Search Gradient-based Evolution Strategy (SGES)

class pypop7.optimizers.nes.sges.SGES(problem, options)[source]

Search Gradient-based Evolution Strategy (SGES).

Note

Here we include SGES (also called vanilla version of NES) only for theoretical and educational purposes, since in practice advanced versions (e.g., ENES, XNES, SNES, and R1NES) are more preferred than SGES in most cases.

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):

    • ’n_individuals’ - number of offspring/descendants, aka offspring population size (int),

    • ’n_parents’ - number of parents/ancestors, aka parental population size (int),

    • ’mean’ - initial (starting) point (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’].

    • ’lr_mean’ - learning rate of distribution mean update (float, default: 0.01),

    • ’lr_sigma’ - learning rate of global step-size adaptation (float, default: 0.01).

Examples

Use the black-box optimizer SGES 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.nes.sges import SGES
 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>>> sges = SGES(problem, options)  # to initialize the optimizer class
12>>> results = sges.optimize()  # to run the optimization process
13>>> print(f"SGES: {results['n_function_evaluations']}, {results['best_so_far_y']}")
14SGES: 5000, 0.0190
lr_mean

learning rate of distribution mean update (should > 0.0).

Type:

float

lr_sigma

learning rate of global step-size adaptation (should > 0.0).

Type:

float

mean

initial (starting) point, aka mean of Gaussian search/sampling/mutation distribution. 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’], by default.

Type:

array_like

n_individuals

number of offspring/descendants, aka offspring population size (should > 0).

Type:

int

n_parents

number of parents/ancestors, aka parental population size (should > 0).

Type:

int

References

Wierstra, D., Schaul, T., Glasmachers, T., Sun, Y., Peters, J. and Schmidhuber, J., 2014. Natural evolution strategies. Journal of Machine Learning Research, 15(1), pp.949-980.

Schaul, T., 2011. Studies in continuous black-box optimization. Doctoral Dissertation, Technische Universität München.

Please refer to the official Python source code from PyBrain (now not actively maintained): https://github.com/pybrain/pybrain/blob/master/pybrain/optimization/distributionbased/ves.py