Overview of Multiobjective Optimization - Multiobjective Optimization Methodology: A Jumping Gene Approach - page 9

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Overview of f Multiobjective Optimization
2.1 ClassificationofOptimizationMethods
Optimization. methods. for. solving. multiobjective. optimization. problems.
(MOPs).can.be.classified.into.three.categories:.enumerative.methods,.deter-
ministic.methods,.and.stochastic.methods.[12,51,58].
2.1.1 enumerative Methods
The.enumerative.method.is.a.simple.and.straightforward.searching.scheme..
It.inspects.every.solution.in.the.search.space..As.a.consequence,.it.is.guar-
anteed. to. obtain. true. Pareto-optimal. solutions.. However,. when. the. search.
space.(i.e.,.the.total.number.of.solutions).is.huge,.it.is.computationally.infea-
sible. to. list. all. the. solutions.. Accordingly,. this. method. is. only. practical. for.
problems.with.a.small.search.space..Unfortunately,.the.search.space.of.many.
problems.is.large,.especially.when.real-world.applications.are.tackled.
2.1.2 Deterministic Methods
To.deal.with.problems.having.enormous.search.spaces,.deterministic.meth-
ods.have. been.suggested.. These.methods.incorporate.the.problem. domain.
knowledge.(heuristics).to.limit.the.search.space.so.that.acceptable.solutions.
can.be.found.within.a.reasonable.time.[51]..Some.typical.examples.of.deter-
ministic.methods.are.given.in . Table 2.1 .
Deterministic.methods.have.been.successfully.adopted.for.solving.a.wide.
variety.of.problems.[10,54]..Nevertheless,.they.face.difficulties.when.coping.
with.high-dimensional,.multimodal,.and.nondeterministic.polynomial-time.
(NP).complete.MOPs..It.is.because.their.search.performances.largely.rely.on.
the.implemented.method,.which.in.turn.is.dependent.on.the.nature.of.the.
error.surface.of.the.search.space.[29,33,39,50,51].
Another.disadvantage.occurs.because.the.deterministic.method.is.basi-
cally.a.point-by-point.approach.[19]..In.a.single.simulation.run,.only.one.
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