(1+1)-Cholesky-CMA-ES 2009 (OPOC2009)

class pypop7.optimizers.es.opoc2009.OPOC2009(problem, options)

(1+1)-Cholesky-CMA-ES 2009 (OPOC2009).

  • 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 OPOC2009 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.opoc2009 import OPOC2009
 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>>> opoc2009 = OPOC2009(problem, options)  # initialize the optimizer class
13>>> results = opoc2009.optimize()  # run the optimization process
14>>> # return the number of function evaluations and best-so-far fitness
15>>> print(f"OPOC2009: {results['n_function_evaluations']}, {results['best_so_far_y']}")
16OPOC2009: 5000, 2.7686802211556655e-17

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


Suttorp, T., Hansen, N. and Igel, C., 2009. Efficient covariance matrix update for variable metric evolution strategies. Machine Learning, 75(2), pp.167-197. https://link.springer.com/article/10.1007/s10994-009-5102-1 (See Algorithm 2 for details.)