Particle Swarm Optimizer (PSO)

class pypop7.optimizers.pso.pso.PSO(problem, options)

Particle Swarm Optimizer (PSO).

This is the abstract class for all PSO classes. Please use any of its instantiated subclasses to optimize the black-box problem at hand.


PSO is a very popular family of swarm-based search algorithms, proposed by an electrical engineer (Russell C. Eberhart) and a psychologist (James Kennedy), two recipients of IEEE Evolutionary Computation Pioneer Award 2012. Its underlying motivation comes from very interesting collective behaviors (e.g. flocking) observed from social animals (such as birds), which are often regarded as a particular form of emergence or self-organization. Recently, PSO-type swarm optimizers are theoretically analyzed under the Consensus-Based Optimization (CBO) framework.

  • problem (dict) –

    problem arguments with the following common settings (keys):
    • ’fitness_function’ - objective function to be minimized (func),

    • ’ndim_problem’ - number of dimensionality (int),

    • ’upper_boundary’ - upper boundary of search range (array_like),

    • ’lower_boundary’ - lower boundary of search range (array_like).

  • options (dict) –

    optimizer options with the following common settings (keys):
    • ’max_function_evaluations’ - maximum of function evaluations (int, default: np.Inf),

    • ’max_runtime’ - maximal runtime to be allowed (float, default: np.Inf),

    • ’seed_rng’ - seed for random number generation needed to be explicitly set (int);

    and with the following particular settings (keys):
    • ’n_individuals’ - swarm (population) size, aka number of particles (int, default: 20),

    • ’cognition’ - cognitive learning rate (float, default: 2.0),

    • ’society’ - social learning rate (float, default: 2.0),

    • ’max_ratio_v’ - maximal ratio of velocities w.r.t. search range (float, default: 0.2).


cognitive learning rate, aka acceleration coefficient.




maximal ratio of velocities w.r.t. search range.




swarm (population) size, aka number of particles.




social learning rate, aka acceleration coefficient.




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Fornasier, M., Huang, H., Pareschi, L. and Sünnen, P., 2022. Anisotropic diffusion in consensus-based optimization on the sphere. SIAM Journal on Optimization, 32(3), pp.1984-2012.

Fornasier, M., Huang, H., Pareschi, L. and Sünnen, P., 2021. Consensus-based optimization on the sphere: Convergence to global minimizers and machine learning. Journal of Machine Learning Research, 22(1), pp.10722-10776.

Blackwell, T. and Kennedy, J., 2018. Impact of communication topology in particle swarm optimization. IEEE Transactions on Evolutionary Computation, 23(4), pp.689-702.

Bonyadi, M.R. and Michalewicz, Z., 2017. Particle swarm optimization for single objective continuous space problems: A review. Evolutionary Computation, 25(1), pp.1-54.

Floreano, D. and Mattiussi, C., 2008. Bio-inspired artificial intelligence: Theories, methods, and technologies. MIT Press. (See [Chapter 7.2 Particle Swarm Optimization] for details.)

Poli, R., Kennedy, J. and Blackwell, T., 2007. Particle swarm optimization. Swarm Intelligence, 1(1), pp.33-57.

Venter, G. and Sobieszczanski-Sobieski, J., 2003. Particle swarm optimization. AIAA Journal, 41(8), pp.1583-1589.

Clerc, M. and Kennedy, J., 2002. The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation, 6(1), pp.58-73.

Eberhart, R.C., Shi, Y. and Kennedy, J., 2001. Swarm intelligence. Elsevier.

Shi, Y. and Eberhart, R., 1998, May. A modified particle swarm optimizer. In IEEE World Congress on Computational Intelligence (pp. 69-73). IEEE.

Kennedy, J. and Eberhart, R., 1995, November. Particle swarm optimization. In Proceedings of International Conference on Neural Networks (pp. 1942-1948). IEEE.