Biomedical Engineering Reference
In-Depth Information
of.all.the.schemata.equally.despite.the.current.distribution.of.the.schemata..
Hence,. the. supergood. chromosomes. that. dominate. the. population. will. be.
suppressed.and.premature.convergence.can.be.prevented..More.discussion.
about. the. theorems. of. equilibrium. and. their. effect. is. presented. in. further.
sections.
4.5.3 Destruction and Construction
From.the.derivation.of.the.schema.evolution.equations,.we.can.observe.that.
both.the.destruction.and.the.construction.of.schemata.play.important.roles..
With.a.higher.destruction.rate.and.a.lower.construction.rate,.the.number.of.
chromosomes.belonging.to.such.a.schema.will.decrease.sharply..In.contrast,.
a.schema.with.a.low.destructive.rate.and.high.constructive.rate.will.domi-
nate.the.whole.population.
Let.us.take.copy-and-paste.as.an.example..According.to.
Equations.(4.14)
.
ξ
. under. a. copy-and-paste. operation. is.
given.by
L L
−
L L
−
g
g
p
L L
∑
∑
[
]
copy
.
(4.69)
PD
=
1
− ∆ ξ
(
,
V
;
ξ
,
G
)
i
k
m
c k
,
2
(
−
+
1)
g
.
c
=
0
k
=
0
where.
tive.rate.can.be.formulated.as
S
m
i
L L
−
L L
−
g
g
p
L L
∑
∑
(
)
copy
.
(4.70)
PC
=
∆ ξ
(
,
V
;
ξ
,
G
)
∆ ξ
,
V
′ ξ
;
,
V
′
i
k
m
c k
,
i
k
n
k
2
(
−
+
1)
g
.
c
=
0
k
=
0
where.
ξ ∈ ξ
ξ
ξ
.
Recall.the.deinition.of.
a
mn
S
,
S
m
n
i
i
( )
.in
.Equation.(4.54);
.
the.destructive.rat
e.
Equation.
(4.69)
.becomes
L L
−
L L
−
g
g
p
L L
∑
∑
copy
PD
=
[1
− ∆ ξ
(
,
V
;
ξ
,
G
)]
i
k
m
c k
,
2
(
−
+
1)
g
c
0
k
0
=
=
.
(4.71)
L L
−
L L
−
g
g
1
∑
∑
=
p
1
−
∆ ξ
(
,
V
;
ξ
,
G
)
copy
i
k
m
c k
,
2
(
L L
−
+
1)
g
c
=
0
k
=
0
(
)
( )
i
=
p
1
−
a
copy
mi
.
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