1. Particle Swarm Optimization
CEE 6410
David Rosenberg

2. Learning Objectives Perform steps on a bead board
Use web app to Identify effects of parameters on results
Solve a more complicated problem with Matlab
Compare to genetic algorithms
CEE 6410

3. Algorithm Overview Each particle: Searches for the global optimum
Moves with velocity (direction)
Remembers local (particle) optimum
Updates velocity as a weighted, random combo of
Current velocity
Direction to local optimum
Direction to swarm optimum (to date)
CEE 6410

4. Particle Motion Visualized
Current particle position
Current velocity
Local particle optimum
Swarm optimum
New particle position
New velocity
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5. Key Steps
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6. Example 1. Use the bead board to solve
Max Z = f(x,y) = 1000 – [(x-1)2 + (y-1)2]
s.t ≤ x ≤ 10
-10 ≤ y ≤ 10
Start with 2 particles
Compute velocities and
positions with
Track particle positions
on board with beads
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7. Example 2. How do swarm parameters effect results?
Symbol
Description n
Swarm size (# of particles) w
Weight on current direction (velocity) c1
Weight on direction to local particle optimum c2
Weight on direction to swarm optimum
Vmax
Maximum allowable velocity
Experiment with the web app at
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8. Example 3. Solve a more complicated problem in Matlab
Min Z = f(x,y) = x * exp(-(x2 + y2))
s.t. -5 ≤ x ≤ 5
-10 ≤ y ≤ 5
See Matlab code
CEE 6410

9. Compare Heuristic Algorithms
Characteristic
Genetic Algorithms
Particle Swarm
Explore strategies (to search new areas)
Exploit strategies (to retain best solutions)
Number of parameters
Optimum guaranteed
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10. Conclusions
Particle swarm optimization use swarm communication to solve complex problems
Can embed simulation models
Smaller number of parameters than genetic algorithms
Lots of public-domain and commercial software available
Many water resources applications
CEE 6410