Overview of Multiobjective Optimization - Multiobjective Optimization Methodology: A Jumping Gene Approach - page 28

START

Update the storage:
Personal best and
global best

Set the required
parameters

Randomly generate the
initial positions and
velocities of particles,
and set g = 0

Get the new positions and
velocities of particles
using (2.16) and (2.17),
respectively

Get the non-dominated
solutions and update
the Pareto-optimal
solutions set if necessary

Yes

g = MAXIMUM
ITERATION?

No

g = g + 1

Objective value
evaluation

Output Pareto-optimal
solutions

Rank assignment
based on
Pareto dominance

END

Figure 2.13
Flow.chart.of.PSO.

2.2.9 Tabu Search

The.TS.was.originally.conceived.in.1986.by.Glover.[35,36]..Since.then,.it.has.
been.successfully.applied.to.combinatorial.optimization.problems.due.to.its.
fast.and.aggressive.search.[1]..It.is.an.optimization.procedure.that.repeatedly.
moves.from.the.current.solution.to.the.best.in.a.list.of.neighboring.solutions.
while.avoiding.being.trapped.in.the.local.optima.by.referring.to.a.tabu.list.
of.forbidden.moves..Thus,.it.is.considered.as.a.local.search.technique.guided.
by.the.use.of.adaptive.or.flexible.memory.structures.[57].
When. the. neighbors. of. the. current. solution. are. searched,. even. if. the.
neighbors.are.worse,.the.TS.may.still.accept.the.new.one.under.some.prob-
abilities.so.that.better.solutions.can.be.explored..The.visited.best.solution.
is.stored.in.a.memory.pool,.called.the.tabu.list,.so.that.searching.backward.
is.prohibited.
The.traditional.TS.only.works.for.single-objective.optimal.problems.as.the.
effort. is. geared. toward. trying. to. get. the. “best”. solution. among. the. neigh-
bors..Therefore,.a.multiobjective.TS.(MOTS).for.multiobjective.optimization.
should.work.with.a.set.of.current.solutions,.which.are.simultaneously.opti-
mized.toward.the.nondominated.frontier.[40].
The.most.direct.way.to.implement.MOTS.is.to.expand.the.working.object.
from.a.single.solution.to.a.population..Among.the.current.population,.a.set.
of. nondominated. solutions. is. saved. in. the. tabu. list;. thus,. a. local. optimum.