A Particle Swarm
Optimization (PSO) Primer
With
Applications
Brian Birge
Overview
p Introduction
p Theory
p Applications
p Computational Intelligence
p Summary
Introduction
p Subset of Evolutionary Computation
n Genetic Algorithms
n Evolutionary Programming
n Evolution Strategies
n Genetic Programming
p Behaviorally Inspired
n Developed out of attempts to model bird flocks and fish
schools
p Emergence
n Complex behavior from simple rules
Theory - Qualitative Details
p PSO Algorithm in a nutshell
p Searches Hyperspace of Problem for Optimum
n Define problem to search
p How many dimensions?
p Solution criteria?
n Initialize Population
p Random initial positions
p Random initial velocities
n Determine Global Best Position
n Determine Personal Best Position
n Update Velocity and Position Equations
Theory - Equations
p The Basic PSO algorithm consists of the
velocity:
p ..and position:
p i – particle index
p k – discrete time index
p v – velocity of ith particle
p x – position of ith particle
p p – best position found by ith particle (personal best)
p G – best position found by swarm (global best, best of personal
bests)
p γ1,2 – random numbers on the interval [0,1] applied to ith
particle
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12
1
iiiiiii
vkvkpxkGxk
γγ+=+−+−
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11
iii
xkxkvk
+=++
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