Performance Measures on Jumping Gene - Multiobjective Optimization Methodology: A Jumping Gene Approach - page 111

Table 5.13
Statistical.Results.of.Binary.ε-Indicator.in.Terms.of.the.Number.of.Occurrences.in.
Three.Different.Cases.for.Constrained.Test.Functions

TestFunction Case MOGA NPGA2 NSGA2 SPEA2 PAES MICROGA

DEB Case.I 1,476 1,679 841 724 2,470 1,984

Case.II 174 106 501 585 0 7

Case.III 850 715 1,158 1,191 30 509

BEL Case.I 2,329 2,341 1,190 1,775 2,374 2,467

Case.II 1 0 39 0 0 7

Case.III 170 159 1,271 725 126 26

SRIN Case.I 1,583 1,783 987 1,419 2,299 1,441

Case.II 471 338 703 465 97 552

Case.III 446 379 810 616 104 507

TAN Case.I 180 169 302 156 2,047 528

Case.II 319 359 202 426 0 24

Case.III 2,001 1,972 1,996 1,918 453 1,948

BINH Case.I 331 470 145 127 1,889 595

Case.II 0 0 76 15 0 0

Case.III 2,169 2,030 2,279 2,358 611 1,905

Source: . Data.from.Chan,.T..M.,.Man,.K..F.,.Kwong,.S.,.Tang,.K..S.,.A.jumping.gene.paradigm.for.
evolutionary.multiobjective.optimization,. IEEETransactionsonEvolutionaryComputation ,.
12(2),.143-159,.2008.
Note: . The.best.result.for.each.case.is.marked.in.bold.

provide.sufficient.diversity.to.prevent.trapping.in.some.local.Pareto-optimal.
fronts.. In. the. constrained. test. functions,. the. JG. also. outperformed. other.
MOEAs.in.DEB,.BEL,.and.SRIN.
In.summary,.it.was.demonstrated.that.the.JG.had.a.powerful.and.effective.
search.ability.to.seek.better.sets.of.nondominated.solutions.with.good.con-
vergence.and.diversity.performance..For.demonstration,.typical.sample.sets.
of.nondominated.solutions.found.by.different.MOEAs.for.the.unconstrained.
and.constrained.test.functions.are.shown.in . Figures 5.2 - 5.4.
The. nondominated. solution. sets. for. the. test. functions. ZIT1,. ZIT2,. ZIT3,.
ZIT4,. and. ZIT6. (both. binary. and. real-number. coding). obtained. by. a.
MICROGA.(microgenetic.algorithm).were.not.included.since.they.were.too.
far.away.from.the.true.Pareto-optimal.front.

5.7.3 an experimental Test of Theorems of equilibrium

As. indicated. by. the. two. theorems. of. equilibrium. given. in. Section. 4.3,. the.
element.in.a.primary.schema.competition.set. S ξ .of.order. o (ξ) = n .will.glob-
ally.asymptotically.converge.to. n

1/2 .under.copy-and-paste.or.cut-and-paste.
operations,.despite.the.initial.proportion.of.the.schemata.in.the.set.
In. theory,. this. effect. can. be. visualized. by. monitoring. the. proportions.
of.schemata..However,.due.to.the.huge.number.of.schemata.in.a.practical.