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The Particle Swarm Optimization Algorithm. Nebojša Trpković 10 th Dec 2010. Problem Definition. optimization of continuous nonlinear functions ↓ finding the best solution in problem space. Example. Importance. function optimization artificial neural network training

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The Particle Swarm Optimization Algorithm

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The Particle Swarm Optimization Algorithm

Nebojša Trpković

10th Dec 2010

Problem Definition

optimization of continuous nonlinear functions

finding the best solution in problem space

Nebojša Trpković


Nebojša Trpković


  • function optimization

  • artificial neural network training

  • fuzzy system control

Nebojša Trpković

Existing Solutions

  • Ant Colony (ACO)

    • discrete

  • Genetic Algorithms (GA)

    • slow convergence

Nebojša Trpković

Particle Swarm Optimization

Very simple classification:

  • a computational method

  • that optimizes a problem

  • by iteratively trying to improve a candidate solution

  • with regard to a given measure of quality

Nebojša Trpković

Particle Swarm Optimization


  • developed by Russell C. Eberhart and James Kennedy in 1995

  • inspired by social behavior of bird flocking or fish schooling

  • similar to evolutionary techniques such as Genetic Algorithms (GA)

Nebojša Trpković

Particle Swarm Optimization


  • faster convergence

  • less parameters to tune

  • easier searching in very large problem spaces

Nebojša Trpković

Particle Swarm Optimization

Basic principle:

let particle swarm move

towards the best position in search space, remembering each particle’s best known position

and global (swarm’s) best known position

Nebojša Trpković

Velocity Change

xi – specific particle

pi – particle’s (personal) best known position

g – swarm’s (global) best known position

vi – particle’s velocity

vi ← ωvi + φprp(pi - xi) + φgrg(g - xi)

inertia cognitive social

Nebojša Trpković

Position Change

xi – specific particle

vi – particle’s velocity

xi ← xi + vi

Nebojša Trpković


For each particle

Initialize particle



For each particle

Calculate fitness value

If the fitness value is better than the best personal fitness value in history, set current value as a new best personal fitness value


Choose the particle with the best fitness value of all the particles, and if that fitness value is better then current global best, set as a global best fitness value

For each particle

Calculate particle velocity according velocity change equation

Update particle position according position change equation


While maximum iterations or minimum error criteria is not attained

Nebojša Trpković

Single Particle

Nebojša Trpković

Parameters selection

Different ways to choose parameters:

  • proper balance between exploration and exploitation

    (avoiding premature convergence to a local optimum yet still ensuring a good rate of convergence to the optimum)

  • putting all attention on exploitation

    (making possible searches in a vast problem spaces)

  • automatization by meta-optimization

Nebojša Trpković

Avoiding Local Optimums

  • adding randomization factor to velocity calculation

  • adding random momentum in a specific iterations

Nebojša Trpković


Nebojša Trpković


“This algorithm belongs ideologically to that philosophical school

that allows wisdom to emerge rather than trying to impose it,

that emulates nature rather than trying to control it,

and that seeks to make things simpler rather than more complex.”

James Kennedy, Russell Eberhart

Nebojša Trpković


  • Wikipedia

  • Swarm Intelligence

  • Application of a particle swarm optimization algorithm for determining optimum well location and type, Jerome Onwunalu and Louis J. Durlofsky, 2009

  • Particle Swarm Optimization, James Kennedy and Russell Eberhart, 1995

  • Robot Swarm driven by Particle Swarm Optimization algorithm, thinkfluid

Nebojša Trpković

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