PSO-ACO-Presentation Particle Swarm Optimization (PSO)

Particle Swarm Optimization
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Particle Swarm Optimization (PSO)
 PSO is stochastic optimization technique proposed
by Kennedy and Eberhart ( 1995) [2].
 A population based search method with position of
particle is representing solution and Swarm of
particles as searching agent.
 PSO is a robust evolutionary optimization
technique
based on the movement and intelligence of swarms.
PSO find the minimum value for the function. 2

• The idea is similar to bird flocks searching for
food.
– Bird = a particle, Food = a solution
– pbest = the best solution (fitness) a particle has
achieved so far.
– gbest = the global best solution of all particles
within the swarm
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PSO Search Scheme
- pbest : the best solution achieved so far by that particle.
- gbest : the best value obtained so far by any particle in the
neighborhood of that particle.
- The basic concept of PSO lies in accelerating each
particle toward its pbest and the gbest locations, with a
random weighted acceleration at each time.
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PSO Search Scheme
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- Each particle is treated as a point (candidate solution)
in a N-dimensional space which adjusts its “flying”
according to its own flying experience as well as the
flying experience of other particles.
- PSO uses a number of agents, i.e., particles, that
constitute a swarm flying in the search space looking for
the best solution.

New Velocity
Position X Personal best
Global best
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X (t+1) = X(t) + V(t+1) (1)
V(t+1) = wV(t) +
c1
×rand ( ) × ( Xpbest
- X(t)) + c2
×rand ( ) × ( Xgbest
- X(t)) (2)
V(t) velocity of the particle at time t
X(t) Particle position at time t
w Inertia weight
c1 , c2 learning factor or accelerating factor
rand uniformly distributed random number
between 0 and 1
Xpbest particle’s best position
Xgbest global best position
Each particle tries to modify its position X using the following
formula:
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Alpine function

f( x1,, xD) sin x1
 sin xD
  x1 xD
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Particle fly and search for the highest peak in the search space

PSO Algorithm
The PSO algorithm pseudocode [2] as following:
Input: Randomly initialized position and velocity of Particles:
Xi (0) andVi (0)
Output: Position of the approximate global minimum X*
1: while terminating condition is not reached do
2: for i = 1 to number of particles do
3: Calculate the fitness function f
4: Update personal best and global best of each particle
5: Update velocity of the particle using Equation 2
6: Update the position of the particle using equation 1
7: end for
8: end while
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References
[1] Ant Colony Optimization website, http://iridia.ulb.ac.be/~mdorigo/ACO/about.html
[2] J. Kennedy and R.C. Eberhart, “Particle swarm optimization,” in IEEE Int. Conf.
on Neural Networks., Perth, Australia, vol. 4, 1995, pp. 1942-1948.
[3] J. Ham and M. Kamber, “Data mining: concepts and techniques (2nd edition,”
Morgan Kaufman Publishers, pp. 1-6, 2006.
[4] Van der Merwe, D. W. and Engelbrecht, A. P. “Data clustering using particle swarm
optimization”. Proceedings of IEEE Congress on Evolutionary Computation 2003
(CEC 2003), Canbella, Australia. pp. 215-220, 2003.
[5] E. Bonabeau, M. Dorigo, and G. Theraulaz. Swarm Intelligence: From Natural to
Artificial System. Oxford University Press, New York, 1999
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PSO-ACO-Presentation Particle Swarm Optimization (PSO)

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