  Galaxies acting as gravitational lenses are surrounded by, at most, a handful
of images. This apparent paucity of information forces one to make the best
possible use of what information is available to invert the lens system. In
this paper, we explore the use of a genetic algorithm to invert in a
non-parametric way strong lensing systems containing only a small number of
images. Perhaps the most important conclusion of this paper is that it is
possible to infer the mass distribution of such gravitational lens systems
using a non-parametric technique. We show that including information about the
null space (i.e. the region where no images are found) is prerequisite to avoid
the prediction of a large number of spurious images, and to reliably
reconstruct the lens mass density. While the total mass of the lens is usually
constrained within a few percent, the fidelity of the reconstruction of the
lens mass distribution depends on the number and position of the images. The
technique employed to include null space information can be extended in a
straightforward way to add additional constraints, such as weak lensing data or
time delay information.

Astrophysics