import numpy as np
from scipy.stats import cauchy
from pypop7.optimizers.de.jade import JADE
[docs]class SHADE(JADE):
"""Success-History based Adaptive Differential Evolution (SHADE).
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, aka offspring population size (`int`, default: `100`),
* 'mu' - mean of normal distribution for adaptation of crossover probability (`float`,
default: `0.5`),
* 'median' - median of Cauchy distribution for adaptation of mutation factor (`float`,
default: `0.5`),
* 'h' - length of historical memory (`int`, default: `100`).
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.de.shade import SHADE
>>> 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': 0}
>>> shade = SHADE(problem, options) # initialize the optimizer class
>>> results = shade.optimize() # run the optimization process
>>> # return the number of function evaluations and best-so-far fitness
>>> print(f"SHADE: {results['n_function_evaluations']}, {results['best_so_far_y']}")
SHADE: 5000, 6.231767087114823e-05
For its correctness checking of coding, refer to `this code-based repeatability report
<https://tinyurl.com/vm3w7se4>`_ for more details.
Attributes
----------
h : `int`
length of historical memory.
median : `float`
median of Cauchy distribution for adaptation of mutation factor.
mu : `float`
mean of normal distribution for adaptation of crossover probability.
n_individuals : `int`
number of offspring, aka offspring population size.
References
----------
Tanabe, R. and Fukunaga, A., 2013, June.
Success-history based parameter adaptation for differential evolution.
In IEEE Congress on Evolutionary Computation (pp. 71-78). IEEE.
https://ieeexplore.ieee.org/document/6557555
"""
def __init__(self, problem, options):
JADE.__init__(self, problem, options)
self.h = options.get('h', 100) # length of historical memory
assert 0 < self.h
self.m_mu = np.ones(self.h)*self.mu # means of normal distribution
self.m_median = np.ones(self.h)*self.median # medians of Cauchy distribution
self._k = 0 # index to update
self.p_min = 2.0/self.n_individuals
def mutate(self, x=None, y=None, a=None):
x_mu = np.empty((self.n_individuals, self.ndim_problem)) # mutated population
f_mu = np.empty((self.n_individuals,)) # mutated mutation factors
x_un = np.vstack((np.copy(x), a)) # union of population x and archive a
r = self.rng_optimization.choice(self.h, (self.n_individuals,))
order = np.argsort(y)[:]
p = (0.2 - self.p_min)*self.rng_optimization.random((self.n_individuals,)) + self.p_min
idx = [order[self.rng_optimization.choice(int(i))] for i in np.ceil(p*self.n_individuals)]
for k in range(self.n_individuals):
f_mu[k] = cauchy.rvs(loc=self.m_median[r[k]], scale=0.1, random_state=self.rng_optimization)
while f_mu[k] <= 0.0:
f_mu[k] = cauchy.rvs(loc=self.m_median[r[k]], scale=0.1, random_state=self.rng_optimization)
if f_mu[k] > 1.0:
f_mu[k] = 1.0
r1 = self.rng_optimization.choice([i for i in range(self.n_individuals) if i != k])
r2 = self.rng_optimization.choice([i for i in range(len(x_un)) if i != k and i != r1])
x_mu[k] = x[k] + f_mu[k]*(x[idx[k]] - x[k]) + f_mu[k]*(x[r1] - x_un[r2])
return x_mu, f_mu, r
def crossover(self, x_mu=None, x=None, r=None):
x_cr = np.copy(x)
p_cr = np.empty((self.n_individuals,)) # crossover probabilities
for k in range(self.n_individuals):
p_cr[k] = self.rng_optimization.normal(self.m_mu[r[k]], 0.1)
p_cr[k] = np.minimum(np.maximum(p_cr[k], 0.0), 1.0)
i_rand = self.rng_optimization.integers(self.ndim_problem)
for i in range(self.ndim_problem):
if (i == i_rand) or (self.rng_optimization.random() < p_cr[k]):
x_cr[k, i] = x_mu[k, i]
return x_cr, p_cr
def select(self, args=None, x=None, y=None, x_cr=None, a=None, f_mu=None, p_cr=None):
# set successful mutation factors, crossover probabilities, fitness differences
f, p, d = np.empty((0,)), np.empty((0,)), np.empty((0,))
for k in range(self.n_individuals):
if self._check_terminations():
break
yy = self._evaluate_fitness(x_cr[k], args)
if yy < y[k]:
a = np.vstack((a, x[k])) # archive of inferior solutions
f = np.hstack((f, f_mu[k])) # archive of successful mutation factors
p = np.hstack((p, p_cr[k])) # archive of successful crossover probabilities
d = np.hstack((d, y[k] - yy)) # archive of successful fitness differences
x[k], y[k] = x_cr[k], yy
if (len(p) != 0) and (len(f) != 0):
w = d/np.sum(d)
self.m_mu[self._k] = np.sum(w*p) # for normal distribution
self.m_median[self._k] = np.sum(w*np.power(f, 2))/np.sum(w*f) # for Cauchy distribution
self._k = (self._k + 1) % self.h
return x, y, a
def iterate(self, x=None, y=None, a=None, args=None):
x_mu, f_mu, r = self.mutate(x, y, a)
x_cr, p_cr = self.crossover(x_mu, x, r)
x_cr = self.bound(x_cr, x)
x, y, a = self.select(args, x, y, x_cr, a, f_mu, p_cr)
if len(a) > self.n_individuals: # randomly remove solutions to keep archive size fixed
a = np.delete(a, self.rng_optimization.choice(len(a), (len(a) - self.n_individuals,), False), 0)
self._n_generations += 1
return x, y, a