(1+1)-Cholesky-CMA-ES 2006 (OPOC2006)

class pypop7.optimizers.es.opoc2006.OPOC2006(problem, options)[source]

(1+1)-Cholesky-CMA-ES 2006 (OPOC2006).

Note

To avoid the computationally expensive eigen-decomposition operation, OPOC2006 uses the Cholesky decomposition with a quadratic time complexity as an alternative. It is highly recommended to first attempt more advanced ES variants (e.g., LMCMA, LMMAES) for large-scale black-box optimization.

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 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’].

Examples

Use the black-box optimizer OPOC2006 to minimize the well-known test function Rosenbrock:

 1>>> import numpy  # engine for numerical computing
 2>>> from pypop7.benchmarks.base_functions import rosenbrock  # function to be minimized
 3>>> from pypop7.optimizers.es.opoc2006 import OPOC2006
 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...            'mean': 3*numpy.ones((2,)),
11...            'sigma': 3.0}  # global step-size may need to be fine-tuned for better performance
12>>> opoc2006 = OPOC2006(problem, options)  # to initialize the optimizer class
13>>> results = opoc2006.optimize()  # to run the optimization/evolution process
14>>> print(f"OPOC2006: {results['n_function_evaluations']}, {results['best_so_far_y']}")
15OPOC2006: 5000, 8.9150e-17

For its correctness checking of Python coding, please refer to this code-based repeatability report for all details. For pytest-based automatic testing, please see test_opoc2006.py.

References

Igel, C., Suttorp, T. and Hansen, N., 2006, July. A computational efficient covariance matrix update and a (1+1)-CMA for evolution strategies. In Proceedings of Annual Conference on Genetic and Evolutionary Computation (pp. 453-460). ACM.