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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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