particle swarm optimization

**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.