Biomedical Engineering Reference
In-Depth Information
By.regrouping.the.items,.the.schema.evolution.equation.under.the.copy-
and-paste.operation.can.be.derived.as
p
L L
(
)
copy
P
,
t
1
(1
p
) ( , )
P
t
ξ
+
=
−
ξ
+
copy
2
(
−
+
1)
g
.
.
(4.30)
L L
−
L L
−
g
g
∑
∑
∑
∑
[
]
×
∆ ξ
( ,
V
;
ξ
,
G
) ( ,
∆ ξ
V
′ ξ
;
,
V P
′
)
(
ξ
, ) (
t P
ξ
, )
t
k
m
c k
,
k
n
k
m
n
ξ
∈
S
ξ ∈
S
c
=
0
k
=
0
..
m
ξ
n
ξ
4.2.3 exact Schema evolution equation for Cut-and-Paste
Similar. to. the. copy-and-paste. operation,. the. cut-and-paste. operation. for.
≤
ξ
n
.. At.
the.same.time,.another.transposon.with.the.same.length.is.cut.from.ξ
n
.and.
pasted.onto.ξ
m
.to.form.
1
L
<
L
. is. cut. from. ξ
m
. and. pasted. onto. ξ
n
. to. form. a. new. schema.
′
g
ξ
m
..To.insert.the.transposons.into.the.selected.loca-
tions.(starting.with.the.bit.locations.
k
m
.and.
k
n
,.respectively),.some.bits.in.the.
original.schemata.have.to.be.shifted.accordingly.
Referring.to.
Figure 4.3
,
.different.regions.are.deined.as.follows:
′
.
1.
Transposonregion
:.
G
c
, ,
indicates.the.bit.locations.of.the.selected.
transposon.cut.from.ξ
j
.that.fall.into.the.deining.length.region.
p
c k
j
i
i
[
,
p
2
.
]
1
of.ξ.after.pasting.into.ξi.
i
.
M
c
m,
k
m
G
c
m
c
n
k
n
ξ
m
k
m
c
m
G
c
n
c
m
k
m
M
c
n,
k
n
c
n
k
n
ξ
n
ξ
n
ξ
´
m
M
c
m,
k
m
M
c
n,
k
n
I
c
n,
k
n
R
c
n,
k
n
R
c
m,
k
m
I
c
m,
k
m
R
c
m,
k
m
ξ
ξ
p
1
p
2
p
1
p
2
Targeted schema
Targeted schema
Figure 4.3
Cut-and-paste. on. schemata. ξ
m
. and. ξ
n
. where.
ξ
. are. the. resultant. schemata. that. will.
be. compared. with. the. targeted. schema. ξ.. (From. Tang,. K.. S.,. Yin,. R.. J.,. Kwong,. S.,. Ng,. K.. T.,.
Man,.K..F.,.A.theoretical.development.and.analysis.of.jumping.gene.genetic.algorithm,.
IEEE
TransactionsonIndustrialInformatics
,.7(3),.2011,.408-418.)
ξ
. and.
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