Particle Swarm
Optimization
Algorithms
Mohamed
Tounsi
1
Learning Outcomes
At the end of the presentation, you will
Get an idea about origin of PSO algorithm
Understand the concept behind Swarm
optimization algorithms
Get an idea about existing research around
PSO algorithms
Know how PSO algorithm can be used for
solving path planning problems
Learn one PSO algorithm for path planning
2
Outline
History
Concepts of PSO Algorithms
Related Works
PSO Algorithm and Path Planning
Path Planning Algorithm using PSO
Algorithm
3
PSO
PSO is a robust stochastic optimization technique
based on the movement and intelligence of
swarms.
PSO applies the concept of social interaction to
problem solving.
It was developed in 1995 by James Kennedy
(social

psychologist) and Russell
Eberhart
(electrical
engineer).
“Best strategy
to find the food is to follow the bird
which is nearest to the
food”
Getting the best solution from the problem by
taking particles and moving them around in the
search space
PSO is a simple but powerful search technique.
4
PSO Search Scheme
It uses a number of agents, i.e.,
particles
, that constitute a swarm
moving around
in the search space
looking for the best solution
.
Each particle is treated as a point in a
N

dimensional
space which adjusts its
“flying”
according to its
own flying
experience
as well as the
flying
experience of other particles
.
5
PSO
Model
pbest
the best solution achieved so far by that particle.
gbest
the best value obtained so far by
all particles
The basic concept of PSO lies in
accelerating each particle
toward its
pbest
and the
gbest
locations, with a
random
weighted acceleration
at each
time.
6
Particle
Flying Model
k
s
k
pbest
k
gbest
k
v
1
k
v
1
k
s
k
pbest
d
k
gbest
d
1 2
k k
pbest
k
gbest
d d
v w w
1
1
()
c r
w
and
2
2
()
c r
w
and
k
v
7
Particle Flying Model
Each particle tries to modify
its position using the
following information:
the
current positions
,
the
current velocities
,
the distance between the
current position and
pbest
,
the distance between the
current position and the
gbest
.
Source: [2][3]
k
s
k
pbest
k
gbest
k
v
k
v
1
k
v
1
k
v
1
k
s
k
pbest
d
k
gbest
d
1 2
k k
pbest
k
gbest
d d
v w w
1
1
()
c r
w
and
2
2
()
c r
w
and
k
v
k
v
8
Particle Flying Model
1 1
k k k
i i i
s s v
1 2
() ( ) () ( )
k k k k k
i i i i
v c rand pbest s c rand gbest s
*
**
Source: [2][3]
k
s
k
pbest
k
gbest
k
v
k
v
1
k
v
1
k
v
1
k
s
k
pbest
d
k
gbest
d
1 2
k k
pbest
k
gbest
d d
v w w
1
1
()
c r
w
and
2
2
()
c r
w
and
k
v
k
v
9
𝑉
2
+
2
=
2
𝑘
+
1
2
1
k k k
i i i
v v v
= W
PSO Algorithm
For each particle
Initialize particle
END
Do
For each particle
Calculate
fitness
value
If the fitness value is better than the best fitness
value
(
pbest
) in history
S
et
current value as the new
pbest
End
Choose the particle with the best fitness value of all the particles
as
the
gbest
For each particle
Calculate particle
velocity
according equation (*)
Update particle
position
according equation (**)
End
While maximum iterations or minimum error criteria is not attained
(Adapted from : [1][4])
10
About Parameters:
Swarm size = 20

50 ([1])
Typical
values for parameters are
w
=0.9
, and
c1=c2=1.
Maximum velocities for some small robots noted
in the literature are 20
cm/sec,
100
cm/sec and
1 m/sec.
A
large
W
favors global search while a small
wi
favors local search
11
Comparison
With GA
No
selection operation mechanisms
All
particles in PSO are kept as members of the
population through the
execution
PSO
is the only algorithm that does not implement
the survival of the fittest.
No
crossover operation in PSO.
No mutation operation in PSO
12
Application
Optimization
Telecommunications
power
systems
signal processing
Artificial neural network training
Fuzzy system control
….Where Genetic Algorithm can be applied.
13
Features
Easy to perform
Few parameters to adjust
Efficient in global search
Fast Convergence
Larger
w:
greater global search ability
Smaller
w:
greater local search ability.
14
15
stut
15
PSO to Robot Path Planning
The positions of globally best particle in each
iteration
are selected, and reached by the
robot
in
sequence
The optimal path is generated with
this
method
when the robot reaches its target
Related works: PSO for Robotic
Obstacle

