Particle Swarm optimization

Evolutionary Algorithm-Particle Swarm Optimization

1. PARTICLE SWARM
OPTIMIZATION
MIDHULA VIJAYAN
ROLL NO:50
S7 CSE
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2. INTRODUCTION
PSO ALGORITHM
MULTI OBJECTIVE PSO
NEW PARTICLE SWARM OPTIMIZATION
APPLICATION
ADVANTAGES
CONCLUSION
REFERENCES
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3. 3
Developed in 1995 by James Kennedy and Russ Eberhart
Applied to a variety of search and optimization problems.
Swarm of n individuals communicate directly or indirectly
PSO is a simple but powerful search technique.
Applies to concept of social interaction to problem solving.

4. (cntd...)
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EachparticleistreatedasapointinaN-dimensionalspace.
Swarmmovingaroundinthesearchspacelookingforthebestsolution
Robusttechniquebasedonmovement&intelligenceofswarms
BASICIDEA
Eachparticleissearchingfortheoptimum
Eachparticleismoving,andhencehasavelocity.
Eachparticlerememberstheposition,whereithaditsbestresultsofar

5. BASIC IDEA 2 (cntd…)
The particles in the swarm co-operate.
In basic PSO
A particle has a neighbourhoodassociated with it.
particle knows the fitnesses of those in its
neighbourhood
Position is simply used to adjust the particle’s velocity
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6. Particle tries to modify its position using the informations
The current position
The current velocities
The distance between the current position and pbest
The distance between the current position and the gbest.
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7. Particle’s position can be mathematically modeled as:
•d =1, 2, . . . D; i=1, 2, . . . , N;
•χ controls the velocity’s magnitude;
•w is the inertial weight;
•c
1and c
2acceleration coefficients; r
1 and r
2 are random numbers
•∆t is the time step
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8. Fig.1 Concept of modification of a searching point by PSO
s
k
: current searching point.
s
k+1
: modified searching point.
v
k
: current velocity.
v
k+1
: modified velocity.
v
pbest: velocity based on pbest.
v
gbest: velocity based on gbests
k
v
k
v
pbest
v
gbest
s
k+1
v
k+1
s
k
v
k
v
pbest
v
gbest
s
k+1
v
k+1
PARTICLE SWARM OPTIMIZATION (PSO)
x
y

9. Step1:Initialize a population array .
Step2:For each particle, evaluate the desired optimization fitness function
Step3:Compare particle’s fitness evaluation with its pbest
i.
If current value is better than pbest
i,then
pbest
i= current value,
p
i =current location x
iin D-dimensional space.
Step4:Identify the particle with the best success so far, and assign its index to
the variable g.
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10. Step5:Change the velocity and position of the particle according
to the equation (3)
Step6:If a criterion is met , exit.
Step7:If criteria are not met, go to step 2
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11. Discrete PSO … can handle discrete binary variables
MINLP PSO… can handle both discrete binary and
continuous variables.
Hybrid PSO…Utilizes basic mechanism of PSO and the
natural selection mechanism.
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12. Used in multi objective systems
Two approaches
1. Each particle evaluate for one objective function at a
time
1.1 Determine the best position by normal PSO
2.Evaluate all objective functions for each particle
2.1 It produce leader,guide the particle
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13. Particle adjust its position according to its previous worst solution.
Adjust its position according to groups worst solution.
It avoid worst solutions
NPSO find better solution than PSO.
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14. Function optimization
Artificial neural network training
Identification of Parkinson’s disease
Extraction of rules from fuzzy networks
Image recognition
Areas where GA can be applied.
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15. (cntd…)
Optimization of electric power distribution networks
Structural optimization
+Optimal shape and sizing design
+Topology optimization
Process biochemistry
System identification in biomechanics
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16. Simple implementation
Easily parallelized for concurrent processing
Derivative free
Very few algorithm parameters
Very efficient global search algorithm
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17. PSO can be effectively used for continuous optimization
problems.
Particle swarm optimization is a viable tool for objective
analysis and decision making.
It can be used in any practical solution.
NPSO is much better than PSO.
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18. 1) Y. Shi and R. C. Eberhart, “A modified particle swarm optimizer,” in
Proc. IEEE Congr. Evol. Comput., 1998, pp. 69–73.
2) Clerc, M. and Kennedy, J.: The particle swarm-explosion, stability
and convergence in a multidimensional complex space.
IEEE Trans. Evol. Comput. Vol.6, no.2, pp.58-73, Feb. 2002.
3) Kennedy, J., and Mendes, R. (2002). Population structure and
particle swarm performance. Proc. of the 2002 World
Congress on Computational Intelligence.
4) T. Krink, J. S. Vesterstroem, and J. Riget, “Particle swarm
optimization with spatial particle extension,” in Proc. Congr.
Evolut. Comput., Honolulu, HI, 2002, pp. 1474–1479.
5) M. Lovbjergand T. Krink, “Extending particle swarm optimizers
with self-organized criticality,” in Proc. Congr. Evol.
Comput., Honolulu, HI, 2002, pp. 1588–1593.
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