Base Station Placement in WLANs - Multiobjective Optimization Methodology: A Jumping Gene Approach - page 182

. subject.to.the.following.three.constraints:

. a.. Each.terminal. i .must.be.allocated.to.only.one.installed.base.sta-

tion. k :. Σ c = 1, ∀ ∈ i T .

ik

k B ∈

. b.. Any.installed.base.station. k .must.be.located.inside.the.loor.plan.

of.the.IC.factory:. o ∈ O , ∀ k ∈ B .

k

. c.. Only.one.base.station.is.to.be.installed.in.a.location.

8.4 ChromosomeRepresentation
A.hierarchical.chromosome.encoding.scheme.[11].is.employed.so.that.differ-
ent.total.numbers.of.base.stations.to.be.installed.were.possible.for.different.
solutions..Similar.to.the.design.in.Section.6.4,.the.hierarchical.chromosome.
consists.of.two.types.of.genes:.control.genes.and.parameter.genes..The.con-
trol.genes.are.in.binary.form.to.control.the.activation.of.a.base.station,.for.
which.the. x-y .coordinates.for.installation.are.speciied.by.a.pair.of.parameter.
genes.encoded.in.floating-point.numbers.
Figure 8.1 . depicts.an.example.of.a.chromosome..Assuming.that.the.maxi-
mum.number.of.base.stations.that.can.be.installed.is.8,.the.hierarchical.chro-
mosome. length. is. then. 24. (8. control. genes. plus. 16. parameter. genes).. If. the.
i th.control.gene's.value.is.1,.the.location.with.the. x .coordinate.in.the.( i +.8)th.
gene.and.the. y .coordinate.in.the.( i +.16)th.gene.is.chosen.for.installing.a.base.
station.and.is.0.otherwise,.where.i = i = 1,2,…,8.
Referring.to.the.example.given.in . Figure 8.1 ,. two.base.stations.were.installed.
at. the. locations. with. x-y . coordinates. (8.457125,. 9.179531). and. (31.583469,.
19.247854). because. their. corresponding. control. genes. were. 1.. However,. no.
base.station.was.to.be.installed.at.the. x-y .coordinates.(20.371952,.17.671589).
since.the.corresponding.control.gene.is.0.

1 0 1 8.457125 20.371952 31.583469 9.179531 17.671589 19.247854

Gene 1 Gene 2 Gene 8 Gene 9 Gene 10 Gene 16 Gene 17 Gene 18 Gene 24

Control genes:
8 binary numbers

Parameter genes:
8 real floating-point numbers
( x coordinates)

Parameter genes:
8 real floating-point numbers
( y coordinates)

Figure 8.1
Encoding. method. for. a. hierarchical. chromosome.. (From. Chan,. T.. M.,. Man,. K.. F.,. Tang,. K. S.,.
Kwong, S.,. A. jumping-genes. paradigm. for. optimizing. factory. WLAN. network, IEEE
TransactionsonIndustrialInformatics ,.3(1),.33-43,.2007.)