Biomedical Engineering Reference
In-Depth Information
G
c,k
ξ
m
c
ξ
n
k
ξ
n
V
k
V
k
ξ
p
1
p
2
Targeted schema
Figure 4.2
Copy-and-paste. on. schemata.
ξ . is. the. resultant. schema. that. will. be. com-
pared.with.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,.
IEEETransactionson
IndustrialInformatics
,.7(3),.2011,.408-418.)
ξ . and.
ξ ,. where.
The. population. size. is. assumed. to. be. ininite,. and. instead. of. calculating.
the.exact.number.of.strings.belonging.to.some.schemata,.the.expected.occur-
rence. probability.
i
. is. the. focus.. The. derivation. of. the. schema.
evolution.equation.follows.the.exact.formulations.of.other.GA.dynamics,.in.
which.the.effects.of.both.destruction.and.construction.are.considered.
Depending.on.the.schemata.
ξ
m
.and.ξ
n
,.four.possible.cases.are.obtained.
P
( , ),
. ξ ∈
ξ
t
i
CaseA
ξ
= ξ
.and. ξ
= ξ
..(A.transposon.is.copied.from.schema.ξ.and.pasted.onto.
m
n
schema.ξ.)
If. the. resultant. schema.
ξ
n
. no. longer. belongs. to. ξ,. that. is,.
′
ξ
′
≠ ξ
,. after. the.
n
transposition,.schema.ξ.is.hence.destroyed,.and.the.condition.is
.
(4.13)
∆ ξ
( ,
V
;
ξ
′
,
V
)
≠
1
⇒ ∆ ξ
( ,
V
;
ξ
,
G
)
≠
1
.
k
n
k
k
c k
,
By.considering.all.the.possible.combinations.of.
c
.and.
k
,.the.destructive.rate.
PD
A
.of.ξ.is.then.computed.as
L L
−
L L
−
g
g
p
L L
∑
∑
copy
PD
=
[1
− ∆ ξ
( ,
V
;
ξ
,
G
)]
.
(4.14)
A
k
c k
,
(
−
+
1)
2
g
.
c
=
0
k
=
0
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