Fitness proportionate selection

Fitness proportionate selection, also known as roulette-wheel selection, is a genetic operator used in genetic algorithms for selecting potentially useful solutions for recombination.

In fitness proportionate selection, as in all selection methods, the fitness function assigns a fitness to possible solutions or chromosomes. This fitness level is used to associate a probability of selection with each individual chromosome.If $f\_i$ is the fitness of individual $i$ in the population, its probability of being selected is $p\_i\; =\; frac\{f\_i\}\{Sigma\_\{j=1\}^\{N\}\; f\_j\}$, where $N$ is the number of individuals in the population.While candidate solutions with a higher fitness will be less likely to be eliminated, there is still a chance that they may be. Contrast this with a less sophisticated selection algorithm, such as truncation selection, which will eliminate a fixed percentage of the weakest candidates. With fitness proportionate selection there is a chance some weaker solutions may survive the selection process; this is an advantage, as though a solution may be weak, it may include some component which could prove useful following the recombination process.

The analogy to a roulette wheel can be envisaged by imagining a roulette wheel in which each candidate solution represents a pocket on the wheel; the size of the pockets are proportionate to the probability of selection of the solution. Selecting N chromosomes from the population is equivalent to playing N games on the roulette wheel, as each candidate is drawn independently.

Other selection techniques, such as stochastic universal sampling [Back, 1996, page 120] or tournament selection, are often used in practice. This is because they have less stochastic noise, or are fast, easy to implement and have a constant selection pressure [Blickle, 1996] .

Note performance gains can be achieved by using a binary chop rather than a linear search to find the right pocket.

External links

* [http://www.cs.ucl.ac.uk/staff/W.Langdon/ftp/gp-code/GProc-1.8b.tar.gz Computer code] (in C) (see selector.cxx) WBL.