Self-Adaptation Evolution Strategy (SAES)

class pypop7.optimizers.es.saes.SAES(problem, options)

Self-Adaptation Evolution Strategy (SAES).

Note

SAES adapts only the global step-size on-the-fly with a relatively small population, often resulting in slow (and even premature) convergence for large-scale black-box optimization (LSBBO), especially on ill-conditioned fitness landscape. Therefore, it is highly recommended to first attempt more advanced ES variants (e.g. LMCMA, LMMAES) for LSBBO. Here we include it only for benchmarking and theoretical purpose.

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’]))),

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

  • ’lr_sigma’ - learning rate of global step-size (float, default: 1.0/np.sqrt(2*problem[‘ndim_problem’])).

Examples

Use the optimizer SAES to minimize the well-known test function Rosenbrock:

>>> import numpy
>>> from pypop7.benchmarks.base_functions import rosenbrock  # function to be minimized
>>> from pypop7.optimizers.es.saes import SAES
>>> problem = {'fitness_function': rosenbrock,  # define problem arguments
...            'ndim_problem': 2,
...            'lower_boundary': -5*numpy.ones((2,)),
...            'upper_boundary': 5*numpy.ones((2,))}
>>> options = {'max_function_evaluations': 5000,  # set optimizer options
...            'seed_rng': 2022,
...            'mean': 3*numpy.ones((2,)),
...            'sigma': 0.1}  # the global step-size may need to be tuned for better performance
>>> saes = SAES(problem, options)  # initialize the optimizer class
>>> results = saes.optimize()  # run the optimization process
>>> # return the number of function evaluations and best-so-far fitness
>>> print(f"SAES: {results['n_function_evaluations']}, {results['best_so_far_y']}")
SAES: 5000, 0.07968852575335955

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

lr_sigma

learning rate of global step-size.

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

Beyer, H.G., 2020, July. Design principles for matrix adaptation evolution strategies. In Proceedings of Annual Conference on Genetic and Evolutionary Computation Companion (pp. 682-700). ACM. https://dl.acm.org/doi/abs/10.1145/3377929.3389870

http://www.scholarpedia.org/article/Evolution_strategies

See its official Matlab/Octave version from Prof. Beyer: https://homepages.fhv.at/hgb/downloads/mu_mu_I_lambda-ES.oct