Gradient-Informed Weighted Sum Multi-Objective Topology Optimization in Electromagnetics

Among all optimization approaches for the design of electromagnetic devices, topology optimization (TO) has recently gained great interest due to the broad spectrum of additive manufacturing (AM) techniques, allowing the realization of components with complex geometries. TO aims at finding the best material distribution within a design domain $\Omega_{d}$ under objective and constraint functions, where the former is retrieved from the solution of a partial differential equation (PDE) governing the physical problem. TO generally lies in the class of large-scale optimization problems and the decision variables $x_{i}$ of TO maps the presence or absence of material in each finite element discretizing $\Omega_{d}$. These variables generally belong to a continuous decision space $x_{i} \in[0,1]$, however, it can be conveniently defined also in a binary space, i.e., $x_{i} \in\{0,1\}$. As shown in Figure 1, in such a case, the material can only be absent $\left(x_{i}=0\right)$ or present $\left(x_{i}=1\right)$ without the appearance of intermediate values.