avoidance
Path Planning for Soccer
Robots Using Particle Swarm Optimization (
2006
)
Obstacle
avoidance with multi

objective
optimization by PSO in dynamic environment (
2005
)
Robot Path Planning using Particle Swarm
Optimization of Ferguson Splines (
2006
)
Path planning for mobile robot using the particle
swarm optimization with mutation operator (
2004
)
Parallel
Learning in Heterogeneous Multi

Robot
Swarms (
2006
,
2007
)
16
Examples of Fitness Functions
17
Fitness function:
Euclidian Distance
Euclidian Distance +
Smoothness
Euclidian
Distance
+
Number obstacles
Neighborhood
Generation
Goal
Range of connectivity
New velocity
heuristics
which solved the
premature convergence
Credit Assignment heuristic which solve the
Local minimum
problem
Hot Zone/Area
heuristic
Communication Range(Multi Robots
)
(
Pugh and
Martinoli
, 2006;
Bogatyreva
and
Shillerov
, 2005)
18
Variants of PSO for Path Planning
Credit Assignment and
Boundary Condition
idea:
Reward
and Punishment
Suspend
factor
Robots positions would
be
suspended
each time
that they cross boundary
lines (similar to TS)
By this conditions they can escape from the areas
that they are stuck in it and it is as useful as
reinitializing the robot states in the environment.
19
Source: [3][4]
Hot Zone/Area Heuristic
The idea is based on dividing the environment to
sub virtual fixed areas with various credits.
Areas
credit defined the proportion of goals and
obstacles positioned in the area.
particles
know the credit of first and second layer
of its current neighborhood
20
Source: [
4
]
Multi Robot: Communication
Methodology
Robots can only communicate with those who are
in their communication range
.
Various communication
ranges could be used.
This
heuristic has major effect on the sub swarm
size.
Help
request signal can provide a chain of
connections.
21
Comparison
Faster than GA
Converge Quickly than GA / Djikstra
Efficient in obstacle avoidance problem
Good for Multi

Robot Path Planning
22
References
1)
Kennedy
, J. and
Eberhart
, R. (
1995
).
“Particle Swarm Optimization”
,
Proceedings of the
1995
IEEE International Conference on Neural
Networks
, pp.
1942

1948
, IEEE Press
.
2)
Xin
, C., Li, Y.M.:
Smooth Path Planning of a Mobile Robot
Using
Stochastic Particle Swarm Optimization
. In: Proceedings of the
2006
IEEE International Conference on
Mechatronics and
Automation,
pp.
1722
–
1727
. Luoyang, China (
2006
)
3)
Li
W.;
Yushu
L.;
Hongbin
D. and
Yuanqing
X.;
Obstacle

avoidance
Path Planning for Soccer Robots Using Particle Swarm Optimization
",
Proc. IEEE Int. Conf. on Rob. and
Biomimetics
(ROBIO '
06
). (
2006
)
pp.
1233

1238
.
4)
Saska
, M.;
Macas
, M.;
Preucil
, L. and
Lhotska
, L.
Robot
Path Planning
using Particle Swarm Optimization of Ferguson Splines"
, Proc.
IEEE/ETFA '
06
, (
2006
) pp.
833

839
.
23
5)
Xin
C
.
and
Yangmin
L
.;
"Smooth
Path
Planning
of
a
Mobile
Robot
Using
Stochastic
Particle
Swarm
Optimization
"
Proc
.
IEEE
on
Mechatronics
and
Aut
.
,
(
2006
)
pp
.
1722

1727
.
6)
Yuan

Qing
Q
.;
De

Bao
S
.;
Ning
L
.
and
Yi

Gang
C
.;
Path
planning
for
mobile
robot
using
the
particle
swarm
optimization
with
mutation
operator
Proc
.
Int
.
Conf
.
on
Machine
Learning
and
Cybernetics,
(
2004
)
pp
.
2473
–
2478
.
7)
Hettiarachchi
,
S
.
(
2006
)
.
Distributed
online
evolution
for
swarm
robotics
.
Autonomous
Agents
and
Multi
Agent
Systems
.
24
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