from pypop7.optimizers.es.maes import MAES # Matrix Adaptation Evolution Strategy
[docs]class FMAES(MAES):
"""Fast Matrix Adaptation Evolution Strategy (FMAES).
.. note:: `FMAES` is a *more efficient* implementation of `MAES` with *quadractic* time complexity w.r.t. each
sampling, which replaces the computationally expensive matrix-matrix multiplication (*cubic time complexity*)
with the combination of matrix-matrix addition and matrix-vector multiplication (*quadractic time complexity*)
for transformation matrix adaptation. It is **highly recommended** to first attempt more advanced `ES` variants
(e.g., `LMCMA`, `LMMAES`) for large-scale black-box optimization, since `FMAES` still has a computationally
intensive *quadratic* time complexity.
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)`).
Examples
--------
Use the black-box optimizer `FMAES` to minimize the well-known test function
`Rosenbrock <http://en.wikipedia.org/wiki/Rosenbrock_function>`_:
.. code-block:: python
:linenos:
>>> import numpy # engine for numerical computing
>>> from pypop7.benchmarks.base_functions import rosenbrock # function to be minimized
>>> from pypop7.optimizers.es.fmaes import FMAES
>>> 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 fine-tuned for better performance
>>> fmaes = FMAES(problem, options) # to initialize the optimizer class
>>> results = fmaes.optimize() # to run the optimization/evolution process
>>> print(f"FMAES: {results['n_function_evaluations']}, {results['best_so_far_y']}")
FMAES: 5000, 1.3259e-17
For its correctness checking of Python coding, please refer to `this code-based repeatability report
<https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/es/_repeat_fmaes.py>`_
for all details. For *pytest*-based automatic testing, please see `test_fmaes.py
<https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/es/test_fmaes.py>`_.
Attributes
----------
mean : `array_like`
initial (starting) point, aka mean of Gaussian search distribution.
n_individuals : `int`
number of offspring, aka offspring population size.
n_parents : `int`
number of parents, aka parental population size.
sigma : `float`
final global step-size, aka mutation strength.
References
----------
Beyer, H.G., 2020, July.
`Design principles for matrix adaptation evolution strategies.
<https://dl.acm.org/doi/abs/10.1145/3377929.3389870>`_
In Proceedings of Annual Conference on Genetic and Evolutionary Computation Companion (pp. 682-700).
Loshchilov, I., Glasmachers, T. and Beyer, H.G., 2019.
`Large scale black-box optimization by limited-memory matrix adaptation.
<https://ieeexplore.ieee.org/abstract/document/8410043>`_
IEEE Transactions on Evolutionary Computation, 23(2), pp.353-358.
Beyer, H.G. and Sendhoff, B., 2017.
`Simplify your covariance matrix adaptation evolution strategy.
<https://ieeexplore.ieee.org/document/7875115>`_
IEEE Transactions on Evolutionary Computation, 21(5), pp.746-759.
Please refer to the *official* Matlab version from Prof. Beyer:
https://homepages.fhv.at/hgb/downloads/ForDistributionFastMAES.tar
"""
def __init__(self, problem, options):
options['_fast_version'] = True # mandatory setting for only FMAES
MAES.__init__(self, problem, options)