Design Optimization of an Electrode-Based Electric Furnace Using a Two-Level Surrogate Model

This paper addresses new optimization approaches for resistance furnaces with electrodes for processing molten slag. The thermal and hydrodynamic behavior of the melt is strongly influenced by the Joule heat distribution generated by the electric current flowing between the electrodes, making electrode geometry a key design variable affecting the final process conditions. The aim of this study is to combine two approaches: a surrogate criterion based on process physics and an additional high-level surrogate criterion generated by a Gaussian process. The solutions were validated using a full model of the slag melting process in a dual-electrode furnace, incorporating electromagnetic and hydrodynamic phenomena to evaluate the target criterion—slag mixing intensity. The results confirm the usefulness of the physics-based surrogate criterion, while also revealing limitations of the Gaussian-process layer under nonlinear geometric constraints. Further development of feasibility-aware acquisition strategies and validation on additional benchmark cases is required to establish its broader applicability.