Particle Swarm Optimization Particle Swarm Optimization (PSO) (PSO) • PSO is a robust stochastic optimization technique based on the movement and intelligence of swarms. • PSO applies the concept of social interaction to problem solving. • It was developed in 1995 by James Kennedy (social-psychologist) and Russell Eberhart (electrical engineer). • It uses a number of agents (particles) that constitute a swarm moving around in the search space looking for the best solution. • Each particle is treated as a point in a N- dimensional space which adjusts its “flying” according to its own flying experience as well as the flying experience of other particles.
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Particle Swarm Optimization-Meander Line Polarizer
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Particle Swarm Optimization (PSO)Particle Swarm Optimization (PSO)• PSO is a robust stochastic optimization technique based on
the movement and intelligence of swarms.
• PSO applies the concept of social interaction to problem solving.
• It was developed in 1995 by James Kennedy (social-psychologist) and Russell Eberhart (electrical engineer).
• It uses a number of agents (particles) that constitute a swarm moving around in the search space looking for the best solution.
• Each particle is treated as a point in a N-dimensional space which adjusts its “flying” according to its own flying experience as well as the flying experience of other particles.
• Each particle keeps track of its coordinates in the solution space which are associated with the best solution (fitness) that has achieved so far by that particle. This value is called personal best , pbest.
• Another best value that is tracked by the PSO is the best value obtained so far by any particle in the neighborhood of that particle. This value is called gbest.
• The basic concept of PSO lies in accelerating each particle toward its pbest and the gbest locations, with a random weighted accelaration at each time step as shown in Fig.1
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
Comments on the Inertial weight factor:Comments on the Inertial weight factor: A large inertia weight (A large inertia weight (ww) facilitates a global search while ) facilitates a global search while
a small inertia weight facilitates a local search.a small inertia weight facilitates a local search.
By linearly decreasing the inertia weight from a relatively By linearly decreasing the inertia weight from a relatively large value to a small value through the course of the large value to a small value through the course of the PSO run gives the best PSO performance compared PSO run gives the best PSO performance compared with fixed inertia weight settings.with fixed inertia weight settings.
Larger w ----------- greater global search abilityLarger w ----------- greater global search abilitySmaller w ------------ greater local search ability.Smaller w ------------ greater local search ability.
Particle Swarm Optimization (PSO)Particle Swarm Optimization (PSO)Flow chart depicting the General PSO Algorithm:
Start
Initialize particles with random position and velocity vectors.
For each particle’s position (p) evaluate fitness
If fitness(p) better than fitness(pbest) then pbest= pL
oop
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Set best of pBests as gBest
Update particles velocity (eq. 1) and position (eq. 3)
Loop
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Stop: giving gBest, optimal solution.
Comparison with other evolutionary Comparison with other evolutionary computation techniques.computation techniques.
• Unlike in genetic algorithms, evolutionary programming and evolutionary strategies, in PSO, there is no selection operation.
• All particles in PSO are kept as members of the population through the course of the run
• PSO is the only algorithm that does not implement the survival of the fittest.
• No crossover operation in PSO.
• eq 1(b) resembles mutation in EP.
• In EP balance between the global and local search can be adjusted through the strategy parameter while in PSO the balance is
achieved through the inertial weight factor (w) of eq. 1(a)
Variants of PSOVariants of PSO
• Discrete PSO ……………… can handle discrete binary variables
• MINLP PSO………… can handle both discrete binary and continuous variables.
• Hybrid PSO…………. Utilizes basic mechanism of PSO and the natural selection mechanism, which is usually
utilized by EC methods such as GAs.
Application of PSO ALGORITHM to Optimize a Meander-line Polarizer for LI→CP conversion
Intialization parameters used for PSO:
wMax=0.41
wMin=0.4
(Note:The inertial weight ,w is linearly decreased from wMax to wMin according the Eq. (2), w is chosen virtually constant in this case for better
local search near the Sun’s Optimized parameters. )
c1=c2=1.49
maxIter=2000
The above parameters are used in conjuction with eqs.(1) & (2)
Swarm size/Population size used for solution search : 25
Application of PSO ALGORITHM to Optimize a Meander-line Polarizer for LI→CP conversion
Frequency band of interest: 3.5 to 6.5 (GHz)
(evaluated at 12 frequency points)
Desired VSWR <= 1.2
Desired AR <= 0.5 (dB)
Total number of fitness evaluations: 100025
Note: For my implementation of the PSO the number of fiteness evaluations are calculated as follows: (2 x swarmsize x maxIter)+ swarmsize = (2 x 25 x 2000)+ 25
The following slides include the results for the broadband case.