Fitness proportionate selection

This fitness level is used to associate a probability of selection with each individual chromosome.

Usually a proportion of the wheel is assigned to each of the possible selections based on their fitness value.

Then a random selection is made similar to how the roulette wheel is rotated.

This is because even though the probability that the weaker solutions will survive is low, it is not zero which means it is still possible they will survive; this is an advantage, because there is a chance that even weak solutions may have some features or characteristics which could prove useful following the recombination process.

[citation needed] Selecting N chromosomes from the population is equivalent to playing N games on the roulette wheel, as each candidate is drawn independently.

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 over the elements of the CDF.

A faster alternative that generates individuals in O(1) time will be to use the alias method.

Certain analysis indicates that the stochastic acceptance version has a considerably better performance than versions based on linear or binary search, especially in applications where fitness values might change during the run.

If you were to visually normalize this between 0.0 and 1.0, it would be grouped like below with [red = 1/10, green = 2/10, blue = 3/10, black = 4/10]: Using the above example numbers, this is how to determine the probabilities: The last index should always be 1.0 or close to it.

This is because they have less stochastic noise, or are fast, easy to implement and have a constant selection pressure.