(1+1)-Active-CMA-ES 2010 (OPOA2010)

class pypop7.optimizers.es.opoa2010.OPOA2010(problem, options)

(1+1)-Active-CMA-ES 2010 (OPOA2010).

  • 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):
    • ’sigma’ - initial global step-size, aka mutation strength (float),

    • ’mean’ - initial (starting) point, aka mean of Gaussian search distribution (array_like),

      • if not given, it will draw a random sample from the uniform distribution whose search range is bounded by problem[‘lower_boundary’] and problem[‘upper_boundary’].


Use the optimizer OPOA2010 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 pypop7.optimizers.es.opoa2010 import OPOA2010
 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...            'mean': 3*numpy.ones((2,)),
11...            'sigma': 0.1}  # the global step-size may need to be tuned for better performance
12>>> opoa2010 = OPOA2010(problem, options)  # initialize the optimizer class
13>>> results = opoa2010.optimize()  # run the optimization process
14>>> # return the number of function evaluations and best-so-far fitness
15>>> print(f"OPOA2010: {results['n_function_evaluations']}, {results['best_so_far_y']}")
16OPOA2010: 5000, 6.573983554197426e-16

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


Arnold, D.V. and Hansen, N., 2010, July. Active covariance matrix adaptation for the (1+1)-CMA-ES. In Proceedings of Annual Conference on Genetic and Evolutionary Computation (pp. 385-392). ACM. https://dl.acm.org/doi/abs/10.1145/1830483.1830556