### 4.2.2 Population Selection     continued...

It is clear that f must always be positive for this scheme to be used. Its range and scaling are also important. For instance, early in a search it is possible for a few superindividuals (solutions with fitness values significantly better than average) to dominate the selection process. Various schemes have been suggested to overcome this potential danger, of which the simplest is linear scaling, whereby f is rescaled through an equation of the form:

Coefficients a and b are chosen each generation so that the average values of f and are equal and so that the maximum value of is a specified multiple of (usually twice) the average. Linear scaling risks the introduction of negative values of for low performance solutions and must, therefore be used with caution.

Baker [3] suggested that should simply be made a (linear) function of the solution's rank within the population. For example, the best solution might be allocated a survival probability of . If this is the case, that for the worst solution is then constrained to be zero, because of the normalization condition that the survival probabilities sum to unity. This ranking scheme has been found to overcome the problems of over- or underselection, without revealing any obvious drawbacks.