Biomedical Engineering Reference
In-Depth Information
Table b.1 (CONTiNueD)
Unconstrained.Test.Functions
TestFunctions
(NatureofTrue
ParetoFront)
Total
Numberof
Variables
n
Variable
Bounds
ObjectiveFunctions
ZIT2.(concave)
30
[0,.1]
f x
( )
=
x
1
1
2
−
x
g x
1
f x
( )
=
g x
( ) 1
2
( )
i
n
9
⋅ Σ
−
x
=
2
i
g x
( )
=
1
+
n
1
ZIT3.(convex.and.
disconnected)
30
[0,.1]
f x
( )
=
x
1
1
x
g x
x
g x
1
1
f x
( )
=
g x
( ) 1
−
−
( )
sin10
π
x
2
1
( )
i
n
9
⋅ Σ
−
x
=
2
i
g x
( )
=
1
+
n
1
ZIT4.(convex)
10
x
∈
[0, 1, ]
.
f x
( )
=
x
1
1
and.
∈ −
x
i
[ 5, 5]
.
for.
2, 3,
x
g x
1
f x
( )
=
g x
( ) 1
−
2
( )
i
=
,
n
(
)
i
n
2
g x
( )
=
1 10(
+
n
−
1)
+ Σ
x
−
10cos 4
π
x
=
2
i
i
ZIT6.(concave.
and.
nonuniformly.
spaced)
10
[0,.1]
6
f x
( )
=
1 exp( 4 )sin 6
−
−
x
π
x
1
1
1
2
−
f x
g x
( )
( )
1
f x
( )
=
g x
( ) 1
2
0.25
i
n
Σ
x
=
2
i
g x
( )
=
1 9
+
n
−
1
Source:
.
Data
from.Chan,.T..M.,.Man,.K..F.,.Kwong,.S.,.Tang,.K..S.,.A.jumping.gene.paradigm.for.
evolutionary.multiobjective.optimization,.
IEEETransactionsonEvolutionaryComputation
,.
12(2),.143-159,.2008.
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