Particle Swarm Optimization (PSO) is a population-based optimization algorithm inspired by the social behavior of bird flocks — particles (candidate solutions) move through the parameter space guided by their own best-found position and the swarm's best-found position.

How PSO Works

• Particles: Each particle has a position (solution) and velocity in the parameter space.
• Personal Best ($p_{best}$): Each particle remembers its own best position.
• Global Best ($g_{best}$): The best position found by any particle in the swarm.
• Update: Velocity is updated as a weighted sum of inertia, attraction to $p_{best}$, and attraction to $g_{best}$.

Why It Matters

• Fast Convergence: PSO typically converges faster than genetic algorithms for continuous optimization.
• Few Parameters: Only tuning parameters are inertia weight, cognitive and social coefficients.
• Process Optimization: Well-suited for continuous process recipe optimization with 5-50 parameters.

PSO is a swarm searching for the optimum — particles collectively exploring the parameter space, sharing information about promising regions.