Langevin Particle Swarm Optimization with Friction-Based Communication

This thesis presents a swarm-based optimization method inspired by the overdamped Langevin dynamics. A swarm consists of particles, each characterized by their position and friction coefficient, and subjected to a random force. The particles communicate by updating their friction coefficients based on relative performance within the swarm. The friction communication mechanism enables better-performing particles to move slower and remain near optimal regions, while worse-performing particles move faster to explore the search space. This creates a balance between exploration of new areas and careful exploitation of promising regions. The communication mechanism leads to emergent annealing behaviour, where average friction increases over time, similar to temperature reduction in simulated annealing. Two types of random forces are considered: Gaussian random force, where the noise variance decreases with the friction coefficient, leading to Brownian motion, and Lévy-stable random force, producing Lévy flight dynamics. The method is experimentally evaluated on benchmark function optimization and neural network training, demonstrating competitive performance compared to existing algorithms. A GPU-based implementation enables efficient parallel execution.