import numpy as np
from pypop7.optimizers.eda.umda import UMDA
[docs]class EMNA(UMDA):
"""Estimation of Multivariate Normal Algorithm (EMNA).
.. note:: `EMNA` learns the *full* covariance matrix of the Gaussian sampling distribution, resulting
in a *cubic* time complexity w.r.t. each sampling. Therefore, it is **rarely** used for
large-scale black-box optimization (LSBBO). It is **highly recommended** to first attempt other more
advanced methods for LSBBO.
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 (`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, offspring population size (`int`, default: `200`),
* 'n_parents' - number of parents, parental population size (`int`, default:
`int(options['n_individuals']/2)`).
Examples
--------
Use the optimizer to minimize the well-known test function
`Rosenbrock <http://en.wikipedia.org/wiki/Rosenbrock_function>`_:
.. code-block:: python
:linenos:
>>> import numpy
>>> from pypop7.benchmarks.base_functions import rosenbrock # function to be minimized
>>> from pypop7.optimizers.eda.emna import EMNA
>>> 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}
>>> emna = EMNA(problem, options) # initialize the optimizer class
>>> results = emna.optimize() # run the optimization process
>>> # return the number of function evaluations and best-so-far fitness
>>> print(f"EMNA: {results['n_function_evaluations']}, {results['best_so_far_y']}")
EMNA: 5000, 0.008375142194038284
For its correctness checking of coding, refer to `this code-based repeatability report
<https://tinyurl.com/2p8xksyy>`_ for more details.
Attributes
----------
n_individuals : `int`
number of offspring, aka offspring population size.
n_parents : `int`
number of parents, aka parental population size.
References
----------
Larrañaga, P. and Lozano, J.A. eds., 2002.
Estimation of distribution algorithms: A new tool for evolutionary computation.
Springer Science & Business Media.
https://link.springer.com/book/10.1007/978-1-4615-1539-5
Larranaga, P., Etxeberria, R., Lozano, J.A. and Pena, J.M., 2000.
Optimization in continuous domains by learning and simulation of Gaussian networks.
Technical Report, Department of Computer Science and Artificial Intelligence,
University of the Basque Country.
https://tinyurl.com/3bw6n3x4
"""
def __init__(self, problem, options):
UMDA.__init__(self, problem, options)
def iterate(self, x=None, y=None, args=None):
order = np.argsort(y)[:self.n_parents]
mean = np.mean(x[order], axis=0)
cov = np.cov(np.transpose(x[order]))
for i in range(self.n_individuals):
if self._check_terminations():
break
x[i] = self.rng_optimization.multivariate_normal(mean, cov)
y[i] = self._evaluate_fitness(x[i], args)
return x, y