CoOperative co-Evolutionary Algorithm (COEA)

class, options)

CoOperative co-Evolutionary Algorithm (COEA).


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.

  • 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).


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

 1>>> import numpy
 2>>> from pypop7.benchmarks.base_functions import rosenbrock  # function to be minimized
 3>>> from import COEA
 4>>> problem = {'fitness_function': rosenbrock,  # define problem arguments
 5...            'ndim_problem': 2,
 6...            'lower_boundary': -5*numpy.ones((2,)),
 7...            'upper_boundary': 5*numpy.ones((2,))}
 8>>> options = {'max_function_evaluations': 5000,  # set optimizer options
 9...            'seed_rng': 2022,
10...            'x': 3*numpy.ones((2,))}
11>>> coea = COEA(problem, options)  # initialize the optimizer class
12>>> results = coea.optimize()  # run the optimization process
13>>> # return the number of function evaluations and best-so-far fitness
14>>> print(f"COEA: {results['n_function_evaluations']}, {results['best_so_far_y']}")
15COEA: 5000, 0.43081941641866195

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


number of individuals/samples, aka population size.




Potter, M.A. and De Jong, K.A., 2000. Cooperative coevolution: An architecture for evolving coadapted subcomponents. Evolutionary Computation, 8(1), pp.1-29.

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.