2. 2
Introduction : Swarm Intelligence
Study of collective behavior in decentralized, self-
organized systems.
Originated from the study of colonies, or swarms of
social organisms.
Collective intelligence arises from interactions.
3. 3
Introduction
Particle Swarm Optimization:
Introduced by Kennedy & Eberhart 1995
Inspired by social behavior of birds and shoals of fish
Swarm intelligence-based optimization
Nondeterministic
Population-based optimization
Performance comparable to Genetic algorithms
4. 4
Particle Swarm Optimization
Swarm : a set of particles (S)
Particle: a potential solution
Position,
Velocity ,
Each particle maintains
Individual best position:
Swarm maintains its global best:
5. 5
PSO Algorithm
Basic algorithm of PSO:
1. Initialize the swarm from the solution space
2. Evaluate fitness of each particle
3. Update individual and global bests
4. Update velocity and position of each particle
5. Go to step 2, and repeat until termination condition
6. 6
PSO Algorithm (cont.)
Original velocity update equation:
with
: acceleration constant
Inertia Cognitive Component Social Component
7. 7
PSO Algorithm (cont.)
Original velocity update equation:
with
: acceleration constant
Position Update:
Inertia Cognitive Component Social Component
8. 8
PSO Algorithm - Parameters
Acceleration constant
Small values limit the movement of the particles
Large values : tendency to explode toward infinity
In general
Maximum velocity
Velocity is a stochastic variable => uncontrolled trajectory
14. 14
Rate of Convergence Improvement
Inertia weight:
Scaling the previous velocity
Control search behavior
High values exploration
Low values exploitation
15. 15
PSO with Inertia weight
can be decreased over time:
Linear [0.9 to 0.4]
Nonlinear
main disadvantage:
once the inertia weight is decreased, the swarm loses
its ability to search new areas (can not recover its
exploration mode).
16. 16
Rate of Convergence Improvement
Constriction Factor:
Canonical PSO
Typically ,
Can converge without using Vmax (velocity clamping)
Improve the convergence by damping the oscillations
17. 17
Swarm Topologies
Two general types of neighborhoods:
Global best (gbest) : fully connected network
Local best (lbest) : according to a topology
gbest
Ring Wheel Von Neumann
lbest
18. 18
Lbest vs. Gbest
Gbest converges fast but may be trapped in a local optima.
Lbest is slower in convergence but has more chances to find
an optimal solution.
Most efficient neighborhood structure, in general,
Fully Informed PSO (FIPS):
Each individual is influenced by successes of all its neighbors.
19. 19
Diversity Improvement
Based on lbest model.
Usually slow down the convergence rate.
Spatial Neighborhoods:
Partition particles based on spatial location.
Calculate the largest distance between any two particles.
Select neighboring particles according to ratio:
Selection threshold can be varied over time.
Start with small ratio (lbest) and gradually increase the ratio.
20. 20
Diversity Improvement
Neighborhood Topologies:
In lbest model, all particles can exchange information
indirectly.
Average path length depends on the topology.
Topology significantly affects the performance (experimentally).
Randomly change some connections can change average path
length.
i i+1 i+2
21. 21
Diversity Improvement
Subpopulations:
Previously used in GA.
Original swarm is partitioned to subpopulations.
PSO is applied to each subpopulation.
An interaction scheme is used for information sharing
between subpopulations.
Each subpopulation can search the smaller region of
search space.
22. 22
Discrete PSO
Binary PSO:
Introduces by kennedy and Eberhart.
Each individual (particle) has to take a binary decision.
Predisposition is derived based on individual and group
performance:
Previous state predisposition
23. 23
Binary PSO (cont.)
determines a threshold in the probability function and
therefore should be bounded in the range of [0.0, 1.0].
state of the dth position in the string at time t:
Where is a random number with a uniform distribution.
Vid
1
24. 24
PSO Variants
Hybrid PSO
Incorporate the capabilities of other evolutionary
computation techniques.
Adaptive PSO
Adaptation of PSO parameters for a better performance.
PSO in complex environments
Multiobjective or constrained optimization problems or tracking
dynamic systems.
Other variants
variations to the original formulation to improve its performance.
25. 25
Hybrid PSO
GA-PSO:
combines the advantages of swarm intelligence and a
natural selection mechanism.
jump from one area to another by the selection
mechanism accelerating the convergence speed.
capability of “breeding”.
replacing agent positions with low fitness values, with
those with high fitness, according to a selection rate
26. 26
Hybrid PSO
EPSO:
Evolutionary PSO
Incorporates a selection procedure
Self-adapting of parameters
The particle movement is defined as:
27. 27
Hybrid PSO : EPSO
Mutation of weights and global best:
Learning parameters can be either fixed or
dynamically changing as strategic parameters.
Survival Selection:
Stochastic tournament.
29. 29
Hybrid PSO : DEPSO
Hybrid of Differential Evolution and PSO.
A DE operator applied to the particle’s best position to
eliminate the particles falling into local minima.
Alternation:
Original PSO algorithm at the odd iterations.
DE operator at the even iterations.
30. 30
Hybrid PSO : DEPSO
DE mutation on particle’s best positions:
where k is a random integer value within [1,n] which
ensures the mutation in at least one dimension.
Trial point:
For each dth dimention:
32. 32
Dynamic Tracking in PSO
The classical PSO is very effective in solving static
optimization problems but is not as efficient when
applied to a dynamic system in which the optimal value
may change repeatedly.
An adaptive approach has been introduced for this
problem:
Detection of environmental changes:
changed-gbest-value
fixed-gbest-values
rerandomizing a certain number of particles
33. 33
Applications
Convenience of realization, properties of low constraint on
the continuity of objective function and joint of search space,
and ability of adapting to dynamic environment, make PSO be
applied in more and more fields.
Some PSO applications:
Electronics and electromagnetic
Signal, Image and video processing
Neural networks
Communication networks
…
