Practical Swarm Optimization (PSO)

1. Department of Mechanical and Material Engineering
Practical Swarm Optimization (PSO)

2. Goal of Optimization
Find values of the variables that minimize or maximize the objective
function while satisfying the constraints.

3. .
Need for optimization
Choose design variables
Formulate constraints
Formulate objective function
Set up variable bounds
Select an optimization algorithm
Obtain solution(s)
Flowchart of Optimal Design Procedure

4. Particle Swarm Optimization
Swarm Intelligence (SI)
• SI is artificial intelligence, based on the collective behavior of decentralized, self-
organized systems.
• The expression was introduced by Gerardo Beni and Jing Wang in 1989, in the
context of cellular robotic systems.
• SI systems are typically made up of a population of simple agents interacting
locally with one another and with their environment.
• Natural examples of SI include ant colonies, bird flocking, animal herding, bacterial
growth, and fish schooling.

5. Particle Swarm Optimization
Some SI Application
• U.S. military is investigating swarm techniques for controlling unmanned vehicles.
• NASA is investigating the use of swarm technology for planetary mapping.

6. Particle Swarm Optimization
• The PSO algorithm was first described in 1995 by James Kennedy and Russell C.
Eberhart inspired by social behavior of bird flocking or fish schooling.
• PSO is an artificial intelligence (AI) technique that can be used to find approximate
solutions to extremely difficult or impossible numeric maximization and minimization
problems.
• Hypotheses are plotted in this space and seeded with an initial velocity, as well as a
communication channel between the particles.
• Simple algorithm, easy to implement and few parameters to adjust mainly the velocity.

7. Particle Swarm Optimization
How it works:
• PSO is initialized with a group of random particles (solutions) and then searches
for optimal by updating generations.
• Particles move through the solution space, and are evaluated according to some
fitness criterion after each time step. In every iteration, each particle is updated by
following two "best" values.
• The first one is the best solution (fitness) it has achieved so far (the fitness value is
also stored). This value is called pbest.

8. Particle Swarm Optimization
How it works:
• Another "best" value that is tracked by the particle swarm optimizer is the best
value obtained so far by any particle in the population. This second best value is a
global best and called gbest.
• When a particle takes part of the population as its topological neighbors, the
second best value is a local best and is called lbest. Neighborhood bests allow
parallel exploration of the search space and reduce the susceptibility of PSO
to falling into local minima, but slow down convergence speed.

9. Particle Swarm Optimization
Each particle tries to modify its current position and velocity according to the distance between its
current position and pbest, and the distance between its current position and gbest.
2
1( ) * ( CurrentPosition ) 2( ) * ( CurrentPositionn n1 1 best,n best,n
)randv v c rand p c gnn
Current Position[n+1] = Current Position [n] + v[n+1]
current position[n+1]: position of particle at n+1th
iteration
current position[n]: position of particle at nth iteration
v[n+1]: particle velocity at n+1th iteration
vn+1: Velocity of particle at n+1 th iteration
Vn : Velocity of particle at nth iteration
c1 : acceleration factor related to gbest
c2 : acceleration factor related to lbest
rand1( ): random number between 0 and 1
rand2( ): random number between 0 and 1
gbest: gbest position of swarm
pbest: pbest position of particle

10. Particle Swarm Optimization
Algorithm
For each particle
Initialize particle with feasible random number
End
Do
For each particle
Calculate the fitness value
If the fitness value is better than the best fitness value (pbest) in history
Set current value as the new pbest
End
Choose the particle with the best fitness value of all the particles as the gbest
For each particle
Calculate particle velocity according to velocity update equation
Update particle position according to position update equation
End
While maximum iterations or minimum error criteria is not attained

11. Particle Swarm Optimization
Swarm Topology
• In PSO, there have been two basic topologies used in the literature
I4
I0
I1
I2I3
I4
I0
I1
I2I3
Star Topology (global neighborhood)Ring Topology (neighborhood of 3)

12. Particle Swarm Optimization
Variant of PSO
.

13. The Basic Variant of PSO
PSO Basic Variant Function Advantages Disadvantages
Velocity Clamping (VC)
Control the global exploration of
the particle.
Reduces the size of the step
velocity, so that the particles remain
in the search area, but it cannot
change the search direction of the
particle
VC reduces the size of the step
velocity so it will control the
movement of the particle
If all the velocity becomes equal to
the particle will continue to
conduct searches within a
hypercube and will probably remain
in the optima but will not converge
in the local area.
Inertia Weight
Controls the momentum of the
particle by weighing the
contribution of the previous
velocity,
A larger inertia weight in the end
of search will foster the
convergence ability.
Achieve optimality convergence
strongly influenced by the inertia
weight
Constriction Coefficient
To ensure the stable convergence
of the PSO algorithm [21]
Similar with inertia weight
when the algorithm converges,
the fixed values of the parameters
might cause the unnecessary
fluctuation of particles
Synchronous and
Asynchronous Updates
Optimization in parallel processing Improved convergence rate
Higher throughput:
More sophisticated finite element
formulations
Higher accuracy (mesh densities)

14. Particle Swarm Optimization
in Summary
The process of PSO algorithm in finding optimal values follows the work of an animal society
which has no leader.
Particle swarm optimization consists of a swarm of particles, where particle represent a
potential solution (better condition).
Particle will move through a multidimensional search space to find the best position in that
space (the best position may possible to the maximum or minimum values).

15. Question and Answer