Biomedical Engineering Reference
In-Depth Information
START
No
crowding distance
assignment (
F
i
)
|
P
t
+1
| + |
F
i
| ≤
N
?
R
t
=
P
t
Q
t
Yes
F
= fast nondominated
sort (
R
t
)
sort (
F
i
,
n
)
P
t
+1
=
P
t
+1
F
i
P
t
+1
=
P
t
+1
F
i
[1 : (
N
- |
P
t
+1
|)]
P
t
+1
=
φ
i
= 1
i
=
i
+ 1
END
Figure 2.8
Flowchart.of.the.elitism.strategy.
raw.fitness,.density.estimation,.and.an.archive.truncation.method..Its.flow-
chart.is.depicted.in
.
Figure 2.9.
2.2.4.1 Strength Value and Raw Fitness
Consider. a. population
P
. and. an. archive.
A
. containing. the. other. solutions.
dominated.by.solution
i
,.the.strength.value.of.solution
i
,.
S
(
i
),.is.speciied.by
S i
( ) |{ : (
=
j
j P A
∈
+
)
∧
(
i
j
)}|
.
(2.9)
.
|•|. is. the. cardinality. of. a. set,. +. is. the. multiset. union,. and.≻. is. the. Pareto.
dominance.relation.deined.in
.
Equation.(2.2)
.
The. raw. fitness. of. the. individual.
i, R
(
i
),
is. acquired. by. summing. the.
strength.values.of.its.dominators.in.both.population.and.archive..In.math-
ematics,.one.has
∑
R i
( )
=
S j
( )
.
(2.10)
.
j P A j
∈ +
;
i
Assuming. that. a. minimization. problem. is. considered,. an. individual.
with.a.zero.raw.fitness.value.is.a.nondominated.one..In.contrast,.an.indi-
vidual.with.a.high.raw.fitness.value.means.that.it.is.dominated.by.many.
other.individuals.
2.2.4.2 Density Estimation
Even.though.the.raw.fitness.assignment.offers.a.sort.of.niching.mechanism.
on.the.basis.of.Pareto.dominance,.it.may.fail.when.most.individuals.do.not.
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