Particle Swarm Optimization vs Gradient Descent

• Algorithm -
  1. PSO
  2. Gradient Descent
• Benchmarks -
  1. Rosenbrock Function
  2. Rastrigin Function

Results -

• PSO on Rosenbrock -
  • 
• PSO on Rastrigin -
  • 

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• GD on Rosenbrock -
  • 
• GD on Rastrigin -
  • 

Experiment 1 -

Running ~50 iterations of PSO and GD independently to generate probability distribution of error against density -

Observation 1 -

While PSO is actively able to achieve the global minima or has very low error, Gradient Descent proves to be ineffective on the benchmarks mentioned.

Experiment 2 -

Effect of Error vs Number of particles in PSO -

Experiment 3 -

Effect of Inertia parameter(‘a’) for velocity update as stated in State of Art - Linearly decreasing the parameter from 0.9 to 0.4 over the defined iterations.

Therefore, we observer that while the error reduces with SOTA params, the difference is not really drastic.

Created with -

1. Dhruv Rathi
2. Justus Erker
3. Caio Guirado