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Rosenbrock with Noise in Fitness
Minimize
f
(
x
)=
n−
1
100(
x
i
−
1)
2
x
i
+1
)
2
+(
x
i
−
IR
N
·
(1 + 0
.
4
|N
(0
,
1)
|
) i h
x
∈
i
=1
(A.4)
minimum
x
∗
=(1
,...,
1)
T
with
f
(
x
∗
) = 0. For higher dimensions the optimum
exhibits a local optimum at
x
=(
1
,...,
1)
T
, with properties like rosenbrock.
−
Rastrigin
Minimize
N
x
i
−
10 cos(2
πx
i
)+10
IR
N
f
(
x
)=
∈
with
x
(A.5)
i
=1
with properties
•
multi-modal, separable
•
huge number of local optima
•
scalable
5
,
5]
N
,
minimum
x
∗
=(0
,...,
0)
T
,
with
•
x
∈
[
−
f
(
x
∗
)=0.
Griewank
Minimize
cos
x
i
+1
N
N
x
i
IR
N
f
(
x
)=
4000
−
√
i
with
x
∈
(A.6)
i
=1
i
=1
15
10
5
50
40
0
30
20
-5
10
0
-10
150
100
50
4
4
0
2
2
-50
0
0
-150
-100
-100
-50
0
-2
-2
50
100
-150
150
-4
-4
Fig. A.3.
Left: plot of the rastrigin function. Right: plot of the griewank function.
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