Selection (evolutionary algorithm)

Selection is a genetic operator in an evolutionary algorithm (EA). An EA is a metaheuristic inspired by biological evolution and aims to solve challenging problems at least approximately. Selection has a dual purpose: on the one hand, it can choose individual genomes from a population for subsequent breeding (e.g., using the crossover operator). In addition, selection mechanisms are also used to choose candidate solutions (individuals) for the next generation. The biological model is natural selection.

Retaining the best individual(s) of one generation unchanged in the next generation is called elitism or elitist selection. It is a successful (slight) variant of the general process of constructing a new population.

The basis for selection is the quality of an individual, which is determined by the fitness function. In memetic algorithms, an extension of EA, selection also takes place in the selection of those offspring that are to be improved with the help of a meme (e.g. a heuristic).

A selection procedure for breeding used early on^[1] may be implemented as follows:

The fitness values that have been computed (fitness function) are normalized, such that the sum of all resulting fitness values equals 1.
Accumulated normalized fitness values are computed: the accumulated fitness value of an individual is the sum of its own fitness value plus the fitness values of all the previous individuals; the accumulated fitness of the last individual should be 1, otherwise something went wrong in the normalization step.
A random number R between 0 and 1 is chosen.
The selected individual is the first one whose accumulated normalized value is greater than or equal to R.

For many problems the above algorithm might be computationally demanding. A simpler and faster alternative uses the so-called stochastic acceptance.

If this procedure is repeated until there are enough selected individuals, this selection method is called fitness proportionate selection or roulette-wheel selection. If instead of a single pointer spun multiple times, there are multiple, equally spaced pointers on a wheel that is spun once, it is called stochastic universal sampling. Repeatedly selecting the best individual of a randomly chosen subset is tournament selection. Taking the best half, third or another proportion of the individuals is truncation selection.

There are other selection algorithms that do not consider all individuals for selection, but only those with a fitness value that is higher than a given (arbitrary) constant. Other algorithms select from a restricted pool where only a certain percentage of the individuals are allowed, based on fitness value.

^ Holland, John H. (1992). Adaptation in natural and artificial systems. PhD thesis, The University of Michigan, 1975. Cambridge, Mass.: MIT Press. ISBN 0-585-03844-9. OCLC 42854623.

[1] Holland, John H. (1992). Adaptation in natural and artificial systems. PhD thesis, The University of Michigan, 1975. Cambridge, Mass.: MIT Press. ISBN 0-585-03844-9. OCLC 42854623.

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