Overview of Multiobjective Optimization - Multiobjective Optimization Methodology: A Jumping Gene Approach - page 16

START START

Fast nondominated sort

Set the required
parameters and
generation counter
g = 0

Yes Yes

g = MAXIMUM
GENERATION?

g = MAXIMUM
GENERATION?

Crowding-distance
assignment

-

No No

Binary tournament
selection

Binary tournament
selection

Replacement

Population initialization Population initialization

g = g + 1 g = g + 1

Objective value
evaluation

Objective value
evaluation

Crossover Crossover

Fast nondominated
sort

Mutation Mutation

sort

Output Pareto-optimal
solutions

Crowding-distance
assignment

Objective value
evaluation

END END

Figure 2.4
Flowchart.of.NSGA2.

No

START

q = |p |? n q n q

Yes

Set the solution
counter p = 0

Yes

Yes

q rank = i + 1

n q

P rank = 1 n p

No

No

S P = φ , n P = 0 q = q Q = Q

{ q }

F 1 = F 1 { p } p = p

No

No

Set the solution
counter q = 0

q = |S p |?

p = |p |?

Yes

Yes

i = i

Yes i =

p dominates q ? S p = S p { q }

F i = Q

No No

F i ≠ φ ?

Yes

n p = n p

q dominates p ?

Yes

p = p

Q = φ

No

No

p = |F i |?

q = q

p = 0

Yes

END

q = 0

Figure 2.5
Flowchart.of.the.fast.nondominated.sorting.approach.