Particle swarm optimization
-
Upload
anurag-singh -
Category
Engineering
-
view
166 -
download
6
Transcript of Particle swarm optimization
![Page 1: Particle swarm optimization](https://reader034.fdocuments.in/reader034/viewer/2022052316/55a69a311a28ab7b668b4659/html5/thumbnails/1.jpg)
Particle Swarm
Optimization
(PSO)
![Page 2: Particle swarm optimization](https://reader034.fdocuments.in/reader034/viewer/2022052316/55a69a311a28ab7b668b4659/html5/thumbnails/2.jpg)
Introduction
Many difficulties such as multi-
modality, dimensionality and
differentiability are associated with the
optimization of large-scale problems.
Traditional techniques such as
steepest decent, linear programing
and dynamic programing generally fail
to solve such large-scale problems
especially with nonlinear objective
functions.
![Page 3: Particle swarm optimization](https://reader034.fdocuments.in/reader034/viewer/2022052316/55a69a311a28ab7b668b4659/html5/thumbnails/3.jpg)
Introduction…
Traditional techniques often fail to
solve optimization problems that have
many local optima.
To overcome these problems, there is
a need to develop more powerful
optimization techniques.
![Page 4: Particle swarm optimization](https://reader034.fdocuments.in/reader034/viewer/2022052316/55a69a311a28ab7b668b4659/html5/thumbnails/4.jpg)
Introduction…
Some of the well-known population-based optimization techniques are:
Genetic Algorithms (GA) Artificial Immune Algorithms (AIA) Ant Colony Optimization (ACO) Particle Swarm Optimization (PSO) Bacteria Foraging Optimization (BFO) Artificial Bee Colony (ABC) Biogeography-Based Optimization (BBO)
Etc.
![Page 5: Particle swarm optimization](https://reader034.fdocuments.in/reader034/viewer/2022052316/55a69a311a28ab7b668b4659/html5/thumbnails/5.jpg)
Particle Swarm Optimization
(PSO) Particle swarm optimization (PSO) is
an evolutionary computation technique
developed by Kennedy and Eberhart.
It exhibits common evolutionary
computation attributes including
initialization with a population of
random solutions and searching for
optima by updating generations.
![Page 6: Particle swarm optimization](https://reader034.fdocuments.in/reader034/viewer/2022052316/55a69a311a28ab7b668b4659/html5/thumbnails/6.jpg)
Concept
A Simulation of a simplified social
system.
The original intent was to graphically
simulate the graceful but
unpredictable choreography of a bird
flock.
Each particle keeps track of its
coordinates in the problem space,
which are associated with the best
solution (fitness) it has achieved so
far.
![Page 7: Particle swarm optimization](https://reader034.fdocuments.in/reader034/viewer/2022052316/55a69a311a28ab7b668b4659/html5/thumbnails/7.jpg)
How it works ??
PSO is initialized with a group of
random particles (solutions) and then
Searches for optima by updating
generations.
Potential solutions, called particles,
are then ‘‘flown’’ through the problem
space by following the current
optimum particles.
![Page 8: Particle swarm optimization](https://reader034.fdocuments.in/reader034/viewer/2022052316/55a69a311a28ab7b668b4659/html5/thumbnails/8.jpg)
How it Works ??
Each particle keeps track of its coordinates in the problem space, which are associated with the best solution (fitness) it has achieved so far.
This value is called ‘pBest’. 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”.
![Page 9: Particle swarm optimization](https://reader034.fdocuments.in/reader034/viewer/2022052316/55a69a311a28ab7b668b4659/html5/thumbnails/9.jpg)
How it works ??
The particle swarm optimization
concept consists of, at each step,
changing the velocity (i.e.
accelerating) of each particle toward
its ‘pBest’ and ‘gBest’ locations (global
version of PSO).
![Page 10: Particle swarm optimization](https://reader034.fdocuments.in/reader034/viewer/2022052316/55a69a311a28ab7b668b4659/html5/thumbnails/10.jpg)
PSO Algorithm (General)
Searches Hyperspace of Problem for Optimum Define problem to search
How many dimensions?
Solution criteria?
Initialize Population
Random initial positions
Random initial velocities
Determine Best Position
Global Best Position
Personal Best Position
Update Velocity and Position Equations
![Page 11: Particle swarm optimization](https://reader034.fdocuments.in/reader034/viewer/2022052316/55a69a311a28ab7b668b4659/html5/thumbnails/11.jpg)
The step-by-step
implementation
![Page 12: Particle swarm optimization](https://reader034.fdocuments.in/reader034/viewer/2022052316/55a69a311a28ab7b668b4659/html5/thumbnails/12.jpg)
Step 1:
Initialize PSO parameters which are necessary for the algorithm.
population size which indicates the number of individuals,
number of generations necessary for the termination criterion,
cognitive constant, social constant,
variation of inertia weight, maximum velocity,
number of design variables and respective ranges for the design variables.
