Having studied this extensively back when they were called Genetic Algorithms, I would like to offer a few insights. 1) One of the biggest reasons they fell out of favor for more "mathematical" approaches was that no one could really explain why exactly they worked. It makes sense on the surface that "survival of the fittest" and doing something akin to multiple stochastic gradient descents would work, but no one has…
My thesis was on Generic Algorithm. I stopped and started working on Deep Learning mainly because like you said, GAs don't really have a strong mathematical foundation. Ironically, no one could really explain why CNNs work mathematically either. I've heard a lot of hand-wavy arguments about local search, local sensitivity, etc. However, no one could really prove anything meaningful. There are some papers around certa…
In fact we have many such problems in our own universe. I can give many examples of things NNs and GAs don't work well on right now. Those are just ignored by the research.