Conclusions - Multiobjective Optimization Methodology: A Jumping Gene Approach - page 200

9
Conclusions
This.book.formulated.all.the.necessary.steps.to.ensure.the.use.of.the.newly.
developed. jumping. gene. (JG). algorithms.. As. JG. is. a. new. addition. to. the.
existing. evolutionary. algorithms,. the. fundamental. materials. (e.g.,. concept,.
theory,. methods. for. verification,. realistic. as. well. as. practical. engineering.
applications).were.sequentially.presented.
Apart.from.the.introduction,.a.thorough.review.of.state-of-the-art.multi-
objective. optimization. (MO). techniques. was. presented. in. Chapter. 2 .. This.
shows. the. way. for. the. development. of. evolutionary. theory,. which. enables.
the.JG.to.further.unravel.the.shortfall.of.MO,.particularly.when.convergence.
and.diversity.are.both.in.demand.
Considering. the. fact. that. the. biogenetic. phenomenon. of. the. JG. is. new. in.
computer.science,.this.book.needed.to.outline.the.basic.biological.gene.trans-
position.process.to.aid.in.comprehension.of.the.concept..The.transformation.
of.gene.manipulation.in.copy-and-paste.and.cut-and-paste.processes.into.a.
computable.language.is.crucial.for.gaining.computationally.executable.cod-
ing..A.full.account.of.development.in.this.area.was.provided.in. Chapter.3 .
As.the.JG.is.so.new.in.the.domain.of.evolutionary.algorithms,.there.was.
no.previously.reported.literature..Thus,.the.task.for.deriving.the.necessary.
proofs.of.the.JG.mathematically.was.daunting..A.number.of.theoretical.pro-
posals.were.considered,.but.only.the.schema.theory.deployed.by.Stephens.
and. Waelbroeck's. model. [2]. was. inally. adopted.. This. naturally. led. to. the.
result.in. Chapter.4 .of.an.exact.mathematical.formulation.for.the.growth.of.
the.schemata.rather.than.the.concept.of.a.lower-bound.selection,.as.initially.
suggested.by.Holland.[1].
As. a. result,. two. mathematical. equations. describing. the. growth. of. sche-
mata.were.established,.one.for.the.copy-and-paste.and.the.other.for.the.cut-
and-paste.operation..These.were.reinforced.by.a.thoughtful.hypothesis.for.
testing.their.evolutionary.capability.with.a.backup.of.purposefully.designed.
statistical.simulation.runs..These.results.were.then.compared.with.the.exist-
ing.evolutionary.operators,.such.as.crossover,.mutation,.and.random.selec-
tion.. It. was. then. revealed. that. the. JG. was. far. more. favorable. for. creating.
nondominated.solutions.and.the.subsequent.solution.for.meeting.the.design.
goal.quickly.
To. reinforce. this. mathematical. rhetoric. so. that. the. JG. can. stand. firmly.
and.be.able.to.withstand.the.challenge.from.other.evolutionary.algorithms,.
relevant. methods. were. devised. for. verifying. these. equations.. The. perfor-
mance.metrics.for.convergence.and.diversity.were.compared.by.introducing.
201