Particle Swarm optimizat
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Particle Swarm optimizat ion. Cooperation example. Outline. Basic Idea of PSO Neighborhood topologies Velocity and position Update rules Choice of parameter value Applications. The basic idea. Each particle is searching for the optimum

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Particle Swarm optimizat ion

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Particle swarm optimizat ion

Particle Swarm optimization


Particle swarm optimizat ion

Cooperation example


Particle swarm optimizat ion

Outline

  • Basic Idea of PSO

  • Neighborhood topologies

  • Velocity and position Update rules

  • Choice of parameter value

  • Applications


The basic idea

The basic idea

  • Each particle is searching for the optimum

  • Each particle is moving and hence has a velocity.

  • Each particle remembers the position it was in where it had its best result so far (its personal best)

  • But this would not be much good on its own; particles need help in figuring out where to search.


The basic idea ii

The basic idea II

  • The particles in the swarm co-operate. They exchange information about what they’ve discovered in the places they have visited

  • The co-operation is very simple. In basic PSO it is like this:

    • A particle has a neighbourhood associated with it.

    • A particle knows the fitnesses of those in its neighbourhood, and uses the position of the one with best fitness.

    • This position is simply used to adjust the particle’s velocity


Initialization positions and velocities

Initialization. Positions and velocities


What a particle does

What a particle does

  • In each timestep, a particle has to move to a new position. It does this by adjusting its velocity.

    • The adjustment is essentially this:

    • The current velocity PLUS

    • A weighted random portion in the direction of its personal best PLUS

    • A weighted random portion in the direction of the neighbourhood best.

  • Having worked out a new velocity, its position is simply its old position plus the new velocity.


Neighbourhoods

Neighbourhoods

geographical

social


Neighbourhoods1

Neighbourhoods

Global


Particle swarm optimizat ion

Particles Adjust their positions according to a ``Psychosocial compromise’’ between what an individual is comfortable with, and what society reckons

My best perf.

pi

Here I am!

The best perf. of my neighbours

x

pg

v


Pseudocode http www swarmintelligence org tutorials php

Pseudocodehttp://www.swarmintelligence.org/tutorials.php


Pso with global best gbest model

PSO with global best (gbest) model


Pso with local best lbest model

PSO with local best (lbest) model


Velocity clamping

Velocity clamping


Particle swarm optimizat ion

Animated illustration

Global optimum


Parameters

Parameters

  • Inertia weight W

  • Number of particles

  • C1 (importance of personal best)

  • C2 (importance of neighbourhood best)

  • Neighborhood size for lbest model


Particle swarm optimizat ion

The right way

This way

Or this way

How to choose parameters


Parameters1

Parameters

  • Number of particles

    (5—30) are reported as usually sufficient.

  • C1 (importance of personal best)

  • C2 (importance of neighbourhood best)

  • Usually C1+C2 = 4.

  • Vmax – too low, too slow; too high, too unstable.

  • Neighborbood: 2-3, or probability; p=1-pow(1-1/(size),3);


Particle swarm optimizat ion

Rastrigin

Griewank

Rosenbrock

Some functions often used for testing real-valued optimisation algorithms


Particle swarm optimizat ion

... and some typical results

Optimum=0, dimension=30

Best result after 40 000 evaluations


Particle swarm optimizat ion

Adaptive swarm size

I try to kill myself

There has been enough improvement

although I'm the worst

I try to generate a new particle

I'm the best

but there has been not enough improvement


Particle swarm optimizat ion

Adaptive coefficients

rand(0…b)(p-x)

av

The better I am, the more I follow my own way

The better is my best neighbour, the more I tend to go towards him


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