Using Interactive Multiobjective Optimization in Continuous Casting of Steel

Abstract

We discuss some pros and cons of using different types of multiobjective optimization methods for demanding real-life problems like continuous casting of steel. In particular, we compare evolutionary approaches that are used for approximating the set of Pareto-optimal solutions to interactive methods where a decision maker actively takes part and can direct the solution process to such Pareto-optimal solutions that are interesting to her/him. Among the latter type of methods, we describe an interactive classification-based multiobjective optimization method: NIMBUS. NIMBUS converts the original objective functions together with preference information coming from the decision maker into scalar-valued optimization problems. These problems can be solved using any appropriate underlying solvers, like evolutionary algorithms. We also introduce an implementation of NIMBUS, called IND-NIMBUS, for solving demanding multiobjective optimization problems defined with different modelling and simulation tools. We apply NIMBUS and IND-NIMBUS in an optimal control problem related to the secondary cooling process in the continuous casting of steel. As an underlying solver we use a real-coded genetic algorithm. The aim in our problem is to find a control resulting with steel of the best possible quality, that is, minimizing the defects in the final product. Since the constraints describing technological and metallurgical requirements are so conflicting that they form an empty feasible set, we formulate the problem as a multiobjective optimization problem where constraint violations are minimized.