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To illustrate the loss of genetic lineages, a modified version of
tournament selection is used. This version represents a caricature
of standard tournament selection, placing emphasis on the selection
of the fitter individuals.
The individuals in a population of size are sorted into
ascending fitness order,
from worst to best. A tournament size defines the number of
equal-sized partitions that divide the sorted
population, where a partition contains
individuals. Partitions
serve to separate the worst fit () from the best
fit individuals (). This assumes a unique fitness value
for each individual.
In a generational algorithm, to produce a child in the next generation,
a tournament is held
to find the root parent. If the population size is ,
then we hold tournaments to produce all the children.
Typically, tournaments are held to select for both
parents for crossover, but since only the root
parent and child are used to define lineages, only the one tournament
to select the root parent is considered.
Every individual in has the expectation of being
selected for a tournament
times.
To further simplify the model, tournament selection will pick
one individual from each partition, where there are partitions.
Thus, in every tournament held, the winner of that tournament will come
from . Every child in the next generation will be of a genetic
lineage that came from .
In practice, individuals are randomly selected from the
population to make a tournament.
To simulate the random nature of tournament selection, it will
be assumed that the number of offspring each individual in
produces for the next generation will be equal.

** Next:** 2 Variation of Loss
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S Gustafson
2004-05-20