Particle swarm intelligence

2. Introduction
 Developed by James Kennedy & Russell Eberhart
in 1995
 Metaheuristic algorithm based on the concept of
swarm intelligence

3. PSO Algorithm – Basic Concept
 Uses the population (called a swarm) of candidate
solutions (called particles)
 Particles searches through the space of an objective
function looking for the best solution
 Each particle in search space adjusts its trajectories according to
its own best known position as well as entire swarm's best known
position
Trajectories: Path described by an object moving in air or space under the influence of forces

4. PSO Algorithm
Goal of an optimization problem
 Determine a variable represented by a vector
x = [x1, x2, x3,…, xd]
that minimizes or maximizes the fitness or objective function f(X)
based on the proposed optimization formulation
 Let
n be the number of particles in a swarm
xi be the position vector for particle i
vi be the velocity for particle i

5. PSO Algorithm
 Each particle keeps track:
 its best solution, personal best, pbest
 the best value of any particle, global best, gbest

6. Pseudo code

7. Update Velocity Vector
 Determine the new velocity vector
 xt
i be the position vector for particle i at t iteration
 vt
i be the velocity for particle i at t iteration
 1 and 2 are two random vectors
 α and β are the learning parameters or acceleration constants, α
≈ β ≈ 2

8. Update Position Vector
 Determine the new velocity vector
 xi be the position vector for particle i
 vi be the velocity for particle I
 1 and 2 are two random vectors
 α and β are the learning parameters or acceleration constants, α
≈ β ≈ 2

9. Introduction to the PSO: Algorithm
Particle’s velocity:
• Makes the particle move in the same
direction and with the same velocity
1. Inertia
2. Personal
Influence
3. Social
Influence
• Improves the individual
• Makes the particle return to a previous
position, better than the current
• Conservative
• Makes the particle follow the best
neighbors direction

10. Velocity Vector
 Makes the particle move in the same direction and with the same velocity
1. Inertia
2. Personal
Influence
3. Social
Influence
 Improves the individual
 Makes the particle return to a previous position, better
than the current
 Conservative
 Makes the particle follow the best neighbors direction

11. Velocity Vector
 Intensification: explores the previous solutions, finds the
best solution of a given region
 Diversification: searches new solutions, finds the regions
with potentially the best solutions

12. THANK
YOU