Resource Management in WCDMA - Multiobjective Optimization Methodology: A Jumping Gene Approach - page 152

subject.to.the.following.constraints:

. 1.. The.transmission.power.of.each.user.must.lie.in.the.range.between.

the.minimum.and.maximum.allowed.power:.

min max

P ≤ p ≤ P , ∀ ∈ i N .

i i i

. 2.. The.transmission.rate.of.each.user.must.lie.in.the.range.between.the.

minimum.and.maximum.allowed.rate:.

min max

R ≤ r R ≤ , ∀ ∈ i N .

i i i

. 3.. 3..Fulfill. the. QoS. requirement. of. each. user. (each. user's. received. bit.

energy-to-noise. density. ratio. must. be. greater. than. or. equal. to. a.
required.minimum.value. γ ,.∀ i ∈ N ):

g p r

E
N

⋅ bi i i

b

= ≥ γ , ∀ ∈ i N

i

o

i

∑

g ⋅ p + η W

bj j

j N
j

∈
≠ i

. .

It.should.be.noted.that.the.objective.function.of. Equation.(7.2) . is.modiied.
so. that. the. task. simply. minimizes. all. three. objective. functions. f , f , f . as.

1 2 3

given.in . Equations.(7.1) - (7.3) .

7.3 ChromosomeRepresentation
The. design. of. the. chromosome. is. depicted. in . Figure 7.1 ;. the. transmission.
power.and.transmission.rate.of.each.connecting.user.are.encoded.in.floating.
point.and.considered.as.the.genes.of.chromosomes..Since.the.transmission.
power.and.the.transmission.rate.of.each.user.are.independent,.the.same.val-
ues.are.possible.as.found.in.a.chromosome.

Assume that there are 6
connecting users in the systems

Transmission power Transmission rate

User 1 User 2 User 5 User 6 User 1 User 2 User 5 User 6

0.052631 0.113584 0.284136 0.062148 8.525836 9.154752 1111.452362 900.156874

Gene 1 Gene 2 Gene 5 Gene 6 Gene 7 Gene 8 Gene 11 Gene 12

Figure 7.1
Chromosome-encoding.method..(From.Chan,.T..M.,.Man,.K..F.,.Tang,.K..S.,.Kwong,.S.,.A.jump-
ing.gene.algorithm.for.multiobjective.resource.management.in.wideband.CDMA.systems,. The
ComputerJournal ,.48(6),.749-768,.2005..With.permission.from.Oxford.University.Press.)