Very little. An FPGA is a set of reprogrammable logic blocks (LUTs) of very small size, plus a number of special purpose peripherals. The "layout" process of assigning functions to LUTs is usually done with simulated annealing and random perturbation. The compiler won't necessarily give the same output from the same input, let alone slightly different input.
The fixed-function blocks and any embedded processors (e.g. Nios) are more targetable. But you could also e.g. set up the clock PLL to leak the FPGA configuration slowly via spread-spectrum modulation.
A genetic algorithm, by contrast, encodes the system into a "string" (like a DNA strand), and then swaps pieces of strings between two "organisms," just like genetic mating does. The most optimal descendants are kept, the least are discarded, and the process is repeated. This would be harder to implement for locations, as you would have to encode locations onto a string, and be able to swap pieces of strings while maintaining the functionality of the LUTs.