Fitness proportionate selection
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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, possible solutions or chromosomes are assigned a fitness by the fitness function. In fitness proportionate selection, this fitness level is used to associate a probability of selection with each individual chromosome. 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.
Others 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 achived by using a binary chop rather than a linear search to find the right pocket. I have some C code http://www.cs.ucl.ac.uk/staff/W.Langdon/ftp/gp-code/GProc-1.8b.tar.gz (see selector.cxx) WBL