![Page 13: Particle swarm optimization](https://reader034.fdocuments.in/reader034/viewer/2022052316/55a69a311a28ab7b668b4659/html5/thumbnails/13.jpg)
Step 2:
Generate random population equal to the population size specified.
Each population member contains the value of all the design variables. This value of design variable is randomly generated in between the design variable range specified.
population means the group of birds (particles) which represents the set of solutions.
![Page 14: Particle swarm optimization](https://reader034.fdocuments.in/reader034/viewer/2022052316/55a69a311a28ab7b668b4659/html5/thumbnails/14.jpg)
Step 3:
Obtain the values of the objective function for all the population members.
For the first iteration, value of objective function indicates the pBest for the respective particle in the solution.
Identify the particle with best objective function value which identifies as gBest.
If the problem is a constrained optimization problem, then a specific approach such as static penalty, dynamic penalty and adaptive penalty is used to convert the constrained optimization problem into the unconstrained optimization problem.
![Page 15: Particle swarm optimization](https://reader034.fdocuments.in/reader034/viewer/2022052316/55a69a311a28ab7b668b4659/html5/thumbnails/15.jpg)
Step 4:
Update the velocity of each particle
and Check for the maximum velocity.
If the velocity obtained exceeds the
maximum velocity,
then reduce the existing velocity to the
maximum velocity.
![Page 16: Particle swarm optimization](https://reader034.fdocuments.in/reader034/viewer/2022052316/55a69a311a28ab7b668b4659/html5/thumbnails/16.jpg)
Step 5:
Update the position of the particles,
Check all the design variables for the
upper and lower limits.
![Page 17: Particle swarm optimization](https://reader034.fdocuments.in/reader034/viewer/2022052316/55a69a311a28ab7b668b4659/html5/thumbnails/17.jpg)
Step 6:
Obtain the value of objective function
for all the particles.
The new solution replaces the pBest if
it has better function value.
Identify the gBest from the population.
Update the value of inertia weight if
required.
![Page 18: Particle swarm optimization](https://reader034.fdocuments.in/reader034/viewer/2022052316/55a69a311a28ab7b668b4659/html5/thumbnails/18.jpg)
Step 7:
Best obtained results are saved using
elitism.
All elite members are not modified
using crossover and mutation
operators but can be replaced if better
solutions are obtained in any iteration.
![Page 19: Particle swarm optimization](https://reader034.fdocuments.in/reader034/viewer/2022052316/55a69a311a28ab7b668b4659/html5/thumbnails/19.jpg)
Step 8:
Repeat the steps (from step 4) until
the specified number of generations or
termination criterion is reached.
![Page 20: Particle swarm optimization](https://reader034.fdocuments.in/reader034/viewer/2022052316/55a69a311a28ab7b668b4659/html5/thumbnails/20.jpg)
Advantages
PSO is based on the intelligence. It can be applied into both scientific research and engineering use.
PSO have no overlapping and mutation calculation.
The search can be carried out by the speed of the particle. During the development of several generations, only the most optimist particle can transmit information onto the other particles, and the speed of the researching is very fast.
![Page 21: Particle swarm optimization](https://reader034.fdocuments.in/reader034/viewer/2022052316/55a69a311a28ab7b668b4659/html5/thumbnails/21.jpg)
Advantages…
The calculation in PSO is very simple.
Compared with the other developing
calculations, it occupies the bigger
optimization ability and it can be
completed easily.
PSO adopts the real number code,
and it is decided directly by the
solution. The number of the dimension
is equal to the constant of the solution.
![Page 22: Particle swarm optimization](https://reader034.fdocuments.in/reader034/viewer/2022052316/55a69a311a28ab7b668b4659/html5/thumbnails/22.jpg)
Disadvantages
The method easily suffers from the
partial optimism, which causes the less
exact at the regulation of its speed and
the direction.
The method can not work out the
problems of scattering and
The method can not work out the
problems of non-coordinate system,
such as the solution to the energy field
and the moving rules of the particles in
the energy field
![Page 23: Particle swarm optimization](https://reader034.fdocuments.in/reader034/viewer/2022052316/55a69a311a28ab7b668b4659/html5/thumbnails/23.jpg)
Thank You !!