CoOperative CO-evolutionary Covariance Matrix Adaptation (COCMA)

class, options)[source]

CoOperative CO-evolutionary Covariance Matrix Adaptation (COCMA).


For COCMA, CMA-ES is used as the suboptimizer, since it could learn the variable dependencies in each subspace to accelerate local convergence. Here, the simplest cyclic decomposition is employed to tackle non-separable objective functions, argurably the common feature of most real-world applications.

  • 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).

    • ’sigma’ - initial global step-size (float, default: problem[‘upper_boundary’] - problem[‘lower_boundary’]/3.0),

    • ’ndim_subproblem’ - dimensionality of subproblem for decomposition (int, default: 30).


Use the black-box optimizer COCMA 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 COCMA
 4>>> problem = {'fitness_function': rosenbrock,  # to define problem arguments
 5...            'ndim_problem': 2,
 6...            'lower_boundary': -5.0*numpy.ones((2,)),
 7...            'upper_boundary': 5.0*numpy.ones((2,))}
 8>>> options = {'max_function_evaluations': 5000,  # to set optimizer options
 9...            'seed_rng': 2022}
10>>> cocma = COCMA(problem, options)  # to initialize the optimizer class
11>>> results = cocma.optimize()  # to run the optimization/evolution process
12>>> print(f"COCMA: {results['n_function_evaluations']}, {results['best_so_far_y']}")
13COCMA: 5000, 0.0004

For its correctness checking of coding, we cannot provide the code-based repeatability report, since this implementation combines different papers. To our knowledge, few well-designed Python code of CC is openly available for non-separable black-box optimization.


number of individuals/samples, aka population size.




initial global step-size.




dimensionality of subproblem for decomposition.




Mei, Y., Omidvar, M.N., Li, X. and Yao, X., 2016. A competitive divide-and-conquer algorithm for unconstrained large-scale black-box optimization. ACM Transactions on Mathematical Software, 42(2), pp.1-24.

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.