Theoretical Analysis of Jumping Gene Operations - Multiobjective Optimization Methodology: A Jumping Gene Approach - page 58

Deinition4.3

The.primary.schemata.competition.set.[3,.10,.19].of.schema.ξ ∈ S .is.deined.as

( )} .

(4.8)

S

= ξ ∈ { S f : ( ξ ) = f ξ

i L i L

.

Remark4.1

If.the.order.of.schema.ξ.is. o (ξ) = n , S .is.called.the. n -order.primary.schemata.
competition.set..Any.two.schemata.in. S .are.said.to.have.an. n -order.primary.
schemata.competition.relation..It.is.also.denoted.that.

S = S \{ } .contains.all. ξ

ξ

ξ

the.competitors.of.schema.ξ.

Example4.1

Let. ξ = **0*0*,. then. f L ξ = ( ) {2, 4} . and. f T ξ ( , {2, 3}) 0 * = .. We. also. have.

,. { * *0 * 1*, * *1* 0*, * *1* 1*} .

S = ξ {* * 0 * 0*, * *0 * 1*, * *1* 0*, * *1* 1*} S =

ξ

Deinition4.4

The. bit. distance. between. two. bits. x i . and. y i ,. where. x y , ∈ {0, 1, *} ≡ B ,. is.

i i

defined.as

x
x

=
≠

*
*,

1
1
0
0.5

i

y ≠ *, x = y

i i i i

( ) =

d x y ,

i i

x *, y *, x y

≠ ≠ ≠ i i i i

x ≠ *, y = *

i i

. . (4.9)

describing.how.close. y i .matches. x i .

Remark4.2

d x y ( , ) d y x ( , ) .

It.should.be.noted.that. ≠ i i i i

Remark4.3

d x y
i

( , ) 0.5. .It.assumes.that.a.don't-care.bit.

For.the.case.of. x i ≠ *.and. y i = *,. = i

has.an.equal.chance.to.be.0.or.1.

Deinition4.5

m

v v , ∈ B

The.regional.similarity.of.two.strings. v 1 .and. v 2 ,.where. ,.is.specified.by

i j

m − 1

∏

( v v , ) d v j v j ( ( ), ( ))

δ =

1 2 1 2

j = 0

. . (4.10)

where. v j

i ( ) .is.the. j th.bit.of. v i ..Note.that.δ v

( , v

2 .ranges.from.0.to.1.

)

1