The listed methods differ mainly in the selection pressure, which can be set by a strategy parameter in the rank selection described below. The higher the selection pressure, the faster a population converges against a certain solution and the search space may not be explored sufficiently. This
premature convergence can be counteracted by
structuring the population appropriately. There is a close correlation between the population model used and a suitable selection pressure.
Roulette wheel selection In the
roulette wheel selection, the probability of choosing an individual for breeding of the next generation is proportional to its fitness, the better the fitness is, the higher chance for that individual to be chosen. Choosing individuals can be depicted as spinning a roulette that has as many pockets as there are individuals in the current generation, with sizes depending on their probability. Probability of choosing individual i is equal to p_i = \frac{f_i}{\Sigma_{j=1}^{N} f_j}, where f_i is the fitness of i and N is the size of current generation (note that in this method one individual can be drawn multiple times).
Stochastic universal sampling Stochastic universal sampling is a development of roulette wheel selection with minimal spread and no bias.
Rank selection In rank selection, the probability for selection does not depend directly on the fitness, but on the fitness rank of an individual within the population. This can be particularly helpful in applications with restrictions, since it facilitates the overcoming of a restriction in several intermediate steps, i.e. via a sequence of several individuals rated poorly due to restriction violations.
Linear rank selection Linear ranking, which goes back to Baker, is often used. It allows the selection pressure to be set by the parameter sp , which can take values between 1.0 (no selection pressure) and 2.0 (high selection pressure). The probability P for n rank positions R_i is obtained as follows: :P(R_i) =\frac{1}{n}\Bigl(sp-(2sp-2)\frac{i-1}{n-1}\Bigr) \quad \quad 1\leq i \leq n ,\quad 1 \leq sp \leq 2 \quad \mathsf{with} \quad P(R_i) \ge 0, \quad \sum_{i=1}^nP(R_i)=1 Another definition for the probability P for rank positions i is: :P(i) =\frac{2*(n-i+1)}{n*(n+1)}
Exponential rank selection Exponential rank selection is defined as follows:
Lexicase selection Most selection algorithms select individual genomes on the basis of scalar fitness values, which in many case will have been derived from multiple training cases. By contrast, Lexicase selection considers performance on individual training cases separately, rather than aggregating performance measures across multiple cases. It considers cases in different random orders, and therefore with different priorities, for each selection event. == See also ==