Resource Management in WCDMA - Multiobjective Optimization Methodology: A Jumping Gene Approach - page 159

center,.and.the.locations.of.all.users.are.randomly.distributed.to.all.the.cells..
The.distance.between.user. i .and.base.station. b .can.be.measured.by

2

( ) ( )

d = x − x + y − y . (7.4)

bi i b i b

.

where. ( x y

i

,

i .and. (

) x y

b

,

b .are.the. x - y .coordinates.of.user. i .and.base.station. b ,.

)

respectively.
The. services. provided. for. all. users. include. voice,. data,. and. video,. and.
users'. requests. are. randomly. generated.. The. link. gain. g bi . between. mobile.
user. i .and.base.station. b .is.modeled.as.follows:

s
d

bi

g =

bi

4

. . (7.5)

bi

where. s bi .is.the.shadow.fading.factor,.and. d bi .is.the.distance.between.mobile.
user. i .and.base.station. b .
The.values.of. s bi .are.generated.through.the.log-normal.distribution.with.
an.expected.value.of.0.dB.and.a.standard.deviation.of.8.dB..For.each.of.two.
scenarios,. 25. users. and. 50. users,. 10. testing. sets. of. different. distributions.
of.user.locations.and.different.requested.user.services.were.considered.in.
the.simulation.
The.JG.is.compared.with.multiobjective.evolutionary.algorithms.(MOEAs),.
including. the. multiobjective. genetic. algorithm. (MOGA),. niched. Pareto.
genetic. algorithm. 2. (NPGA2),. nondominated. sorting. genetic. algorithm. 2.
(NSGA2),.strength.Pareto.evolutionary.algorithm.2.(SPEA2),.Pareto.archived.
evolution. strategy. (PAES),. and. microgenetic. algorithm. (MICROGA),. and.
their. parameters. are. given. in . Table 7.5. . Apart. from. these. MOEAs,. a. modi-
fied.GA,.which.only.relies.on.the.mutation.operation.proposed.in.Shayestch,.
Menhaj,. and. Nobary. [20],. is. also. included.. They. reported. that. its. perfor-
mance.was.much.better.than.a.common.GA.and.close.to.the.optimum.detec-
tor;.at.the.same.time,.it.requires.less.computational.complexity.
To.realize.the.performance.of.the.sets.of.nondominated.solutions.found.by.
each.MOEA,.the.two.performance.metrics.(Deb.and.Jain.convergence.metric.
and.spread,.mentioned.in.Sections.5.2.and.5.3.of. Chapter.5 ,.respectively).were.
adopted..The.means.and.standard.deviations.of.the.two.performance.metrics.
were.obtained.based.on.50.simulation.runs.performed.for.each.MOEA.in.each.
of.10.testing.sets.for.the.two.different.scenarios. ( Tables 7.6 - 7.9 ).
Since. the. true. Pareto-optimal. set. is. unknown. for. each. case,. a. set. of. ref-
erence. solutions. was. found. to. approximate. the. true. Pareto-optimal. set,. as.
explained. in. Section. 5.2.. This. reference. set. was. obtained. by. incorporating.
the.MOEAs.together.with.some.arbitrarily.sufficient.large.number.of.genera-
tions.or.iterations..(It.was.set.as.200.generations.for.MOGA,.NPGA2,.NSGA2,.
SPEA2,.and.JG;.10,000.iterations.for.PAES;.and.2,500.iterations.for.MICROGA.
for.both.scenarios.)