Non-dominated Sorting Genetic Algorithm (NSGA-II)

cathamAI and Robotics

Oct 23, 2013 (3 years and 8 months ago)

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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