"""Online documentation:
https://pypop.readthedocs.io/en/latest/benchmarks.html#rotated-shifted-forms
"""
import numpy as np # engine for numerical computing
from pypop7.benchmarks import base_functions
from pypop7.benchmarks.shifted_functions import load_shift_vector
from pypop7.benchmarks.rotated_functions import load_rotation_matrix
# helper function
[docs]def load_shift_and_rotation(func, x, shift_vector=None, rotation_matrix=None):
"""Load both the shift vector and rotation matrix which need to be generated **in advance**.
.. note:: When `None`, the shift vector should have been generated and stored in *txt* form
**in advance**. When `None`, the rotation matrix should have been generated and stored
in *txt* form **in advance**.
Parameters
----------
func : str or func
function name.
x : array_like
decision vector.
shift_vector : array_like
shift vector with the same size as `x`.
rotation_matrix : ndarray
rotation matrix of size [`len(x)` * `len(x)`].
Returns
-------
shift_vector : ndarray (of dtype np.float64)
shift vector with the same size as `x`.
rotation_matrix : ndarray
rotation matrix of size [`len(x)` * `len(x)`].
"""
shift_vector = load_shift_vector(func, x, shift_vector)
rotation_matrix = load_rotation_matrix(func, x, rotation_matrix)
return shift_vector, rotation_matrix
[docs]def sphere(x, shift_vector=None, rotation_matrix=None):
"""**Sphere** test function.
Parameters
----------
x : ndarray
input vector.
shift_vector : array_like
shift vector with the same size as `x`.
rotation_matrix : ndarray
rotation matrix of size [`len(x)` * `len(x)`].
Returns
-------
y : float
scalar fitness.
"""
shift_vector, rotation_matrix = load_shift_and_rotation(sphere, x, shift_vector, rotation_matrix)
x = np.dot(rotation_matrix, x - shift_vector)
y = base_functions.sphere(x)
return y
[docs]def cigar(x, shift_vector=None, rotation_matrix=None):
"""**Cigar** test function.
Parameters
----------
x : ndarray
input vector.
shift_vector : array_like
shift vector with the same size as `x`.
rotation_matrix : ndarray
rotation matrix of size [`len(x)` * `len(x)`].
Returns
-------
y : float
scalar fitness.
"""
shift_vector, rotation_matrix = load_shift_and_rotation(cigar, x, shift_vector, rotation_matrix)
x = np.dot(rotation_matrix, x - shift_vector)
y = base_functions.cigar(x)
return y
[docs]def discus(x, shift_vector=None, rotation_matrix=None):
"""**Discus** test function.
Parameters
----------
x : ndarray
input vector.
shift_vector : array_like
shift vector with the same size as `x`.
rotation_matrix : ndarray
rotation matrix of size [`len(x)` * `len(x)`].
Returns
-------
y : float
scalar fitness.
"""
shift_vector, rotation_matrix = load_shift_and_rotation(discus, x, shift_vector, rotation_matrix)
x = np.dot(rotation_matrix, x - shift_vector)
y = base_functions.discus(x)
return y
[docs]def cigar_discus(x, shift_vector=None, rotation_matrix=None):
"""**Cigar-Discus** test function.
Parameters
----------
x : ndarray
input vector.
shift_vector : array_like
shift vector with the same size as `x`.
rotation_matrix : ndarray
rotation matrix of size [`len(x)` * `len(x)`].
Returns
-------
y : float
scalar fitness.
"""
shift_vector, rotation_matrix = load_shift_and_rotation(cigar_discus, x, shift_vector, rotation_matrix)
x = np.dot(rotation_matrix, x - shift_vector)
y = base_functions.cigar_discus(x)
return y
[docs]def ellipsoid(x, shift_vector=None, rotation_matrix=None):
"""**Ellipsoid** test function.
Parameters
----------
x : ndarray
input vector.
shift_vector : array_like
shift vector with the same size as `x`.
rotation_matrix : ndarray
rotation matrix of size [`len(x)` * `len(x)`].
Returns
-------
y : float
scalar fitness.
