Cooperative Coevolving Particle Swarm Optimizer (CCPSO2)

class pypop7.optimizers.pso.ccpso2.CCPSO2(problem, options)

Cooperative Coevolving Particle Swarm Optimizer (CCPSO2).

Note

CCPSO2 employs the popular cooperative coevolution framework to extend PSO for large-scale black-box optimization (LSBBO) with random grouping/partitioning. However, it may suffer from performance degradation on non-separable functions (particularly ill-conditioned), owing to its axis-parallel decomposition strategy (see the classical coordinate descent from the mathematical programming community for detailed mathematical explanation).

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: 30),

  • ’p’ - probability of using Cauchy sampling distribution (float, default: 0.5),

  • ’group_sizes’ - a pool of candidate dimensions for grouping (list, default: [2, 5, 10, 50, 100, 250]).

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.ccpso2 import CCPSO2
>>> problem = {'fitness_function': rosenbrock,  # define problem arguments
...            'ndim_problem': 500,
...            'lower_boundary': -5*numpy.ones((500,)),
...            'upper_boundary': 5*numpy.ones((500,))}
>>> options = {'max_function_evaluations': 1000000,  # set optimizer options
...            'seed_rng': 2022}
>>> ccpso2 = CCPSO2(problem, options)  # initialize the optimizer class
>>> results = ccpso2.optimize()  # run the optimization process
>>> # return the number of function evaluations and best-so-far fitness
>>> print(f"CCPSO2: {results['n_function_evaluations']}, {results['best_so_far_y']}")
CCPSO2: 1000000, 1150.0205163111475

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

group_sizes

a pool of candidate dimensions for grouping.

Type:

list

n_individuals

swarm (population) size, aka number of particles.

Type:

int

p

probability of using Cauchy sampling distribution.

Type:

float

References

Li, X. and Yao, X., 2012. Cooperatively coevolving particle swarms for large scale optimization. IEEE Transactions on Evolutionary Computation, 16(2), pp.210-224. https://ieeexplore.ieee.org/document/5910380/

Potter, M.A. and De Jong, K.A., 1994, October. A cooperative coevolutionary approach to function optimization. In International Conference on Parallel Problem Solving from Nature (pp. 249-257). Springer, Berlin, Heidelberg. https://link.springer.com/chapter/10.1007/3-540-58484-6_269