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 (LBO), especially on ill-conditioned fitness landscapes. Therefore, it is recommended to first attempt more advanced ES variants (e.g. LMCMA, LMMAES) for LBO. Here we include SAES mainly 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 black-box optimizer SAES 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.saes import SAES
>>> 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 tuned
>>> saes = SAES(problem, options)  # to initialize the optimizer class
>>> results = saes.optimize()  # to run the optimization/evolution process
>>> # to return the number of function evaluations and the best-so-far fitness
>>> print(f"SAES: {results['n_function_evaluations']}, {results['best_so_far_y']}")
SAES: 5000, 0.012622712890954227

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

best_so_far_x

final best-so-far solution found during entire optimization.

Type:

array_like

best_so_far_y

final best-so-far fitness found during entire optimization.

Type:

array_like

lr_sigma

learning rate of global step-size adaptation.

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 (changed during optimization).

Type:

float

References

Beyer, H.G., 2020, July. Design principles for matrix adaptation evolution strategies. In Proceedings of ACM Conference on Genetic and Evolutionary Computation Companion (pp. 682-700). ACM.

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