Theoretical Analysis of Jumping Gene Operations - Multiobjective Optimization Methodology: A Jumping Gene Approach - page 84

0.5

000
001
010
011
100
101
110
111

0.375

0.25

0.125

0

0 100 200 300 400 500

No. of Generations
(a)

0.5

000
001
010
011
100
101
110
111

0.375

0.25

0.125

0

0 100 200 300 400 500

No. of Generations
(b)

Figure 4.6 (See COlOr iNSerT.)
The.proportion.of.schemata.against.generations.in.a.finite.population.using.(a).copy-and-paste.
and.(b).cut-and-paste.operations..(From.Tang,.K..S.,.Yin,.R..J.,.Kwong,.S.,.Ng,.K..T.,.Man,.K..F.,.A.
theoretical.development.and.analysis.of.jumping.gene.genetic.algorithm,. IEEETransactionson
IndustrialInformatics ,.7(3),.2011,.408-418.)

for.mutation.with.a.rate.of.0.5..It.is.obvious.that.crossover.operations.were.
incapable.of.achieving.the.task,.while.random.generation.also.failed.as.it.was.
only.statistically.possible.
A.similar.result.was.obtained.for.the.second.case,.as.shown.in . Figure 4.7b, .
where. all. the. chromosomes. in. the. population. were. identical. but. with. ran-
domly.generated.genes..It.is.remarked.that.no.new.individual.can.be.obtained.
by.crossover.operations.as.the.parents.are.the.same.

4.5.5 The effect of the Jg in a ga

As.indicated. by.the.theorem.of.equilibrium,.JG.operations.try.to.maintain.
all.the.schemata.in.equal.proportion.despite.the.current.distribution.of.sche-
mata.. This. effect. can. be. further. demonstrated. by. introducing. the. cut-and-
paste.or.copy-and-paste.operation.into.a.conventional.GA.