Non

dominated Sorting Genetic
Algorithm (NSGA

II)
Karthik
Sindhya
,
PhD
Postdoctoral Researcher
Industrial Optimization Group
Department of Mathematical Information Technology
Karthik.sindhya@jyu.fi
http://users.jyu.fi/~kasindhy/
Objectives
The objectives of this lecture is to:
•
Understand the basic concept and
working of NSGA

II
•
Advantages and disadvantages
•
Non

dominated sorting genetic algorithm
–
II
was proposed by Deb et al. in 2000.
•
NSGA

II procedure has three features:
–
It uses an elitist principle
–
It emphasizes non

dominated solutions
.
–
It uses an explicit diversity preserving mechanism
NSGA

II
•
NSGA

II
ƒ
1
ƒ
2
Crossover &
Mutation
NSGA

II
•
Crowded tournament selection operator
–
A solution x
i
wins a tournament with another solution
x
j
if any of the following conditions are true:
•
If solution
x
i
has a better rank, that is,
r
i
<
r
j
.
•
If they have the same rank but solution
x
i
has a better
crowding distance than solution x
j
, that is,
r
i
=
r
j
and
d
i
>
d
j
.
NSGA

II
Objective space
•
Crowding distance
–
To get an estimate of the density of solutions
surrounding a particular solution.
•
Crowding distance assignment procedure
–
Step 1:
Set l = F, F is a set of solutions in a front.
Set d
i
= 0,
i
= 1,2,…,l.
–
Step 2:
For every objective function m = 1,2,…,M,
sort the set in worse order of f
m
or find sorted
indices vector: I
m
= sort(f
m
).
NSGA

II
•
Step 3: For m = 1,2,…,M, assign a large distance to
boundary solutions, i.e. set them to ∞ and for all
other solutions j = 2 to (l

1),
assign as follows:
i
i+1
i

1
NSGA

II
•
Advantages:
–
Explicit diversity preservation mechanism
–
Overall complexity of NSGA

II is at most O(MN
2
)
–
Elitism does not allow an already found Pareto
optimal solution to be deleted.
•
Disadvantage:
–
Crowded comparison can restrict the
convergence.
–
Non

dominated sorting on 2N size.
NSGA

II
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