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    In the description I would not reveal what the underlying task is (i.e. we are just trying to reach some fixed bitstring and that the fitness function calculates the difference between the individual and the solution).

    This already means that there is a unique maximum for the fitness function and it can easily be solved by optimizing individually for each bit (just for each bit test whether 0 or 1 gives a higher fitness value). So there are no dependencies between the bits and the solution cannot get stuck in a local maximum. That's the reason why you need the roulette selection method, the crossover and mutations to begin with, to get out of local maximums but if there are none then what's the point?