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.
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
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
BASIC IDEA 2
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
Position is simply used to adjust the particle’s velocity
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.
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;
c1 and c2 acceleration coefficients; r1 and r2 are random numbers
∆t is the time step
PARTICLE SWARM OPTIMIZATION (PSO)
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
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,
= 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.
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
Discrete PSO … can handle discrete binary variables
can handle both discrete binary and
Utilizes basic mechanism of PSO and the
natural selection mechanism.
Used in multi objective systems
1. Each particle evaluate for one objective function at a
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
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.
Artificial neural network training
Identification of Parkinson’s disease
Extraction of rules from fuzzy networks
Areas where GA can be applied.
Optimization of electric power distribution networks
+Optimal shape and sizing design
System identification in biomechanics
Easily parallelized for concurrent processing
Very few algorithm parameters
Very efficient global search algorithm
PSO can be effectively used for continuous optimization
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.
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.