import numpy as np # engine for numerical computing
from pypop7.optimizers.de.de import DE # abstract class of all differential evolution (DE)
[docs]class TDE(DE):
"""Trigonometric-mutation Differential Evolution (TDE).
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: `30`),
* 'f' - mutation factor (`float`, default: `0.99`),
* 'cr' - crossover probability (`float`, default: `0.85`),
* 'tm' - trigonometric mutation probability (`float`, default: `0.05`).
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.tde import TDE
>>> 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}
>>> tde = TDE(problem, options) # initialize the optimizer class
>>> results = tde.optimize() # run the optimization process
>>> # return the number of function evaluations and best-so-far fitness
>>> print(f"TDE: {results['n_function_evaluations']}, {results['best_so_far_y']}")
TDE: 5000, 6.420787226215637e-21
For its correctness checking of coding, refer to `this code-based repeatability report
<https://tinyurl.com/56frubv2>`_ for more details.
Attributes
----------
cr : `float`
crossover probability.
f : `float`
mutation factor.
tm : 'float
trigonometric mutation probability.
n_individuals : `int`
number of offspring, aka offspring population size.
References
----------
Fan, H.Y. and Lampinen, J., 2003.
A trigonometric mutation operation to differential evolution.
Journal of Global Optimization, 27(1), pp.105-129.
https://link.springer.com/article/10.1023/A:1024653025686
"""
def __init__(self, problem, options):
DE.__init__(self, problem, options)
self.n_individuals = options.get('n_individuals', 30) # population size
self.f = options.get('f', 0.99) # mutation factor
self.tm = options.get('tm', 0.05) # trigonometric mutation probability
self.cr = options.get('cr', 0.85) # crossover probability
def initialize(self, args=None):
x = self.rng_initialization.uniform(self.initial_lower_boundary, self.initial_upper_boundary,
size=(self.n_individuals, self.ndim_problem)) # population
y = np.empty((self.n_individuals,)) # fitness
for i in range(self.n_individuals):
if self._check_terminations():
break
y[i] = self._evaluate_fitness(x[i], args)
return x, y
def mutate(self, x=None, y=None):
v = np.empty((self.n_individuals, self.ndim_problem))
for i in range(self.n_individuals):
r = self.rng_optimization.permutation(self.n_individuals)[:4]
r = r[r != i][:3] # a simple yet effective trick
if self.rng_optimization.random() < self.tm: # trigonometric mutation
p = np.abs(y[r[0]]) + np.abs(y[r[1]]) + np.abs(y[r[2]])
p1, p2, p3 = np.abs(y[r[0]])/p, np.abs(y[r[1]])/p, np.abs(y[r[2]])/p
v[i] = ((x[r[0]] + x[r[1]] + x[r[2]])/3.0 + (p2 - p1)*(x[r[0]] - x[r[1]]) +
(p3 - p2)*(x[r[1]] - x[r[2]]) + (p1 - p3)*(x[r[2]] - x[r[0]]))
else: # same as the original DE version (`DE/rand/1/bin`)
v[i] = x[r[0]] + self.f*(x[r[1]] - x[r[2]])
return v
def crossover(self, v=None, x=None):
for i in range(self.n_individuals):
k = self.rng_optimization.integers(self.ndim_problem)
for j in range(self.ndim_problem):
if (self.rng_optimization.random() <= self.cr) or (k == j):
continue
else:
v[i][j] = x[i][j]
return v
def select(self, v=None, x=None, y=None, args=None):
for i in range(self.n_individuals):
if self._check_terminations():
break
yy = self._evaluate_fitness(v[i], args)
if yy <= y[i]:
x[i], y[i] = v[i], yy
return x, y
def iterate(self, x=None, y=None, args=None):
return self.select(self.crossover(self.mutate(x, y), x), x, y, args)
def optimize(self, fitness_function=None, args=None):
fitness = DE.optimize(self, fitness_function)
x, y = self.initialize(args)
while not self._check_terminations():
self._print_verbose_info(fitness, y)
x, y = self.iterate(x, y, args)
self._n_generations += 1
return self._collect(fitness, y)