141
2.2 Selection
CGA uses proportional selection, the population of the next generation is
determined by n independent random experiments; the probability that individ-
ual x
i
is selected from the tuple (x
1
,x
2
, ..., x
m
) to be a member of the next
generation at each experiment is given by
P{x
i
is selected}=
f(x
i
)
∑
m
j=1
f(x
j
)
>0. (1)
This process is also called roulette wheel parent selection and may be viewed
as a roulette wheel where each member of the population is represented by a
slice that is directly proportional to the member’s fitness. A selection step is
then a spin of the wheel, which in the long run tends to eliminate the least fit
population members.
2.3 Crossover
Crossover is an important random operator in CGA and the function of the
crossover operator is to generate new or ‘child’ chromosomes from two ‘parent’
chromosomes by combining the information extracted from the parents. The
method of crossover used in CGA is the one-point crossover as shown in
Fig. 2(a). By this method, for a chromosome of a length l, a random number
c between 1 and l is first generated. The first child chromosome is formed by
appending the last l−c elements of the first parent chromosome to the first c
elements of the second parent chromosome. The second child chromosome is
formed by appending the last l−c elements of the second parent chromosome
to the first c elements of the first parent chromosome. Typically, the probability
for crossover ranges from 0.6 to 0.95.
2.4 Mutation
Mutation is another important component in CGA, though it is usually con-
ceived as a background operator. It operates independently on each individual
FIG. 2 One-point crossover and mutation operators.
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