I watched a video about what would happen to the human species if there were only two people left on Earth. Basically humanity would be almost guarunteed to go extinct from incest induced genetic illness.

But that made me wonder: what would it take to prevent that? For example, what if they were able to recreate or maintain advanced fertility technology? In other words, what if the mother and father froze their eggs and sperm and their children acted as surrogate parents for their own generic brothers and sisters long after their genetic parents had passed on?

If death is no obstacle, what is the fastest and most efficient strategy for weeding out genetic illness? What would it take to recover a stable population?