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| [[Image:Fitness proportionate selection example.png|thumb|270px|Example of the selection of a single individual]]
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| '''Fitness proportionate selection''', also known as '''roulette wheel selection''', is a [[genetic operator]] used in [[genetic algorithm]]s for selecting potentially useful solutions for recombination.
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| In fitness proportionate selection, as in all selection methods, the [[fitness function]] assigns a fitness to possible solutions or [[chromosome]]s. This fitness level is used to associate a [[probability]] of selection with each individual chromosome.
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| If <math>f_i</math> is the fitness of individual <math>i</math> in the population, its probability of being selected is <math>p_i = \frac{f_i}{\Sigma_{j=1}^{N} f_j}</math>, where <math>N</math> is the number of individuals in the population.
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| This could be imagined similar to a Roulette wheel in a casino. Usually a proportion of the wheel is assigned to each of the possible selections based on their fitness value. This could be achieved by dividing the fitness of a selection by the total fitness of all the selections, thereby normalizing them to 1. Then a random selection is made similar to how the roulette wheel is rotated.
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| 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.
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| 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.
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| Other selection techniques, such as [[stochastic universal sampling]]<ref>Bäck, Thomas, ''Evolutionary Algorithms in Theory and Practice'' (1996), p. 120, Oxford Univ. Press</ref> 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].
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| The naive implementation is carried out by first generating the [[Cumulative probability distribution function|cumulative probability distribution]] (CDF) over the list of individuals using a probability proportional to the fitness of the individual. A [[uniform distribution (continuous)|uniform random]] number from the range [0,1) is chosen and the inverse of the CDF for that number gives an individual. This corresponds to the roulette ball falling in the bin of an individual with a probability proportional to its width. The "bin" corresponding to the inverse of the uniform random number can be found most quickly by using a [[Binary search algorithm|binary search]] over the elements of the CDF. It takes in the [[Big O notation|O(logn)]] time to choose and individual. A faster alternative that generates individuals in O(1) time will be to use the [[alias method]].
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| ==See also==
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| *[[Stochastic universal sampling]]
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| *[[Tournament selection]]
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| *[[Reward-based selection]]
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| ==External links==
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| *[http://www.cs.ucl.ac.uk/staff/W.Langdon/ftp/gp-code/GProc-1.8b.tar.gz C implementation] (.tar.gz; see selector.cxx) WBL
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| *[http://www.edc.ncl.ac.uk/highlight/rhjanuary2007g02.php/ Example on Roulette wheel selection]
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| ==References==
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| {{Reflist}}
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| {{DEFAULTSORT:Fitness Proportionate Selection}}
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| [[Category:Genetic algorithms]]
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