import numpy as np
from pypop7.optimizers.ga.ga import GA
[docs]class GL25(GA):
"""Global and Local genetic algorithm (GL25).
.. note:: `25` means that 25 percentage of function evaluations (or runtime) are first used for *global* search
while the remaining 75 percentage are then used for *local* search.
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`):
* 'alpha' - global step-size for crossover (`float`, default: `0.8`),
* 'n_female_global' - number of female at global search stage (`int`, default: `200`),
* 'n_male_global' - number of male at global search stage (`int`, default: `400`),
* 'n_female_local' - number of female at local search stage (`int`, default: `5`),
* 'n_male_local' - number of male at local search stage (`int`, default: `100`),
* 'p_global' - percentage of global search stage (`float`, default: `0.25`),.
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.ga.gl25 import GL25
>>> 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}
>>> gl25 = GL25(problem, options) # initialize the optimizer class
>>> results = gl25.optimize() # run the optimization process
>>> # return the number of function evaluations and best-so-far fitness
>>> print(f"GL25: {results['n_function_evaluations']}, {results['best_so_far_y']}")
GL25: 5000, 1.0505276479694516e-05
For its correctness checking of coding, refer to `this code-based repeatability report
<https://tinyurl.com/ytzffmbc>`_ for more details.
Attributes
----------
alpha : `float`
global step-size for crossover.
n_female_global : `int`
number of female at global search stage.
n_female_local : `int`
number of female at local search stage.
n_individuals : `int`
population size.
n_male_global : `int`
number of male at global search stage.
n_male_local : `int`
number of male at local search stage.
p_global : `float`
percentage of global search stage.
References
----------
García-Martínez, C., Lozano, M., Herrera, F., Molina, D. and Sánchez, A.M., 2008.
Global and local real-coded genetic algorithms based on parent-centric crossover operators.
European Journal of Operational Research, 185(3), pp.1088-1113.
https://www.sciencedirect.com/science/article/abs/pii/S0377221706006308
"""
def __init__(self, problem, options):
GA.__init__(self, problem, options)
self.alpha = options.get('alpha', 0.8)
assert self.alpha > 0.0
self.p_global = options.get('p_global', 0.25) # percentage of global search stage
assert 0.0 <= self.p_global <= 1.0
self.n_female_global = options.get('n_female_global', 200) # number of female at global search stage
assert self.n_female_global > 0
self.n_male_global = options.get('n_male_global', 400) # number of male at global search stage
assert self.n_male_global > 0
self.n_female_local = options.get('n_female_local', 5) # number of female at local search stage
assert self.n_female_local > 0
self.n_male_local = options.get('n_male_local', 100) # number of male at local search stage
assert self.n_male_local > 0
self.n_individuals = int(np.maximum(self.n_male_global, self.n_male_local))
self._assortative_mating = 5
self._n_selected = np.zeros((self.n_individuals,)) # number of individuals selected as female
# set maximum of function evaluations and runtime for global search stage
self._max_fe_global = self.p_global*self.max_function_evaluations
self._max_runtime_global = self.p_global*self.max_runtime
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 iterate(self, x=None, y=None, n_female=None, n_male=None, args=None):
order = np.argsort(y)
x_male, female = x[order[range(n_male)]], order[range(n_female)]
x_female, _n_selected = x[female], self._n_selected[female]
# use the uniform fertility selection (UFS) as female selection mechanism
female = np.argmin(_n_selected)
_n_selected[female] += 1
self._n_selected[order[range(n_female)]] = _n_selected
female = x_female[female]
# use negative assortative mating (NAM) as male selection mechanism
distances = np.empty((self._assortative_mating,))
male = self.rng_optimization.choice(n_male, size=self._assortative_mating, replace=False)
for i, m in enumerate(male):
distances[i] = np.linalg.norm(female - x_male[m])
male = x_male[male[np.argmax(distances)]]
# use the parent-centric BLX crossover operator
interval = np.abs(female - male)
l, u = female - interval*self.alpha, female + interval*self.alpha
xx = self.rng_optimization.uniform(np.clip(l, self.lower_boundary, self.upper_boundary),
np.clip(u, self.lower_boundary, self.upper_boundary))
yy = self._evaluate_fitness(xx, args)
# use the replace worst (RW) strategy
if yy < y[order[-1]]:
x[order[-1]], y[order[-1]], self._n_selected[order[-1]] = xx, yy, 0
self._n_generations += 1
return x, yy
def optimize(self, fitness_function=None, args=None):
fitness, is_switch = GA.optimize(self, fitness_function), True
x, y = self.initialize(args)
yy = y # only for printing
while not self._check_terminations():
self._print_verbose_info(fitness, yy)
if self.n_function_evaluations >= self._max_fe_global or self.runtime >= self._max_runtime_global:
if is_switch: # local search
init, is_switch = range(np.maximum(self.n_female_local, self.n_male_local)), False
x, y, self._n_selected = x[init], y[init], self._n_selected[init]
x, yy = self.iterate(x, y, self.n_female_local, self.n_male_local, args)
else: # global search
x, yy = self.iterate(x, y, self.n_female_global, self.n_male_global, args)
return self._collect(fitness, yy)