Particle Swarm Optimization Algorithms - What is iroboapp?

skoptsytruculentAI and Robotics

Nov 15, 2013 (3 years and 8 months ago)

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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