This document discusses particle swarm optimization (PSO), which is an optimization technique inspired by swarm intelligence. It summarizes that PSO was developed in 1995 and can be applied to various search and optimization problems. PSO works by having a swarm of particles that communicate locally to find the best solution within a search space, balancing exploration and exploitation.
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.
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4. (cntd...)
Each particle is treated as a point in a N-dimensional space .
Swarm moving around in the search space looking for the best solution
Robust technique based on movement & intelligence of swarms
BASIC IDEA
Each particle is searching for the optimum
Each particle is moving , and hence has a velocity.
Each particle remembers the position ,where it had its best result so far
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5. BASIC IDEA 2
(cntd…)
The particles in the swarm co-operate.
In basic PSO
A particle has a neighbourhood associated 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;
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χ controls the velocity’s magnitude;
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w is the inertial weight;
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c1 and c2 acceleration coefficients; r1 and r2 are random numbers
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∆t is the time step
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8. PARTICLE SWARM OPTIMIZATION (PSO)
y
sk+1
vk
vk+1
sk
vgbest
vpbest
x
Fig.1 Concept of modification of a searching point by PSO
sk : current searching point.
sk+1: modified searching point.
vk: current velocity.
vk+1: modified velocity.
vpbest : velocity based on pbest.
vgbest : velocity based on gbest
9. Step1: Initialize a population array .
Step2: For each particle, evaluate the desired optimization fitness function
Step3: Compare particle’s fitness evaluation with its pbesti.
If current value is better than pbesti,then
pbesti = current value,
pi
= current location xi in 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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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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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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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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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. Lovbjerg and 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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