The aim of this paper is to construct a numerical scheme for solving a
class of bilateral free boundaries problem. First, using a shape
functional and some regularization terms, an optimal control problem is
formulated, in addition, we prove its solution existence's. The first
optimality conditions and the shape gradient are computed. the proposed
numerical scheme is a genetic algorithm guided conjugate gradient
combined with the finite element method, at each mesh regeneration, we
perform a mesh refinement in order to avoid any domain singularities.
Some numerical examples are shown to demonstrate the validity of the
theoretical results, and to prove the robustness of the proposed scheme.