Separable Covariance Matrix Adaptation Evolution Strategy (SEPCMAES)

class pypop7.optimizers.es.sepcmaes.SEPCMAES(problem, options)[source]

Separable Covariance Matrix Adaptation Evolution Strategy (SEPCMAES).

Note

SEPCMAES learns only the diagonal elements of the full covariance matrix explicitly, leading to a linear time complexity (w.r.t. each sampling) for large-scale black-box optimization. It is highly recommended to first attempt more advanced ES variants (e.g., LMCMA, LMMAES) for large-scale black-box optimization, since typically the performance of SEPCMAES deteriorates significantly on non-separable, ill-conditioned fitness landscape.

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(options[‘ndim_problem’]))),

    • ’n_parents’ - number of parents, aka parental population size (int, default: int(options[‘n_individuals’]/2)),

    • ’c_c’ - learning rate of evolution path update (float, default: 4.0/(options[‘ndim_problem’] + 4.0)).

Examples

Use the black-box optimizer SEPCMAES 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.sepcmaes import SEPCMAES
 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': 3.0*numpy.ones((2,)),
11...            'sigma': 3.0}  # global step-size may need to be fine-tuned for better performance
12>>> sepcmaes = SEPCMAES(problem, options)  # to initialize the optimizer class
13>>> results = sepcmaes.optimize()  # to run the optimization/evolution process
14>>> print(f"SEPCMAES: {results['n_function_evaluations']}, {results['best_so_far_y']}")
15SEPCMAES: 5000, 0.0093

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_sepcmaes.py.

c_c

learning rate of evolution path update.

Type:

float

mean

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

Type:

array_like

n_individuals

number of offspring, aka offspring population size.

Type:

int

n_parents

number of parents, aka parental population size.

Type:

int

sigma

final global step-size, aka mutation strength.

Type:

float

References

Ros, R. and Hansen, N., 2008, September. A simple modification in CMA-ES achieving linear time and space complexity. In International Conference on Parallel Problem Solving from Nature (pp. 296-305). Springer, Berlin, Heidelberg.