Diagonal Decoding Covariance Matrix Adaptation (DDCMA)

class pypop7.optimizers.es.ddcma.DDCMA(problem, options)

Diagonal Decoding Covariance Matrix Adaptation (DDCMA).

Note

DDCMA is a latest improvement version of the well-designed CMA-ES algorithm, which enjoys both two worlds of SEP-CMA-ES (faster adaptation on nearly-separable problems) and CMA-ES (more robust adaptation on ill-conditioned non-separable problems) via adaptive diagonal decoding. It is highly recommended to first attempt other ES variants (e.g., LMCMA, LMMAES) for large-scale black-box optimization, since it has a quadratic time complexity (w.r.t. each sampling).

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’].

  • ’n_individuals’ - number of offspring, aka offspring population size (int, default: 4 + int(3*np.log(problem[‘ndim_problem’]))).

Examples

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

>>> import numpy  # engine for numerical computing
>>> from pypop7.benchmarks.base_functions import rosenbrock  # function to be minimized
>>> from pypop7.optimizers.es.ddcma import DDCMA
>>> problem = {'fitness_function': rosenbrock,  # to define problem arguments
...            'ndim_problem': 2,
...            'lower_boundary': -5.0*numpy.ones((2,)),
...            'upper_boundary': 5.0*numpy.ones((2,))}
>>> options = {'max_function_evaluations': 5000,  # to set optimizer options
...            'seed_rng': 2022,
...            'mean': 3.0*numpy.ones((2,)),
...            'sigma': 3.0}  # global step-size may need to be fine-tuned for better performance
>>> ddcma = DDCMA(problem, options)  # to initialize the optimizer class
>>> results = ddcma.optimize()  # to run the optimization/evolution process
>>> print(f"DDCMA: {results['n_function_evaluations']}, {results['best_so_far_y']}")
DDCMA: 5000, 3.0714e-19

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_ddcma.py.

mean

initial (starting) point, aka mean of Gaussian search distribution.

Type:

array_like

n_individuals

number of offspring, aka offspring population size.

Type:

int

sigma

final global step-size, aka mutation strength.

Type:

float

References

Akimoto, Y. and Hansen, N., 2020. Diagonal acceleration for covariance matrix adaptation evolution strategies. Evolutionary Computation, 28(3), pp.405-435.

Please refer to its official Python implementation from Prof. Akimoto: https://gist.github.com/youheiakimoto/1180b67b5a0b1265c204cba991fa8518