Particle Swarm Optimization (PSO)

Both are population-based metaheuristics for optimization, but they differ in mechanism. A genetic algorithm evolves a population through selection, crossover, and mutation operators inspired by biological evolution. PSO instead moves particles through a continuous space by updating velocities based on personal and social memory — there is no crossover or mutation. PSO typically has fewer parameters to tune and often converges faster on continuous problems, while genetic algorithms can be more naturally adapted to discrete or combinatorial spaces.

The three core parameters are the inertia weight (w), which controls how much of the previous velocity is retained; the cognitive coefficient (c1), which scales attraction toward a particle's personal best; and the social coefficient (c2), which scales attraction toward the global best. A common starting point from the literature is w around 0.7–0.9, c1 and c2 around 1.5–2.0. The inertia weight is often decreased linearly over iterations to shift the swarm from exploration early on toward exploitation later.

Standard PSO is defined for continuous search spaces and applies velocity and position updates that assume real-valued coordinates. Discrete or combinatorial variants exist — such as binary PSO — but these require non-trivial modifications to the update equations. For purely combinatorial problems like routing or scheduling, Ant Colony Optimization is often the more natural choice.

Track the global best fitness value across iterations. If the curve flattens long before the iteration budget is exhausted and the reported solution is not satisfactory, premature convergence has likely occurred. Common remedies include increasing the inertia weight, restarting the swarm from new random positions, or increasing the swarm size. If the computation budget does not allow more iterations, Bayesian optimization may be a more efficient alternative.