Even if the differences between the subjects are very strong, or weak, the difference between probabilities of reproduction only depends on the ranking of the subjects. To illustrate these methods, let's consider a population of four subjects to check the effect of scaling. For each subject, we give the fitness and the corresponding selection probability. Exponential flattens the distribution. It's very useful when a super-subject induces an excessively fast convergence.
Linear transformation plays slightly the same role than exponential.
At last, linear normalization is neutral towards the distribution of the fitness and only depends on the ranking. It avoids as well super-subjects as a too homogeneous distribution. Conclusion Genetic algorithms are original systems based on the supposed functioning of the Living 12 . The method is very different from classical optimization algorithms 13 . Use of the encoding of the parameters, not the parameters themselves.