Biomedical Engineering Reference
In-Depth Information
Appendix
B: Benchmark Test Functions
The.unconstrained.and.constrained.test.functions.used.in.our.study.are.pro-
vided.in.
Tables.B.1
.a
nd
.
B.2
,.
respectively..The.natures.of.true.Pareto-optimal.
fronts.of.the.test.functions.are.also.shown.in.the.first.columns.of.each.table..
Moreover,.the.true.Pareto-optimal.sets.and.the.corresponding.true.Pareto-
optimal.fronts.of.both.unconstrained.and.constrained.test.functions.utilized.
Table b.1
Unconstrained.Test.Functions
TestFunctions
(NatureofTrue
ParetoFront)
Total
Numberof
Variables
n
Variable
Bounds
ObjectiveFunctions
SCH.(convex)
1
[-10
5
,.10
5
]
f
1
(
x
).=.
x
2
f
2
(
x
).=.(
x-
2)
2
FON.(concave)
3
[-.4,.4]
n
∑
2
1
f x
( )
=
1 exp
−
−
x
−
1
i
n
i
=
1
n
∑
2
1
f x
( )
=
1 exp
−
−
x
+
2
i
n
i
=
1
POL.(convex.and.
disconnected)
2
[
−π π
,
]
f x
( )
=
1 (
+
A B
−
)
2
+
(
A B
−
)
2
1
1
1
2
2
f x
( )
=
(
x
+
3)
2
+
(
x
+
1)
2
2
1
2
A
=
0.5sin1 2 cos1 sin 2 1.5cos2
− + −
1.5sin1 cos1 2 sin 2 0.5cos2
A
=
−
+
−
B
=
0.5sin
x
−
2 cos
x
+
sin
x
−
1.5cos
x
1
1
1
2
2
B
=
1.5sin
x
−
cos
x
+
2 sin
x
−
0.5cos
x
2
1
1
2
2
ZIT1.(convex)
30
[0,.1]
f x
( )
=
x
1
1
x
g x
1
f x
( )
=
g x
( ) 1
−
2
( )
9
⋅ Σ
−
n
x
i
=
2
i
g x
( )
=
1
+
n
1
(
continued
)
221
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