Particle Swarm Optimization (PSO) (Kennedy & Eberhart 1995) simulates the social behavior of bird flocks. Each particle has a position x and velocity v updated by: v ← ωv + c₁r₁(pBest−x) + c₂r₂(gBest−x), x ← x + v, where pBest is the particle's personal best position and gBest is the global best found by any particle. The inertia weight ω controls exploration vs. exploitation — high ω maintains momentum for global search, low ω improves local convergence. Cognitive coefficient c₁ pulls toward personal memory; social coefficient c₂ pulls toward the swarm's collective knowledge. Trails show recent history; cyan star marks the global best.