target = "METHINKS IT IS LIKE A WEASEL";
alphabet = Append[CharacterRange["A", "Z"], " "];
fitness = HammingDistance[target, #] &;
mutate[str_String, rate_ : 0.01] := StringReplace[
  str,
  _ /; RandomReal[] < rate :> RandomChoice[alphabet]
]

mutationRate = 0.02; c = 100;
NestWhileList[
   First@MinimalBy[
      Thread[mutate[ConstantArray[#, c], mutationRate]],
      fitness
   ] &,
   mutate[target, 1],
   fitness@# > 0 &
] // ListAnimate