"""
shift_vector, rotation_matrix = load_shift_and_rotation(ellipsoid, x, shift_vector, rotation_matrix)
x = np.dot(rotation_matrix, x - shift_vector)
y = base_functions.ellipsoid(x)
return y
[docs]def different_powers(x, shift_vector=None, rotation_matrix=None):
"""**Different-Power** test function.
Parameters
----------
x : ndarray
input vector.
shift_vector : array_like
shift vector with the same size as `x`.
rotation_matrix : ndarray
rotation matrix of size [`len(x)` * `len(x)`].
Returns
-------
y : float
scalar fitness.
"""
shift_vector, rotation_matrix = load_shift_and_rotation(different_powers, x, shift_vector, rotation_matrix)
x = np.dot(rotation_matrix, x - shift_vector)
y = base_functions.different_powers(x)
return y
[docs]def schwefel221(x, shift_vector=None, rotation_matrix=None):
"""**Schwefel221** test function.
Parameters
----------
x : ndarray
input vector.
shift_vector : array_like
shift vector with the same size as `x`.
rotation_matrix : ndarray
rotation matrix of size [`len(x)` * `len(x)`].
Returns
-------
y : float
scalar fitness.
"""
shift_vector, rotation_matrix = load_shift_and_rotation(schwefel221, x, shift_vector, rotation_matrix)
x = np.dot(rotation_matrix, x - shift_vector)
y = base_functions.schwefel221(x)
return y
[docs]def step(x, shift_vector=None, rotation_matrix=None):
"""**Step** test function.
Parameters
----------
x : ndarray
input vector.
shift_vector : array_like
shift vector with the same size as `x`.
rotation_matrix : ndarray
rotation matrix of size [`len(x)` * `len(x)`].
Returns
-------
y : float
scalar fitness.
"""
shift_vector, rotation_matrix = load_shift_and_rotation(step, x, shift_vector, rotation_matrix)
x = np.dot(rotation_matrix, x - shift_vector)
y = base_functions.step(x)
return y
[docs]def schwefel222(x, shift_vector=None, rotation_matrix=None):
"""**Schwefel222** test function.
Parameters
----------
x : ndarray
input vector.
shift_vector : array_like
shift vector with the same size as `x`.
rotation_matrix : ndarray
rotation matrix of size [`len(x)` * `len(x)`].
Returns
-------
y : float
scalar fitness.
"""
shift_vector, rotation_matrix = load_shift_and_rotation(schwefel222, x, shift_vector, rotation_matrix)
x = np.dot(rotation_matrix, x - shift_vector)
y = base_functions.schwefel222(x)
return y
[docs]def rosenbrock(x, shift_vector=None, rotation_matrix=None):
"""**Rosenbrock** test function.
Parameters
----------
x : ndarray
input vector.
shift_vector : array_like
shift vector with the same size as `x`.
rotation_matrix : ndarray
rotation matrix of size [`len(x)` * `len(x)`].
Returns
-------
y : float
scalar fitness.
"""
shift_vector, rotation_matrix = load_shift_and_rotation(rosenbrock, x, shift_vector, rotation_matrix)
x = np.dot(rotation_matrix, x - shift_vector)
y = base_functions.rosenbrock(x)
return y
[docs]def schwefel12(x, shift_vector=None, rotation_matrix=None):
"""**Schwefel12** test function.
Parameters
----------
x : ndarray
input vector.
shift_vector : array_like
shift vector with the same size as `x`.
rotation_matrix : ndarray
rotation matrix of size [`len(x)` * `len(x)`].
Returns
-------
y : float
scalar fitness.
"""
shift_vector, rotation_matrix = load_shift_and_rotation(schwefel12, x, shift_vector, rotation_matrix)
x = np.dot(rotation_matrix, x - shift_vector)
y = base_functions.schwefel12(x)
return y
[docs]def exponential(x, shift_vector=None, rotation_matrix=None):
"""**Exponential** test function.
Parameters
----------
x : ndarray
input vector.
shift_vector : array_like
shift vector with the same size as `x`.
rotation_matrix : ndarray
rotation matrix of size [`len(x)` * `len(x)`].
Returns
-------
y : float
scalar fitness.
"""
shift_vector, rotation_matrix = load_shift_and_rotation(exponential, x, shift_vector, rotation_matrix)
x = np.dot(rotation_matrix, x - shift_vector)
y = base_functions.exponential(x)
return y
[docs]def griewank(x, shift_vector=None, rotation_matrix=None):
"""**Griewank** test function.
