing technological and metallurgical requirements result in an empty set of the feasible controls of the cooling process, the aim of the study is to find a control that violates the constraints as little as possible. The problem is formulated as a multi-criteria optimization problem and the constraint violations play the role of selection criteria. Our approach is based on the application of both a nonlinear mathematical model of the cooling process that features a system of partial differential equations, and a new decision support technique, called Interactive Decision Maps technique, that uses the on-line visualization of the non-dominated frontier.