Particle Swarm Optimizer (PSO)

class pypop7.optimizers.pso.pso.PSO(problem, options)[source]

Particle Swarm Optimizer (PSO).

This is the abstract class of all PSO classes. Please use any of its instantiated subclasses to optimize the black-box problem at hand. The unique goal of this abstract class is to unify the common interfaces of all its subclasses (different algorithm versions).

Note

PSO is a very popular family of swarm-based search algorithms, originally 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 interesting collective behaviors (e.g. flocking) observed in social animals (such as birds), which are often regarded as a particular form of emergence or self-organization. Recently, PSO-type swarm optimizers have been theoretically analyzed under the Consensus-Based Optimization (CBO) or Swarm Gradient Dynamics framework, with more or less modifications to the standard PSO implementation for mathematical tractability.

For some interesting applications of PSO/CBO, refer to [Melis et al., 2024, Nature], [Venter&Sobieszczanski-Sobieski, 2003, AIAAJ], just to name a few.

Parameters:

  • 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).

cognition

cognitive learning rate, aka acceleration coefficient.

Type:

float

max_ratio_v

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

Type:

float

n_individuals

swarm (population) size, aka number of particles.

Type:

int

society

social learning rate, aka acceleration coefficient.

Type:

float

References

Bolte, J., Miclo, L. and Villeneuve, S., 2024. Swarm gradient dynamics for global optimization: The mean-field limit case. Mathematical Programming, 205(1), pp.661-701.

Cipriani, C., Huang, H. and Qiu, J., 2022. Zero-inertia limit: From particle swarm optimization to consensus-based optimization. SIAM Journal on Mathematical Analysis, 54(3), pp.3091-3121.

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. https://epubs.siam.org/doi/abs/10.1137/21M140941X

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. https://jmlr.csail.mit.edu/papers/v22/21-0259.html

Blackwell, T. and Kennedy, J., 2018. Impact of communication topology in particle swarm optimization. IEEE Transactions on Evolutionary Computation, 23(4), pp.689-702. https://ieeexplore.ieee.org/abstract/document/8531770

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. https://direct.mit.edu/evco/article-abstract/25/1/1/1040/Particle-Swarm-Optimization-for-Single-Objective

https://www.cs.cmu.edu/~arielpro/15381f16/c_slides/781f16-26.pdf

Floreano, D. and Mattiussi, C., 2008. Bio-inspired artificial intelligence: Theories, methods, and technologies. MIT Press. https://mitpress.mit.edu/9780262062718/bio-inspired-artificial-intelligence/ (See [Chapter 7.2 Particle Swarm Optimization] for details.)

http://www.scholarpedia.org/article/Particle_swarm_optimization

Poli, R., Kennedy, J. and Blackwell, T., 2007. Particle swarm optimization. Swarm Intelligence, 1(1), pp.33-57. https://link.springer.com/article/10.1007/s11721-007-0002-0

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.

PSOs: