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RE: Genetic Algorithm
It is impossible to guarantee finding the global maximum. In the case of highly corrugated surfaces, the algorithm does not get stuck when getting into a local maximum, in contrast to Gradient Descent.
You should look into the methods of Applied Algebraic Geometry Groebner Bases (Symbolic) or Homotopy Methods (Numeric) which can guarantee finding a global maximum.
Oh, it's really good recommendation. Thank you! I will definitely be studying this issue.
And the reason that it doesn't get stuck (permanently) is that the genetic algorithm is usually stochastic, meaning that the recombination of the parental programs is somewhat random, so it can "jump" local bumps, given enough time.