Search Gradient-based Evolution Strategy (SGES)¶
- class pypop7.optimizers.nes.sges.SGES(problem, options)¶
Search Gradient-based Evolution Strategy (SGES).
Note
Here we include it only for theoretical and/or educational 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):
’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’].
’sigma’ - initial global step-size, aka mutation strength (float),
’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 optimizer 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, # define problem arguments 5... 'ndim_problem': 2, 6... 'lower_boundary': -5*numpy.ones((2,)), 7... 'upper_boundary': 5*numpy.ones((2,))} 8>>> options = {'max_function_evaluations': 5000, # set optimizer options 9... 'seed_rng': 2022, 10... 'mean': 3*numpy.ones((2,)), 11... 'sigma': 0.1} # the global step-size may need to be tuned for better performance 12>>> sges = SGES(problem, options) # initialize the optimizer class 13>>> results = sges.optimize() # run the optimization process 14>>> # return the number of function evaluations and best-so-far fitness 15>>> print(f"SGES: {results['n_function_evaluations']}, {results['best_so_far_y']}") 16SGES: 5000, 0.01906602832229609
- lr_mean¶
learning rate of distribution mean update.
- Type:
float
- lr_sigma¶
learning rate of global step-size adaptation.
- Type:
float
- mean¶
initial (starting) point, aka mean of Gaussian search/sampling/mutation distribution.
- Type:
array_like
- n_individuals¶
number of offspring/descendants, aka offspring population size.
- Type:
int
- n_parents¶
number of parents/ancestors, aka parental population size.
- Type:
int
- sigma¶
global step-size, aka mutation strength (i.e., overall std of Gaussian search distribution).
- Type:
float
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. https://jmlr.org/papers/v15/wierstra14a.html
Schaul, T., 2011. Studies in continuous black-box optimization. Doctoral Dissertation, Technische Universität München. https://people.idsia.ch/~schaul/publications/thesis.pdf
See the official Python source code from PyBrain: https://github.com/pybrain/pybrain/blob/master/pybrain/optimization/distributionbased/ves.py