FPGA Genetic algorithm
This could be a very big job!

FPGAs are not bags of transistors (at least not user-accessible ones) - they are a sea of lookup tables and flipflops.  You could potentially build a circuit full of LUTs and then use your GA to configure the content of them - you can manipulate the content of LUTs on the fly relatively straightforwardly (at least in Xilinx devices).

Xilinx used to have low-level bitstream manipulation tools available for research use, but I haven't heard of them for a long while.  

In olden-times (mid 1990s), they had a family which you could feed random bitstreams to without fear of damage.  Adrian Thompson (no relation!) used this to create a frequency discriminator:

http://www.informatics.sussex.ac.uk/users/adrianth/gp96/paper.ps

http://www.sussex.ac.uk/Users/adrianth/gp96/ref.html