Particle Swarm Optimization Routine for Function Minimization

In this article, I present a practical implementation of Particle Swarm Optimization (PSO) for function minimization. This routine demonstrates core PSO concepts through well-commented code structure, making it highly accessible for understanding the algorithm's mechanics. Particle Swarm Optimization is a population-based optimization technique inspired by collective behaviors such as bird flocking or fish schooling, designed to solve complex optimization problems by iteratively improving candidate solutions.

The algorithm operates through coordinated updates of particle velocities and positions using mathematical formulations that balance exploration and exploitation. Key implementation components include: velocity calculation incorporating cognitive and social components, position updates based on current velocity vectors, and fitness evaluation through objective function computation. The iterative process continuously refines particle positions toward global optima by maintaining personal best positions (pBest) and tracking the swarm's global best solution (gBest).

This implementation employs fundamental mathematical operations and controlled iteration cycles to demonstrate PSO's convergence behavior. By examining the code structure, readers can grasp essential algorithm aspects including initialization parameters, termination conditions, and solution refinement mechanisms - providing practical insights for adapting PSO to custom optimization challenges.