Overview of Multiobjective Optimization - Multiobjective Optimization Methodology: A Jumping Gene Approach - page 11

2.2 MultiobjectiveAlgorithms
The. following. summarizes. some. major. stochastic. optimization. methods.
widely. used. for. MOPs,. including. evolutionary. algorithms,. swarm. algo-
rithms,.and.the.tabu.search.(TS).
Evolutionary.algorithms.emulate.the.process.of.natural.selection.for.which.
the.philosopher.Herbert.Spencer.coined.the.phrase.“survival.of.the.fittest”.
[7,52,67]..There.are.in.general.three.proposed.classes:.evolutionary.program-
ming,.evolution.strategies,.and.genetic.algorithms.(GAs)..They.share.a.num-
ber.of.common.properties.and.genetic.operations;.their.main.differences.are.
listed.in. Table 2.3 . .Our.focus.is.on.the.algorithms.addressing.MOPs;.hence,.
more. details. are. given. for. the. distinct. features. found. in. major. multiobjec-
tive.evolutionary.algorithms.(MOEAs)..Most.of.these.MOEAs.are.GA.based;.
however,.similar.operations.can.also.be.applied.for.evolutionary.program-
ming. and. evolution. strategies.. Details. of. evolutionary. programming. and.
evolution.strategies.can.be.obtained.in.[3-5,8,25,28-30,61,62].
In.addition.to.evolutionary.algorithms,.two.main.classes.of.swarm.algo-
rithms,.namely,.the.ant.colony.[16,17].and.the.particle.swarm.optimizations.
(PSOs).[46],.are.commonly.used.for.solving.optimization.problems..They.are.
also. inspired. by. the. natural. world,. but. their. searching. performances. rely.
on. a. decentralized. group. of. agents,. for. which. their. local. interactions. lead.
to.a.certain.level.of.global.search..Last,.the.TS,.which.was.proposed.by.Fred.
Glove,. is. also. briely. introduced.. It. acts.as. an. effective. algorithm. for. many.
problems.for.which.solutions.are.searched.by.repeatedly.moving.from.the.
current.one.to.the.best.of.its.neighbors.

2.2.1 Multiobjective genetic algorithm

The.multiobjective.genetic.algorithm.(MOGA).was.proposed.by.Fonseca.and.
Fleming.[31,32]..It.has.three.features:.a.modified.ranking.scheme,.modified.
fitness.assignment,.and.niche.count..The.flowchart.of.the.MOGA.is.shown.
in . Figure 2.1 .
A.modified.ranking.scheme.[32],.which.is.slightly.different.from.the.one.
proposed. by. Goldberg,. is. used. in. the. MOGA.. Figure 2.2 . depicts. such. a.

Table 2.3
Differences.between.Three.Evolutionary.Algorithms

EvolutionaryAlgorithm Representation GeneticOperators

Evolutionary.programming Real.values Mutation.and.(μ + λ).selection

Evolution.strategies Real.values.and.

strategy.parameters

Crossover,.mutation,.and.(μ + λ).or.(μ,.λ)
selection.where.μ.and.λ.are.the.number.
of.parents.and.children,.respectively

Genetic.algorithms Binary.or.real.values Crossover,.mutation,.and.selection