In this paper, stochastic optimization of the shielding of an axisymmetric induction heating system is performed by means of the self-adaptive low-high evaluations evolutionary algorithm (SALHE-EA). The finite element formulation of the electromagnetic problem is based on the magnetic vector potential. The hybrid finite element method Dirichlet boundary condition iteration (FEM-DBCI) method is used to deal with the unbounded nature of the field problem and to reduce the computing effort required for optimization.