Gravitational lensing provides a direct means for measuring the masses of 
galaxies
and galaxy clusters. Provided that enough constraints are available, one might 
even
hope to obtain a handle on the precise distribution of the mass, which in turn 
may
reveal information about the spatial distribution of the dark matter.

We present an approach using genetic algorithms, allowing the user to 'breed'
solutions which are compatible with available strong lensing data. The procedure
allows various types of constraints to be used, including positional information,
null-space information, and time-delay measurements. The method is non-
parametric in
the sense that it does not assume a particular shape of the mass distribution. 
This
is accomplished by placing circularly symmetric basis functions -- projected 
Plummer
spheres -- on a dynamic grid in the lens plane.

Using simulations, we show that our procedure is able construct a mass 
distribution
and source positions that are compatible with a given set of observations. We 
discuss
the degeneracies that are inherent to lens inversion (and hence any lens 
inversion
technique) and that limit the potential of strong lensing to yield precise 
estimates
of the dark-matter distribution. We show how these degeneracies cause of the
differences between inversions of the same lensing cluster by different authors,
using the famous cluster Cl 0024+1654 as a working example.