The work [21] proposed the solution where the genetic algorithm generates the input parameters for the XFEM model and receives a response with the optimization criterion value. The entire process takes place in a loop until the stop condition of the algorithm is met. The work [22] used the FEM with a gradient-based optimization algorithm. A mesh is generated with given input parameters, where the simulation result is passed to the optimization algorithm, which calculates new input parameters for the local minimum found, for which the mesh is readjusted. Next, the publication [23] proposed the optimization method for electrode placement in radiofrequency ablation, RFA. In this method, the optimization algorithm iteratively generates the new electrode position, which is given to the FEM model, which calculates the new criterion value, which is the Arrhenius survival fraction. This paper is about one of the design elements of an electrode resistance furnace, which is the geometry of its electrodes. The modification of the furnace design in this respect is technically very simple to carry out, and as the research has shown, it allows for a significant improvement of an important process parameter, which is the intensity of mixing of the processed bath (e.g., slag). Joule heat, which is generated by the flow of electric current between electrodes in a resistance furnace, plays a critical role in the melting and heating of the charge. However, its impact extends beyond these primary functions. The heat also induces the mixing of the molten material within the furnace, a factor that is crucial for the overall process efficiency. This increased mixing contributes to a more homogeneous distribution of temperature and chemical composition within the molten bath, leading to improved results of the technological process. This paper introduces a novel methodology aimed at optimizing the geometry of electrodes in resistance furnaces. The proposed approach is distinctive in that it leverages a surrogate criterion based solely on the electromagnetic submodel. The criterion is intimately connected to the process hydrodynamics within the furnace. The idea has already been used in a process where magnetohydrodynamic phenomena played a leading role [24; 25]. In the analyzed process, natural convection plays a leading role, but the principle of omitting the hydrodynamic model in optimization is similar. The effectiveness of the developed methodology is demonstrated through its application to a resistance furnace equipped with two electrodes. The results highlight the potential of this approach to enhance furnace performance by improving the mixing of the molten material, thereby offering a significant advancement in the optimization of resistance furnace operations. The primary contribution of the presented study lies in the development of a novel surrogate criterion, which significantly enhances the efficiency of numerical optimization for determining mixing intensity within electrode resistance furnaces. This criterion allows for a substantial reduction in the computation time required for optimization, achieving a level of time efficiency that is considerably greater than that of the conventional approach, which relies on the flow velocity criterion derived from a hydrodynamic model.