Biomedical Engineering Reference
In-Depth Information
Appendix C: Chromosome
Representa
tion
Two. types. of. chromosome. representations,. real. and. binary,. were. adopted.
for. the. evaluation. of. test. functions.. Regarding. the. real. representation,. the.
encoding.and.decoding.of.genes.are.straightforward..One.decision.variable.
can.be.directly.encoded.to.a.gene,.and.this.gene.can.be.decoded.back.to.the.
original.decision.variable.with.no.extra.effort..But.a.method.of.determining.
the.total.length.of.a.chromosome.and.a.decoding.function.are.required.for.
binary.representation.[2]..Their.details.are.given.next.
First,. let. us. consider. the. former. method. and. assume. that. there. are. two.
decision. variables. in. an. optimization. problem,. and. both. of. their. bounds.
are.
4, 4
− ..If.the.required.precision.is.six.decimal.places,.the.range.
4,
[
− .
should. be. divided. into. at. least. 8. ×. 1000000. + 1. equal. size. ranges.. Since.
2
[
]
22 23
< < ,. it. turns. out. that. 23. bits. are. needed. to. represent. one.
decision. variable,. and. the. total. length. of. a. chromosome. for. encoding. two.
decision.variables.is.46.bits.
On.the.other.hand,.the.decoding.function.starts.with.converting.a.binary.
string.
(
8, 000, 001 2
b
b
......
b
)
.to.the.corresponding.decimal.value.
a
.using.the.formula
n
1
n
2
0
−
−
n
−
1
∑
i
.
(C.1)
a
=
b
⋅
2 ,
∀
b
∈
{0, 1}
i
i
.
i
=
0
where.
n
is.the.total.number.of.bits.in.the.string.
Then,.the.value.of.a.decision.variable.
x
.can.be.obtained.by
a
x B
=
+
⋅
(
B
−
B
)
.
(C.2)
L
U
L
n
2
−
1
.
where.
B
L
.and.
B
U
.are.the.lower.and.upper.bounds.of.the.decision.variable,.
respectively.
Consider.an.example.of.a.binary.string.(10100001000100001001001).with.
n
.=.
23.bits;.the.value.of.
a
.is.5277769..Assuming.that.
B
L
= − .and.
4
B
U
= ,.the.value.
4
of.the.decision.variable.is
5277769
2
x
= −
4
+
⋅
(4 ( 4)) 1.0333
− −
≈
23
−
1
.
.
229
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