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The following commentator writes:

Having studied this extensively back when they were called Genetic Algorithms, I would like to offer a few insights.

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 really been able to produce a mathematical proof as to why.

Since other folks are producing good examples of "explainable AI", I don't know how Genetic Algorithms/programming could be made 'explainable' as to why they achieved an optimal solution other than hand-waving to how evolution works in nature.

Steven Wolfram has published the book A New Kind of Science, in which he posits that mathematical proofs aren't relevant to this approach, and the algorithm is itself the science. Many considered this unsatisfactory.

We know that Cellular Automaton rule 110 is Turing complete. (And phenomenal things have been done with Conway's Game of Life).

My question is: Are there satisfying explanations for why genetic algorithms work?

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    $\begingroup$ Your question is problematic: what would evidence for absence of something look like? $\endgroup$ – Raphael Mar 24 '18 at 11:02
  • $\begingroup$ That said, I think there's ample evidence that genetic algorithms don't work in the sense of classic algorithms. They are fancy heuristic search algorithms and as such sometimes yield good results, and sometimes bad, and most of the time (if the problem is really hard) you won't be able to tell the difference. $\endgroup$ – Raphael Mar 24 '18 at 11:03
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    $\begingroup$ Words of my former lecturer: "when genetic algorithm works and you know how it works, it's probably when you have a good insight on the problem. In that case, you'll probably be writing a more direct algorithm anyway." $\endgroup$ – Billiska Mar 24 '18 at 11:08
  • $\begingroup$ Thanks @Raphael that’s helpful- I’ll update the question. $\endgroup$ – hawkeye Mar 24 '18 at 11:40
  • $\begingroup$ Are all the "many" mathematicians? Because if they are, that would be a pretty simple explanation of the criticism. Turkeys don't vote for Christmas, and it would add validity to your question. $\endgroup$ – Paul Uszak Mar 24 '18 at 14:11

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