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}
where
c
j
(
Ab
i
) is the serial number of
j
th
city in the route. Here,the formulation
of the difference function is given as follows:
{
c
1
(
Ab
i
)
,c
2
(
Ab
i
)
,c
3
(
Ab
i
)
...c
j
(
Ab
i
)
...c
k
(
Ab
i
)
j
=1
| c
j
(
Ab
m
)
−c
j
(
Ab
i
)
|
)
.
(
|
aff
(
Ab
m
)
−
aff
(
Ab
i
)
|
)
k
f
diff
(
Ab
i
)=(
(6)
In this formulation,
j
=1
|
c
j
(
Ab
m
)
−
c
j
(
Ab
i
)
|
is the cumulative difference, and
|
is the anity difference. In the proposed algorithm, the
product of these two difference values is considered as a measurement of the
difference of each two antibody.
Then, the normalized antibody difference ([0,1]) can be computed as
aff
(
Ab
m
)
−
aff
(
Ab
i
)
|
f
diff
(
Ab
i
)
−
min(
f
diff
(
.
))
diff
(
Ab
i
)=
(7)
max(
f
diff
(
.
))
−
min(
f
diff
(
.
))
Considering the difference of memory antibody, we have
min(
f
diff
)=
f
diff
(
Ab
m
)=0
(8)
So that,
f
diff
(
Ab
i
)
max(
f
diff
(
.
))
diff
(
Ab
i
)=
(9)
3.3 Hormonal Regulation
To implement regulation of hormone, there are two operators for the bidirec-
tional hormonal regulation: Elimination and Mutation. And then the H updating
function is defined by
H
(
Ab
i
)=
1
90
(
atan
(2
∗
diff
(
Ab
i
)
−
1) + 45)
(10)
The elimination probability of any antibody
Ab
i
is defined by
H
(
Ab
i
). Randomly
generate a number
r
[0
,
1), if,
r<H
(
Ab
i
) antibody
Ab
i
would be eliminated. In
this way, bad individuals with higher difference value will be eliminated.
The mutation probability of remaining antibody
Ab
i
after elimination opera-
tor is defined by
H
(
Ab
i
). Randomly generate a number
r
[0
,
1), if
r<H
(
Ab
i
)
, antibody
Ab
i
would mutate to a random position. Here, we adopt a muta-
tion method of multipoint mutation, in which points or positions of mutation
operators change randomly.
Note that the main feature of this the hormonal regulation is that it implement
a two-way regulation intended to maintain the network in a dynamic steady
state. That is, antibodies with low difference are suppressed to mutate; while
antibodies with high difference are promoted. Meanwhile, new antibodies will
be generated after elimination and mutation such that the scale of antibody
population remains the same size
n
.
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