import numpy as np
from pypop7.optimizers.es.es import ES
from pypop7.optimizers.es.r1es import R1ES
[docs]class RMES(R1ES):
"""Rank-M Evolution Strategy (RMES).
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_evolution_paths' - number of evolution paths (`int`, default: `2`),
* 'generation_gap' - generation gap (`int`, default: `problem['ndim_problem']`),
* '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)`),
* 'c_cov' - learning rate of low-rank covariance matrix (`float`, default:
`1.0/(3.0*np.sqrt(problem['ndim_problem']) + 5.0)`),
* 'd_sigma' - delay factor of cumulative step-size adaptation (`float`, default: `1.0`).
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.es.rmes import RMES
>>> 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,
... 'mean': 3*numpy.ones((2,)),
... 'sigma': 0.1} # the global step-size may need to be tuned for better performance
>>> rmes = RMES(problem, options) # initialize the optimizer class
>>> results = rmes.optimize() # run the optimization process
>>> # return the number of function evaluations and best-so-far fitness
>>> print(f"RMES: {results['n_function_evaluations']}, {results['best_so_far_y']}")
RMES: 5000, 5.7278132941412774e-08
For its correctness checking of coding, refer to `this code-based repeatability report
<https://tinyurl.com/wx3wakxj>`_ for more details.
Attributes
----------
c_cov : `float`
learning rate of low-rank covariance matrix adaptation.
d_sigma : `float`
delay factor of cumulative step-size adaptation.
generation_gap : `int`
generation gap.
mean : `array_like`
initial (starting) point, aka mean of Gaussian search distribution.
n_evolution_paths : `int`
number of evolution paths.
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
----------
Li, Z. and Zhang, Q., 2018.
A simple yet efficient evolution strategy for large-scale black-box optimization.
IEEE Transactions on Evolutionary Computation, 22(5), pp.637-646.
https://ieeexplore.ieee.org/abstract/document/8080257
"""
def __init__(self, problem, options):
R1ES.__init__(self, problem, options)
self.n_evolution_paths = options.get('n_evolution_paths', 2)
self.generation_gap = options.get('generation_gap', self.ndim_problem)
self._a = np.sqrt(1.0 - self.c_cov)
self._a_m = np.power(self._a, self.n_evolution_paths)
self._b = np.sqrt(self.c_cov)
def initialize(self, args=None, is_restart=False):
x, mean, p, s, y = R1ES.initialize(self, args, is_restart)
mp = np.zeros((self.n_evolution_paths, self.ndim_problem)) # multiple evolution paths
t_hat = np.zeros((self.n_evolution_paths,))
return x, mean, p, s, mp, t_hat, y
def iterate(self, x=None, mean=None, mp=None, y=None, args=None):
for k in range(self.n_individuals):
if self._check_terminations():
return x, y
z = self.rng_optimization.standard_normal((self.ndim_problem,))
sum_p = np.zeros((self.ndim_problem,))
for i in np.arange(self.n_evolution_paths) + 1:
r = self.rng_optimization.standard_normal()
sum_p += np.power(self._a, self.n_evolution_paths - i)*r*mp[i - 1]
x[k] = mean + self.sigma*(self._a_m*z + self._b*sum_p)
y[k] = self._evaluate_fitness(x[k], args)
return x, y
def _update_distribution(self, x=None, mean=None, p=None, s=None,
mp=None, t_hat=None, y=None, y_bak=None):
mean, p, s = R1ES._update_distribution(self, x, mean, p, s, y, y_bak)
# update multiple evolution paths
t_min = np.min(np.diff(t_hat))
i_apostrophe = np.argmin(np.diff(t_hat))
i_apostrophe += 1
if (t_min > self.generation_gap) or (self._n_generations < self.n_evolution_paths):
i_apostrophe = 0
for i in range(i_apostrophe, self.n_evolution_paths - 1):
mp[i], t_hat[i] = mp[i + 1], t_hat[i + 1]
mp[-1], t_hat[-1] = p, self._n_generations
return mean, p, s, mp, t_hat
def restart_reinitialize(self, args=None, x=None, mean=None, p=None, s=None,
mp=None, t_hat=None, y=None, fitness=None):
if self.is_restart and ES.restart_reinitialize(self, y):
x, mean, p, s, mp, t_hat, y = self.initialize(args, True)
self._print_verbose_info(fitness, y[0])
self.d_sigma *= 2.0
return x, mean, p, s, mp, t_hat, y
def optimize(self, fitness_function=None, args=None): # for all generations (iterations)
fitness = ES.optimize(self, fitness_function)
x, mean, p, s, mp, t_hat, y = self.initialize(args)
self._print_verbose_info(fitness, y[0])
while not self.termination_signal:
y_bak = np.copy(y)
# sample and evaluate offspring population
x, y = self.iterate(x, mean, mp, y, args)
self._n_generations += 1
self._print_verbose_info(fitness, y)
if self._check_terminations():
break
mean, p, s, mp, t_hat = self._update_distribution(x, mean, p, s, mp, t_hat, y, y_bak)
x, mean, p, s, mp, t_hat, y = self.restart_reinitialize(
args, x, mean, p, s, mp, t_hat, y, fitness)
results = self._collect(fitness, y, mean)
results['p'] = p
results['s'] = s
return results