Theoretical Analysis of Jumping Gene Operations - Multiobjective Optimization Methodology: A Jumping Gene Approach - page 79

4.4 SimulationResultsandAnalysis
In.previous.sections,.the.convergence.to.equilibrium.of.a.primary.schemata.
competition.set.based.on.copy-and-paste.and.cut-and-paste.operations.was.
mathematically.proved..For.illustration,.some.simulations.follow.

4.4.1 Simulation 4.1: existence of equilibrium

Consider.primary.schemata.competition.set. S .where.

= {* * * #* #* * * #* * * * * *},

ξ

#.is.the.actual.bit.
Figures 4.4a .and . 4.4b .d epict.the.proportions.of.schemata.in.the.population.
against. generations. under. copy-and-paste. and. cut-and-paste. operations.

0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0

000
001
010
011
100
101
110
111

0 10 20 30 40 50

No. of Generations
(a)

0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0

000
001
010
011
100
101
110
111

0 10 20 30 40 50

No. of Generations
(b)

Figure 4.4 (See COlOr iNSerT.)
The. proportion. of. schemata. against. generations. using. (a). copy-and-paste. and. (b). cut-and-
paste.operations,.where.000.stands.for.***0*0***0******.and.so.on..(From.Yin,.J..J.,.Yeung,.S..H.,.
Tang,.W..K..S.,.Man,.K..S.,.Kwong,.S.,.Enhancement.of.multiobjective.search:.A.Jumping-genes.
approach,.in. ProceedingsofIEEEInternationalSymposiumonIndustrialElectronics ,.Vigo,.Spain,.
June.2007,.1855-1858.)