Performance Measures on Jumping Gene - Multiobjective Optimization Methodology: A Jumping Gene Approach - page 96

set.is.acquired.from.each.run,.the.value.of.a.particular.unary.performance.
metric. can. then. be. calculated.. Last,. the. mean. and. standard. deviation. of. K .
different.metric.values.can.be.obtained.as.the.basic.performance.indicator.
Furthermore,.the.statistical.comparison.of.pairs.of.nondominated.fronts.
is.adopted.for.the.binary.ε-indicator..Each.MOEA.should.perform. K .simu-
lation.runs.to.generate. K .nondominated.solution.sets..To.obtain.this.met-
ric,. each. solution. in. the. K . nondominated. sets. of. an. MOEA. is. compared.
with.those.of.another.MOEA,.one.by.one..Therefore,.there.are.a.total.of. K 2 .
comparisons;.each.comparison.results.in.one.of.the.three.comparison.cases.
mentioned.in.Section.5.5..Finally,.the.number.of.occurrences.for.each.case.
is.counted.and.compared.
5.7 JumpingGeneVerificationandResults
Just.like.other.genetic.operations,.such.as.crossover.and.mutation,.jumping.
gene.(JG).transposition.can.easily.be.integrated.into.any.general.framework.
of.an.MOEA.(see.Section.2.2.in. Chapter.2. for.details.of.an.MOEA)..Based.on.
our.studies,.note.that.the.inclusion.of.JG.transposition.in.the.nondominated.
sorting.genetic.algorithm.2.(NSGA2).[9].can.result.in.a.good.search.perfor-
mance..For.differentiation,.this.algorithm.is.referred.to.as.JG.in.the.following.
discussion.
To.verify.the.effectiveness.of.JG.in.multiobjective.optimization,.the.most.
straightforward.approach.is.to.use.some.well-known.benchmark.test.func-
tions.for.evaluating.its.performance..The.true.Pareto-optimal.fronts.of.these.
test. functions. should. be. obtainable. with. various. characteristics. (e.g.,. con-
cave,.convex,.disconnected,.etc.)..In.the.following,.eight.unconstrained.(SCH.
[14];.FON.[10];.POL.[13];.ZIT1,.-2,.-3,.-4,.and.-6.[21]).and.five.constrained.(DEB.
[9],. BEL. [1],. SRIN. [15],. TAN. [16],. and. BINH. [2]). benchmark. test. functions.
were.chosen..The.descriptions.of.these.benchmark.test.functions.are.given.
in.Appendix.B.
As.mentioned.in. Chapter.3, .JG.transposition.is.workable.for.different.data.
types..Thus,.we.adopted.binary.chromosome.representation.for.the.13.test.
functions,.while.real-number.chromosome.representations.were.also.applied.
for. the. test. functions. ZIT1,. ZIT2,. ZIT3,. ZIT4,. and. ZIT6.. Further. details. on.
the.encoding.and.decoding.techniques.of.binary.and.real-number.chromo-
somes.are.provided.in.Appendix.C.
5.7.1 Jg Parameter Study
The. success. of. the. JG. relies. on. three. important. parameters:. jumping. rate,.
number. of. transposons,. and. length. of. transposon.. Any. variation. of. these.
parameters. can. affect. its. performance. on. convergence. and. diversity..