  This article develops a solution for an inverse problem through the
generalized method of lines. We consider a Laplace equation on a domain with
internal and external boundaries with standard Dirichlet boundary conditions.
Also, we specify a third non-homogeneous Newmann type boundary condition for
the external boundary, and consider the problem of finding the optimal shape
for the internal boundary such that all the prescribed boundary conditions are
satisfied. The novelty here presented is the application of the generalized
method of lines as a tool to compute a solution for such an inverse
optimization problem.
