CoOperative co-Evolutionary Algorithm (COEA)

class pypop7.optimizers.cc.coea.COEA(problem, options)

CoOperative co-Evolutionary Algorithm (COEA).

Note

This is a slightly modified version of COEA, where the more common real-valued representation is used for continuous optimization rather than binary-coding used in the original paper. For the suboptimizer, the GENITOR is used, owing to its simplicity.

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 setting (key):

  • ’n_individuals’ - number of individuals/samples, aka population size (int, default: 100).

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.cc.coea import COEA
>>> 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,
...            'x': 3*numpy.ones((2,))}
>>> coea = COEA(problem, options)  # initialize the optimizer class
>>> results = coea.optimize()  # run the optimization process
>>> # return the number of function evaluations and best-so-far fitness
>>> print(f"COEA: {results['n_function_evaluations']}, {results['best_so_far_y']}")
COEA: 5000, 0.43081941641866195

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

n_individuals

number of individuals/samples, aka population size.

Type:

int

References

Potter, M.A. and De Jong, K.A., 2000. Cooperative coevolution: An architecture for evolving coadapted subcomponents. Evolutionary Computation, 8(1), pp.1-29. https://direct.mit.edu/evco/article/8/1/1/859/Cooperative-Coevolution-An-Architecture-for

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