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In-Depth Information
N
x
j
(
x
i
(
g
(
k
)
m
Pi
(
k
)
m
Aj
(
k
)
[
k
)
−
k
)
]
1
m
Ii
(
a
i
(
k
)
=
i
σ
j
,
(8.19)
k
)
X
i
(
k
)
−
X
j
(
k
)
+
ε
j
=
1
,
j
=
m
Pi
(
are the active gravitational mass, the passive gravitational
mass and the inertia mass of
i
th agent,
k
)
,
m
Aj
(
k
)
and
m
Ii
(
k
)
ε>
0 is a relatively small constant, and
σ
i
,
0
≤
σ
i
1, is a random generated number.
The masses in Eq. (
8.19
) are computed using
≤
N
n
i
(
k
)
=[
f
i
(
k
)
−
w(
k
)
]
/
[
b
(
k
)
−
w(
k
)
]
,
m
i
(
k
)
=
n
i
(
k
)/
[
n
j
(
k
)
]
,
m
Ai
=
m
Ii
=
m
i
,
j
=
1
(8.20)
the term
b
(
k
)
corresponds to the best agent, and the term
w(
k
)
corresponds to the
worst agent
b
(
k
)
=
min
f
j
(
k
), w(
k
)
=
max
f
j
(
k
).
(8.21)
j
=
1
...
N
j
=
1
...
N
d
and the next position
x
i
(
The next velocity
v
i
(
k
+
1
)
k
+
1
)
of
i
th agent are
obtained by the state-space equations
d
d
a
i
(
v
i
(
k
+
1
)
=
ρ
i
v
i
(
k
)
+
k
),
(8.22)
x
i
(
x
i
(
d
k
+
1
)
=
k
)
+
v
i
(
k
+
1
)
where
1 is a uniform random variable.
The first adaptive GSA operates with fixed length stages. The five stages of the
first adaptive GSA are presented in Fig.
8.3
. The exploration (stage II) is conducted
for the first
r
e
1
k
max
=
ρ
i
,0
≤
ρ
i
≤
15
k
max
iterations in the search process using the depreciation
law from Eq. (
8.16
), where
r
e
1
is the ratio of exploration runs, 0
0
.
<
r
e
1
<
1. The
explanation (stage III) is conducted for the next
r
e
2
k
max
=
.
45
k
max
iterations using
the depreciation law from Eq. (
8.17
), where
r
e
2
is the ratio of explanation runs,
0
0
1. The last gravitational constant in the previous stage is used as the
initial value for this stage, and the parameter
<
e
e
2
<
ε
is reduced starting with the preset
value
ε
0
>
0 in terms of the law
ε
=
ε
0
(
k
max
−
k
)/(
0
.
85
k
max
).
(8.23)
4
k
max
iterations with Eq. (
8.23
), and the worst fitness and position values are reset to the best
values after each iteration. The evaluation (stage V) applies the tuned parameters to
the TS PI-FLCs in the real-world process, and experiments are conducted to evaluate
the fuzzy control system behaviors.
The second adaptive GSA operates with fuzzy logic-based adaptive lengths. Two
Single Input-Single Output (SISO) fuzzy logic blocks, referred to as SISO FLB1
and SISO FLB2, compute the values of
r
e
1
and
r
e
2
. This version of adaptive GSA
The elaboration (stage IV) is conducted for the last
(
1
−
r
e
1
−
r
e
2
)
k
max
=
0
.
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