In the context of optimization using finite element method (FEM), many issues arise, mainly numerical noise due to re-meshing when dealing with geometric parameters furthermore the computational time of the overall optimization can be prohibitive. In this paper, we compare different approaches to deal with these issues. In some approaches, optimization method is coupled directly to FEM simulation while other approaches aim to replace the expensive simulation with cheap meta-models that reduce the overall time of optimization. As treating different approaches, a comparison protocol is proposed and two electromagnetic optimization benchmarks are treated.