# Separable Natural Evolution Strategies (SNES)¶

class pypop7.optimizers.nes.snes.SNES(problem, options)

Separable Natural Evolution Strategies (SNES).

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).

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.snes import SNES
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>>> snes = SNES(problem, options)  # initialize the optimizer class
13>>> results = snes.optimize()  # run the optimization process
14>>> # return the number of function evaluations and best-so-far fitness
15>>> print(f"SNES: {results['n_function_evaluations']}, {results['best_so_far_y']}")
16SNES: 5000, 0.49730042657448875
```
lr_cv

learning rate of covariance matrix 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

Schaul, T., Glasmachers, T. and Schmidhuber, J., 2011, July. High dimensions and heavy tails for natural evolution strategies. In Proceedings of Annual Conference on Genetic and Evolutionary Computation (pp. 845-852). ACM. https://dl.acm.org/doi/abs/10.1145/2001576.2001692

See the official Python source code from PyBrain: https://github.com/pybrain/pybrain/blob/master/pybrain/optimization/distributionbased/snes.py