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function is used to select chromosomes for deletion,
i.e
.
n
old chromosomes are
deleted and the population is refilled by
n
new chromosomes that are formed by
selection. The best chromosome is always preserved in the population (elitist
selection).
The probability that a selected chromosome will undergo a crossover operation
is 95%, whereas the probability of mutation is selected as 5%. When a
chromosome is selected for crossover (or mutation), one of the crossover (or
mutation) operators described below is applied with equal probability.
5.2.3.1.2 Crossover Operators for Real-coded Genetic Algorithms
For crossover operations, the chromosomes are selected in pairs (
s
a
,
s
b
):
x Simple arithmetic crossover, in which
s
are crossed over at the
k
th
position such that the resulting two offspring are:
g
s
and
g
"!
and
"!
,
g
1
g
1
s
aab b
,
,
,
,
,
s
bba
,
,
,
,
,
a
a
1
kk
1
L
b
1
kk
1
L
chrom
chrom
where
k
is selected randomly from {2, 3, ..., (
L
chrom
-1)}.
x Whole arithmetic crossover, in which a linear combination of
g
s
and
g
b
s
results in
and
.
g
1
g
g
g
1
g
g
s
r
s
1
r
s
s
r
s
1
r
s
a
a
b
b
b
a
x Heuristic crossover, in which
g
s
and
g
s
are combined such that
and
.
g
g
g
g
g
g
g
g
s
1
s
r
s
s
s
1
s
r
s
s
a
a
b
a
b
b
a
b
It is to be noted that the heuristic crossover described above is very similar to
the trial vector of differential evolution of type one (DE1; see Section 5.5), except
for
r
, which is a random number within 0 to 1 here, whereas in DE1 it is a constant
within the same 0 to 1 range.
5.2.3.1.3 Mutation Operators
Similar to crossover, there are various mutation operators. However, for the
mutation operation only one chromosome is selected through the RW.
x Uniform mutation, in which a randomly selected element
a
,
^
`
is replaced by
a
c
, which is a random number in the range
k
"
1, 2,
,
L
,
chrom
k
""
.
x Multiple uniform mutation is a uniform mutation of
n
randomly selected
elements, where
n
is selected at random and
^
¼
. The resulting chromosome is
ª
min
max
º
g
a
1
aa
,
s
aaa
1
,
,
,
,
¬
k
k
k
L
chrom
`
.
n
"
1, 2,
,
L
chrom
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