Overview of Multiobjective Optimization - Multiobjective Optimization Methodology: A Jumping Gene Approach - page 23

Yes

START

c dominates m ?

Discard m

No

Set the required
parameters and
iteration counter
g = 0

Replace c with m ,
and add m to the
archive

Yes

m dominates c ?

No

Generate a
random solution c

m is dominated by
any member of
the archive?

Yes

Discard m

Objective value
evaluation

No

Apply test ( c , m , archive) to determine
which becomes the new current solution
and whether to add m to the archive

Add the solution c
to the archive

Mutate the solution c
to produce a new
solution m

No

g = MAXIMUM
ITERATION?

Yes

Output Pareto-
optimal solutions

Objective value
evaluation

END

Figure 2.10
Flowchart.of.PAES.

objective;.the.required.grid.location.can.be.acquired.by.repetitively.bisecting.
the.range.in.each.objective.and.finding.in.which.half.the.solution.lies..The.
location.of.the.solution.is.marked.with.a.binary.string.of.length. 2 × .where.

b is. the. number. of. bisections. of. the. space. for. each. objective,. and. M is. the.
number.of.objectives.
If.the.solution.is.located.at.the.larger.half.of.the.bisection.of.the.space,.the.
corresponding.bit.in.the.binary.string.is.set..To.record.the.number.and.which.
nondominated.solutions.reside.in.each.grid,.a.map.of.the.grid.is.maintained.
throughout. the. run.. Grid. locations. are. recalculated. when. the. range. of. the.
objective.space.of.the.archived.solutions.changes.by.a.threshold.amount.to.
avoid.recalculating.the.ranges.too.frequently..Only.one.parameter.(i.e.,.the.
number.of.divisions.of.the.space.required).needs.to.be.set.

b M

2.2.6 Microgenetic algorithm

The. microgenetic. algorithm. (MICROGA). was. suggested. by. Coello. Coello.
and.Toscano.Pulido.[13,14],.and.its.lowchart.is.shown.in . Figure 2.11. .I t.has.
three. peculiarities:. population. memory,. an. adaptive. grid. algorithm,. and.
three.types.of.elitism..These.are.briefly.described.next.