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influences on schema, where
C
2
,C
3
,C
6
are the instances of schema ******1*#.
The average intensity of this schema is as follows:
v(******1*#) =
0
+
2
+
2
= 1.33
3
C
3
,C
5
,C
8
is the instances of schema *00*#*****. Its average intensity is as
follows:
v(*00*#*****) =
2
+
2
+
1
= 1.67
3
In genetic algorithm, if only simple crossover operator is applied, then after a
generation, the average proportion of each schema
H
from
B
(
t
) in population
changes as follows:
δ
(
H
)
1
f
(
H t
f t
, )
( )
p
P(H
t
+1)
²
(1-
(1-P(H
t
)))
P(H
t
)
(13.23)
c
l
−
where
p
c
denotes crossover probability. It can be concluded that as long as
δ
(
H
)
)
²
[1+
f
f
(
H,t
]
(t), the number of the instances of schema H will increase.
l
−
Pt. of interchange
[ Crossover ]
C
3
[Parents ]
v (C
2
, t)
[No . Offspring ]
C
3'
[ Offspring ]
1110 ### 0 #
1
6
1110 ## 11 #
1## 0111 ##
0
0001 ### 0 #
0001 ## 11 #
2
0001 ## 11 #
010 ##1000
0
#00 #### 11
#00 #### 11
2
#00 #### 11
17
0# 01## 10 #
0# 01## 10 #
2
### 100100
0
000 ## 0111
1
100 ## 0111
1
1# 01## 10 #
Fig. 13.9. Genetic operators
13.6.4
Mutation operation
For each individual
a
=
s
1
s
2
…s
l
in pupolation
B
(
t
), the simple mutation operation
is described as follows:
