Standard Particle Swarm Optimizer with a Local topology (SPSOL)

class pypop7.optimizers.pso.spsol.SPSOL(problem, options)

Standard Particle Swarm Optimizer with a Local (ring) topology (SPSOL).

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).

Examples

Use the optimizer to minimize the well-known test function Rosenbrock:

>>> import numpy
>>> from pypop7.benchmarks.base_functions import rosenbrock  # function to be minimized
>>> from pypop7.optimizers.pso.spsol import SPSOL
>>> problem = {'fitness_function': rosenbrock,  # define problem arguments
...            'ndim_problem': 2,
...            'lower_boundary': -5*numpy.ones((2,)),
...            'upper_boundary': 5*numpy.ones((2,))}
>>> options = {'max_function_evaluations': 5000,  # set optimizer options
...            'seed_rng': 2022}
>>> spsol = SPSOL(problem, options)  # initialize the optimizer class
>>> results = spsol.optimize()  # run the optimization process
>>> # return the number of function evaluations and best-so-far fitness
>>> print(f"SPSOL: {results['n_function_evaluations']}, {results['best_so_far_y']}")
SPSOL: 5000, 3.470837498146212e-08

For its correctness checking of coding, refer to this code-based repeatability report for more details.

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

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

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.)

Venter, G. and Sobieszczanski-Sobieski, J., 2003. Particle swarm optimization. AIAA Journal, 41(8), pp.1583-1589. https://arc.aiaa.org/doi/abs/10.2514/2.2111

Shi, Y. and Eberhart, R., 1998, May. A modified particle swarm optimizer. In IEEE World Congress on Computational Intelligence (pp. 69-73). IEEE. https://ieeexplore.ieee.org/abstract/document/699146

Kennedy, J. and Eberhart, R., 1995, November. Particle swarm optimization. In Proceedings of International Conference on Neural Networks (pp. 1942-1948). IEEE. https://ieeexplore.ieee.org/document/488968

Eberhart, R. and Kennedy, J., 1995, October. A new optimizer using particle swarm theory. In Proceedings of International Symposium on Micro Machine and Human Science (pp. 39-43). IEEE. https://ieeexplore.ieee.org/abstract/document/494215