Cooperative Particle Swarm Optimizer (CPSO)

class pypop7.optimizers.pso.cpso.CPSO(problem, options)

Cooperative Particle Swarm Optimizer (CPSO).

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: 1.49),

  • ’society’ - social learning rate (float, default: 1.49),

  • ’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.cpso import CPSO
>>> 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}
>>> cpso = CPSO(problem, options)  # initialize the optimizer class
>>> results = cpso.optimize()  # run the optimization process
>>> # return the number of function evaluations and best-so-far fitness
>>> print(f"CPSO: {results['n_function_evaluations']}, {results['best_so_far_y']}")
CPSO: 5000, 0.3085868239334274

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

Van den Bergh, F. and Engelbrecht, A.P., 2004. A cooperative approach to particle swarm optimization. IEEE Transactions on Evolutionary Computation, 8(3), pp.225-239. https://ieeexplore.ieee.org/document/1304845