Particle Swarm Optimization Author :

Pooya Sagharchi Ha

April 18, 2015

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Agenda

Introduction to PSO What’s goal of optimization?

Who were described first PSO? When presented PSO? What inspired PSO?

Particle Swarm Optimization

How it works?

PSO Algorithm / Pseudocode NPSO Algorithm

Summary Advantages

Applications

Conclusion

References

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Introduction to PSO

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

The PSO algorithm was first described in 1995 by James Kennedy and Russell C. Eberhart.

The PSO inspired by social behavior of bride flocking or fish schooling.

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How does it work?

In the PSO algorithm each individual is called a “particle”, each particle have memory and store the position.

PSO is initialized with a group of random particles and then searches for optimal by updating generations. Each particle is searching for the optimum. Each particle is moving, and hence has a velocity.

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Particles are evaluated according to some fitness criterion after each time step, In every iteration , each particle is updated by following two “best”values.

The second best value is a global best and called gbest, it is the best value obtained so far any particle in the population.

The first one is the best solution ( fitness ) it has achieved so far ( the fitness value is also stored ), This value is called pbest.

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Vt

Xt+1

gbest

pbest

Xt

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Xi(t+1) = Xi(t) + Vi(t+1)

Vi(t+1) = W * Vi(t) + c1 * r1 * (Pbi - Xi(t)) + c2 * r2 * (Gbi - Xi(t))

→ → →

→ → → → → →

Velocity of particle at n+1 iteration

Current position

Modify position

Inertial weight

C1 and c2 acceleration factor

R1 and R2 are random numbers

Pbi personal best position of swarm

Gbi global best position of particle

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Psudocode

For each particle Initialize particle with feasible random number End Do For each particle Calculate the fitness value if the fitness value is better the best fitness value (pbest) 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

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What is NPSO ?

NPSO stand for New Particle Swarm Optimization.

NPSO is modified form of the basic PSO and was introduced in 2005.

Each particle adjusts its group’s previous worst to find the optimal value.

NPSO determines the most promising direction based on the negative of the worst particle position.

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Vt

Xt+1

gbest

pbest

Xt

prtposji+1

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prtops j i = prtops j i-1 + prtvel j i

prtvel j i = X * [ w * prtvel j i-1 +

c1 * r1 * (prtops j i-1 - pworst j i-1) +

c1 * r1 * (prtops j i-1 - gworst j i-1)

]

→ →→

the position of particle j in iteration i

the velocity of the particle j in iteration

→ →

→ →

→ →

the worst position of particle j in iteration i

the worst position in the swarm till iteration i

X = 2 / abs( 2 - y - sqrt ( y^2 - 4y ) )

y = y1 + y2 > 4

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Advantages

Simple implementation

Easily parallelized for concurrent processingVery few algorithm parameters Very efficient global search algorithm

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Application

Object tracking

Path planningTelecommunications Signal processing

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Conclusion

The process of PSO algorithm in finding optimal values follows the work of an animal society.

PSO can be effectively used for continuous optimization problems. Particle will move through a multidimensional search space to find the best position in that space.

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References J. Kennedy and R. Eberhart. A discrete binary version of the particle swarm algorithm. In Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, pages 4104-4108, IEEE Press, Piscataway, NJ, 1997

Shi, Y.; Eberhart, R.C. (1998). "A modified particle swarm optimizer". Proceedings of IEEE International Conference on Evolutionary Computation. pp. 69–73. Kennedy, J.; Eberhart, R.C. (2001). Swarm Intelligence. Morgan Kaufmann

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Any Questions ?!