A shape reconstruction problem of axisymmetric radiating structures is considered. This reads as an inverse problem. The direct problem - expression of the electric field w.r.t. a given geometry - is approximated by a simple model. For the inverse problem - find the shape whose radiation has been measured - a parametric shape functional is defined for which the \emph{Free-Form Deformation} method is introduced. Two different strategies to solve numerically the inverse problem (minimize the functional) is discussed: the first one is deterministic and the other one semi-stochastic. It appears that the functional is highly multimodal. At last, a multilevel strategy is proposed for which we discuss both robustness and convergence.