Resource Management in WCDMA - Multiobjective Optimization Methodology: A Jumping Gene Approach - page 156

7.. i .=. i .+.1..If. i .≤. N ,.go.to.step.4.

8.. k .=. k .+.1..If. k .≤. N p ,.go.to.step.3.

. 9.. End.

An.example.of.this.operation.is.given.in . Figure 7.2 . .Assume.that.25.users.are.
connecting. to. the. system;. there. exist. 2. ×. 25. = 50. genes. in. the. chromosome.
as.shown..Suppose.that.only.genes.1,.2,.and.50.are.going.to.be.mutated;.it.is.
deduced.that.user.1.(voice.user),.user.2.(voice.user),.and.user.25.(video.user).
belong.to.cases.A,.B,.and.C,.respectively..After.mutation,.the.value.of.gene.1.
(the.power.value.of.user.1).is.decreased..The.values.of.gene.2.(the.power.value.
of. user. 2). and. gene. 27. (the. rate. value. of. user. 2). are. increased. and. reduced,.
respectively..However,.gene.50.(the.rate.value.of.user.25).will.not.be.mutated.
and.remains.unchanged.as.the.value.of.

( ) .belongs.to.case.C.

E
N b
o

7.7 RankingRule
The.standard.Pareto.ranking.(see.Section.2.2.1.in. Chapter.2 ).may.not.be.suit-
able.for.this.optimization.problem..This.is.because.the.third.objective. f .(i.e.,.
the.total.number.of.QoS-violating.users).is.more.crucial.than.the.other.two.
objectives.[see . Equations.(7.1) - (7.3) .f or.the.deinition.of.the.objectives].
Let.us.consider.two.chromosomes.I 1 .and.I 2 .with.objective.values.

f .

f , f ,

1 2 3

and. f ′ , f ′ , f ′,. respectively. [

f . are. defined. in. Equations. (7.1) - (7.3) ]. . If. f , f , 1 2 3

1 2 3

′ ,. I .should.be.preferable.to. I .regardless.of.the.values.of.

f , f , f ′,.and.

f < f 1 2 1

3 3

f ′..Therefore,.the.ranking.rule.is.slightly.modified.as.follows:

I 1 .is.preferable.to. I 2 .if.and.only.if

.

′ .or.(∀ m = 1,2,3. f

f ′ .and.∃ n = 1,2.s.t.. f < f ′ )

( f < f ) ≤ m m n n

3 3

The. main. benefit. of. this. modified. ranking. rule. is. that. it. can. direct. the.
search. toward. solutions. with. fewer. QoS-violating. users. or. even. zero. such.
users,. while. it. can. identify. multiple. trade-off. solutions. for. different. total.
numbers.of.QoS-violating.users.

7.8 ResultsandDiscussion
The.parameters.of.WCDMA.systems.and.user.services.are.assumed.and.are.
listed.in .Tables 7.3 .and . 7.4, . respectively..The.system.model.contains.9.hexago-
nal.cells,.as.shown.in. Figure 7.3. .Each.cell.has.a.base.station.located.at.the.