Biomedical Engineering Reference
In-Depth Information
where.α.is.a.constant.to.determine.the.shape.of.the.sharing.function,.σ
share
.is.
the.niche.radius.chosen.by.the.user.for.the.minimal.separation.desired,.and.
d
ij
.is.the.distance.specifying.the.similarity.of.two.individuals.
The.shared.fitness.of.a.chromosome.is.computed.by
f i
c
i
( )
.
(2.4)
f
′
i
=
( )
.
and.
c
i
.is.the.niche.count,.deined.as
N
∑
c
=
sf d
(
)
.
(2.5)
i
ij
.
j
=
1
where.
N
is.the.population.size.
2.2.2 Niched Pareto genetic algorithm 2
The.niched.Pareto.genetic.algorithm.2.(NPGA2),.which.is.an.improved.ver-
sion.of.the.NPGA.[42],.was.suggested.by.Erickson.et.al..[26]..The.flowchart.
of. NPGA2. is. shown. in
.
Figure 2.3
..
The. special. feature. of. this. algorithm. is.
the.use.of.fitness.sharing.when.the.tournament.selection.ends.in.a.tie..A.tie.
means.that.both.picked.individuals.are.dominated.or.nondominated..If.a.tie.
START
START
Crossover
Crossover
Yes
Yes
g
= MAXIMUM
GENERATION?
g
= MAXIMUM
GENERATION?
Set the required
parameters and
generation counter
g
= 0
Set the required
parameters and
generation counter
g
= 0
Mutation
Mutation
No
No
Specialized binary
tournament selection:
Specialized binary
tournament selection:
Objective value
evaluation
Objective value
evaluation
Population initialization
Use degree of domination
as rank
Use degree of domination
as rank
g
= g
+ 1
g
= g
+ 1
If solution 1 dominated,
select solution 2
If solution 1 dominated,
select solution 2
Objective value
evaluation
Objective value
evaluation
Else if solution 2 dominated,
select solution 1
Else if solution 2 dominated,
select solution 1
Output Pareto-optimal
solutions
Else if both solutions dominated
or both not dominated, perform
specialized fitness sharing and
then return solution with lower
niche count
Else if both solutions dominated
or both not dominated, perform
specialized fitness sharing and
then return solution with lower
niche count
END
END
Figure 2.3
Flowchart.of.NPGA2.
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