Optimizing Surface Profiles during Hot Rolling: A Genetic Algorithms based Multi-objective Analysis

A hot rolled strip produced by any integrated steel plant would require satisfying some stringent requirements of its surface profile. Crown and Flatness are two industrially accepted quantifiers that relate to the geometric tolerances in the rolled strips. This study attempts to regulate both crown and flatness within an acceptable limit, satisfying more than one objective at a time. Mathematically, this leads to a multi-objective optimization problem where the solution is no longer unique and a family of equally feasible solutions leads to the so called Pareto-Front, where each member is simply as good as the others. To implement this concept in the present context, one needs to realize that the surface deformation, which is ultimately imparted to the rolled sheets, comes from more than one source. The wear of the rolls, their thermal expansion, bending, and also deformation, contribute significantly towards the crown and flatness that is ultimately observed. During this study a detailed mathematical model has been worked out for this process incorporating all of these phenomena. Computation for the Pareto-optimality has been carried out using different forms of biologically inspired Genetic Algorithms, often integrated with an Ant Colony Optimization Scheme. Ultimately the model has been fine tuned for the hot rolling practice in a major integrated steel plant and tested against their actual operational data.