In rank-based fitness assignment, the population is sorted according to the objective values. The fitness assigned to each individual depends only on its position in the individuals rank and not on the actual objective value.
Rank-based fitness assignment overcomes the scaling problems of the proportional fitness assignment. (Stagnation in the case where the selective pressure is too small or premature convergence where selection has caused the search to narrow down too quickly.) The reproductive range is limited, so that no individuals generate an excessive number of offspring. Ranking introduces a uniform scaling across the population and provides a simple and effective way of controlling selective pressure. (Selective pressure indicates the probability of the best individual being selected compared to the average probability of selection of all individuals.)
Consider Nind the number of individuals in the population, Pos the position of an individual in this population (least fit individual has Pos=1, the fittest individual Pos=Nind) and SP the selective pressure. The fitness value for an individual is calculated as:
Linear ranking allows values of selective pressure in [1.0, 2.0].
A new method for ranking using a non-linear distribution is introduced. The use of non-linear ranking permits higher selective pressures than the linear ranking method.
Figure 2 compares linear and non-linear ranking graphically.