Particle Swarm Optimization (PSO) Sampler

Abstract

Particle Swarm Optimization (PSO) is a population-based stochastic optimizer inspired by flocking behavior, where particles iteratively adjust their positions using personal and global bests to search for optima. This sampler supports single-objective, continuous optimization only.

Note: Categorical distributions are suggested by the underlaying RandomSampler.

Note: Multi-objective optimization is not supported.

For details on the algorithm, see Kennedy and Eberhart (1995): Particle Swarm Optimization.

APIs

• PSOSampler(search_space: dict[str, BaseDistribution] | None = None, n_particles: int = 10, inertia: float = 0.5, cognitive: float = 1.5, social: float = 1.5, seed: int | None = None)
  • search_space: A dictionary containing the search space that defines the parameter space. The keys are the parameter names and the values are the parameter’s distribution. If the search space is not provided, the sampler will infer the search space dynamically. Example:

    search_space = {
        "x": optuna.distributions.FloatDistribution(-10, 10),
        "y": optuna.distributions.FloatDistribution(-10, 10),
    }
    PSOSampler(search_space=search_space)
    

  • n_particles: Number of particles (population size). Prefer total n_trials to be a multiple of n_particles to run full PSO iterations. Larger swarms can improve exploration when budget allows.
  • inertia: Inertia weight controlling momentum (influence of previous velocity). Higher values favor exploration, lower favor exploitation.
  • cognitive: Personal-best acceleration coefficient (c1). Controls attraction toward each particle’s own best.
  • social: Global-best acceleration coefficient (c2). Controls attraction toward the swarm’s best.
  • seed: Seed for random number generator.

Example

import optuna
import optunahub


def objective(trial: optuna.Trial) -> float:
    x = trial.suggest_float("x", -10, 10)
    y = trial.suggest_float("y", -10, 10)
    return x**2 + y**2

n_trials = 100
n_generations = 5

sampler = optunahub.load_module(package="samplers/pso").PSOSampler(
    {
        "x": optuna.distributions.FloatDistribution(-10, 10),
        "y": optuna.distributions.FloatDistribution(-10, 10),
    },
    n_particles=int(n_trials / n_generations),
    inertia=0.5,
    cognitive=1.5,
    social=1.5,
)

study = optuna.create_study(sampler=sampler)
study.optimize(objective, n_trials=n_trials)
print(study.best_trials)