2. • Swarm Intelligence.
• Particle Swarm Optimization
• The procedure for implementation of PSO.
• modifications in the basic structure of PSO.
• PSO features.
• Parameter selection in PSO.
Agenda
3. • The term swarm is used to represent an
aggregation of the animals or insects which
work collectively to accomplish their day to
day tasks in an intelligent and efficient
manner.
• Swarm may be school of fishes, flocks of
birds and social insects like ants, bees etc.
Swarm Intelligence
4. • Swarms are capable of performing tasks which
are complex enough to be performed by an
individual animal or insect.
example of Ants
Ants are capable of finding the shortest path
for their food and they do it by
communicating through their environment
using a chemical substance called pheromones
as they can’t communicate directly.
5. • The PSO algorithm is a population-based
optimization technique. In a PSO system, multiple
candidate solutions coexist and collaborate
simultaneously.
• Each solution called a particle, flies in the problem
search space looking for the optimal position to
land.
• A particle, during the generations, adjusts its
position according to its own experience as well
as the experience of neighboring particles.
Particle swarm optimization
6. • A particle status on the search space is
characterized by two factors:
– its position (Xi)
– and velocity(Vi).
And will be updated according to the following
equations:
7. • Eq. (1)
• first part , Vi [k], represents particle’s previous
velocity.
• It stores previous flight direction .
• to prevent the particle from drastically changing its
direction and alignment it to its current direction.
• second part, C1 Rand (.)(pbesti [k]-Xi[k]),
• is called cognition part and resembles individual
memoryof the position that was best for the particle.
• its effect is to linearly attract the particle towards its
own best experience .
8. • third part, C2rand (.) (gbest [k] -Xi [k]), is called
social or cooperation component
• resembles a group standard which individuals seek to
attain.
• The effect of this term is to attract the particle towards
the best experience of the all particles in the swarm
scaled by random weight .
9. a. Initialize each particle with a random velocity
and position.
b. Calculate the objective value of all particles .
c. Set the position and objective of each particle as
Pi and Pbest ,respectively.
d. Set the position and objective of the particle
with the best fitness (least objective) as Pg and
gbest, respectively.
The procedure for
implementation of PSO
10. e. Update Particles’ Vi and Xi according to
Equations (1) and (2).
f. Update each particle’s Pbest and Pi, that is, if the
current Pbest of the particle is better(less) than its
Pbest, then Pbest and Pi are replaced with current
objective value and position vector, respectively.
g. Update Pg and gbest, that is,
if the current gbest of the whole swarm is fitter than
gbest, then gbest and Pg are replaced with current best
objective and its corresponding position
vector, respectively.
11. h. Steps e –g are repeated until stopping criterion
(usually a prespecified number of iterations or a
quality threshold for objective value) is reached.
12. 1. Selection of maximum velocity:
the velocities may become too high so that the particles
become uncontrolled and exceed search space.
Therefore, velocities are bounded to a maximum value
Vmax, that is
important modifications in the
basic structure of PSO
13. • Large value of Vmax increases the convergence
speed and convergence to a local minimum .
• small value of Vmax decreases the efficiency of
the algorithm.
Notes,
14. 2. Adding inertia weight:
a new parameter w for the PSO, named inertia
Weight is added in order to better control the scope of the
search .
So, Eq. (1) is now becomes:
15. • high value large velocities find the global
optimum neighborhood in a fast way.
• low value narrow the particles’ search region.
Notes,
16. 3. Constriction factor:
if running algorithm without restraining the
velocity, so the system will explodes after a few
iterations .
so, induce a constriction coefficient in
order to control the convergence properties.
17. • with the constriction factor , the PSO equation
for computing the velocity is:
• Note that ,
– if C = 5 then = 0.38 from Eq. (4), will cause a very
pronounced damping effect.
– But , if C is set to 4 then is thus 0.729, which works
fine.
18. • The advantage of using this factor is that
– there is no need to use Vmax nor to guess the values for
any parameters which govern the convergence and
prevent explosion.
Notes,
19. • has less parameters to be tuned by user,compared
with other heuristics.
• Simple and coding is very easy.
• provides fast convergence.
• provides high accuracy.
• less affected by initial solutions,compared with
other heuristics.
• ...........,other features.
PSO features
20. 1. Using PSO variants with fixed parameters,so
parameter values (accepted values , set on trial-
and-error basis).
2. Using PSO variants with dynamic or adaptive
parameters.
3. Using parameter-free PSO variants which do
not require any parameter setting process.
4. Using composite PSO but,it have a big problem
that it will increase complexity of the problem.
Strategies for setting PSO
parameters
21. • Swarm size
– Too few particles the algorithm will trap in local
optima.
– too many particles slow down the algorithm.
– So no exact rule for selection of swarm size, But when the
dimension of problem increases, the swarm size should
also be increased.
Parameter selection in PSO
22. • Maximum velocity
– If it is too high , the particles move erratically and are
swiftly attracted to global best (gbest) without enough
exploration of search space and may exceed search space.
– if it is too small, the computational overhead increases
and the algorithm may be unable to converge.
– Value for Vmax
– NI is the number of intervals in the dth dimension.
– Xmax and Xmin are the maximum and minimum values of
particles .
23. • Inertia weight
– There are different procedures for setting inertia weight:
– fixed inertia weight.
– Linearly decreasing.
– linearly increasing.
– non-linear ,fuzzy adaptive, random....etc.
– Taking into account both simplicity and
efficiency, linearly decreasing inertia weight is the most
appropriate method for setting inertia weight.
Accepted values of w
24. • Acceleration coefficients(C1,C2)
– if too high the particles move abruptly and fall in
false optima.
– if too low the particles move too slowly and the
algorithm couldn’t converge.
– If C1 increases it could increase attraction to Pbest
and decrease attraction to Gbest.
– If C2 increases it could increase attraction to Gbest
and decrease attraction to Pbest.
– So, setting C1 ,C2 =2 for most of problems.
Vi= [vi1,vi2, ...,vin] called the velocity for particlei.Xi= [xi1,xi2, ..., xin]represents the position of particle i.Pbest :represents thebest previous position of particle i(i.e., local-best positionor its experience)Gbest :represents the best positionamong all particles in the population X= [X1,X2, . . .,XN](i.e. global-best position)Rand(.)and rand(.): are two random variables between [0,1].C1and C2 : are positive numberscalled acceleration coefficients that guide eachparticle toward the individual best and the swarm bestpositions, respectively.
Yi(t+1) :best position of the particleF: fitness functionX(t+1): current position of the particle.Y’(t):best position of the particle according to all particles.
Vmax is set according to the characteristics of the problem.
Abido (2001, 2002) has put forward the following valueforVmax