Parameters
----------
x : ndarray
input vector.
shift_vector : array_like
shift vector with the same size as `x`.
rotation_matrix : ndarray
rotation matrix of size [`len(x)` * `len(x)`].
Returns
-------
y : float
scalar fitness.
"""
shift_vector, rotation_matrix = load_shift_and_rotation(griewank, x, shift_vector, rotation_matrix)
x = np.dot(rotation_matrix, x - shift_vector)
y = base_functions.griewank(x)
return y
[docs]def bohachevsky(x, shift_vector=None, rotation_matrix=None):
"""**Bohachevsky** test function.
Parameters
----------
x : ndarray
input vector.
shift_vector : array_like
shift vector with the same size as `x`.
rotation_matrix : ndarray
rotation matrix of size [`len(x)` * `len(x)`].
Returns
-------
y : float
scalar fitness.
"""
shift_vector, rotation_matrix = load_shift_and_rotation(bohachevsky, x, shift_vector, rotation_matrix)
x = np.dot(rotation_matrix, x - shift_vector)
y = base_functions.bohachevsky(x)
return y
[docs]def ackley(x, shift_vector=None, rotation_matrix=None):
"""**Ackley** test function.
Parameters
----------
x : ndarray
input vector.
shift_vector : array_like
shift vector with the same size as `x`.
rotation_matrix : ndarray
rotation matrix of size [`len(x)` * `len(x)`].
Returns
-------
y : float
scalar fitness.
"""
shift_vector, rotation_matrix = load_shift_and_rotation(ackley, x, shift_vector, rotation_matrix)
x = np.dot(rotation_matrix, x - shift_vector)
y = base_functions.ackley(x)
return y
[docs]def rastrigin(x, shift_vector=None, rotation_matrix=None):
"""**Rastrigin** test function.
Parameters
----------
x : ndarray
input vector.
shift_vector : array_like
shift vector with the same size as `x`.
rotation_matrix : ndarray
rotation matrix of size [`len(x)` * `len(x)`].
Returns
-------
y : float
scalar fitness.
"""
shift_vector, rotation_matrix = load_shift_and_rotation(rastrigin, x, shift_vector, rotation_matrix)
x = np.dot(rotation_matrix, x - shift_vector)
y = base_functions.rastrigin(x)
return y
[docs]def scaled_rastrigin(x, shift_vector=None, rotation_matrix=None):
"""**Scaled-Rastrigin** test function.
Parameters
----------
x : ndarray
input vector.
shift_vector : array_like
shift vector with the same size as `x`.
rotation_matrix : ndarray
rotation matrix of size [`len(x)` * `len(x)`].
Returns
-------
y : float
scalar fitness.
"""
shift_vector, rotation_matrix = load_shift_and_rotation(scaled_rastrigin, x, shift_vector, rotation_matrix)
x = np.dot(rotation_matrix, x - shift_vector)
y = base_functions.scaled_rastrigin(x)
return y
[docs]def skew_rastrigin(x, shift_vector=None, rotation_matrix=None):
"""**Skew-Rastrigin** test function.
Parameters
----------
x : ndarray
input vector.
shift_vector : array_like
shift vector with the same size as `x`.
rotation_matrix : ndarray
rotation matrix of size [`len(x)` * `len(x)`].
Returns
-------
y : float
scalar fitness.
"""
shift_vector, rotation_matrix = load_shift_and_rotation(skew_rastrigin, x, shift_vector, rotation_matrix)
x = np.dot(rotation_matrix, x - shift_vector)
y = base_functions.skew_rastrigin(x)
return y
[docs]def levy_montalvo(x, shift_vector=None, rotation_matrix=None):
"""**Levy-Montalvo** test function.
Parameters
----------
x : ndarray
input vector.
shift_vector : array_like
shift vector with the same size as `x`.
rotation_matrix : ndarray
rotation matrix of size [`len(x)` * `len(x)`].
Returns
-------
y : float
scalar fitness.
"""
shift_vector, rotation_matrix = load_shift_and_rotation(levy_montalvo, x, shift_vector, rotation_matrix)
x = np.dot(rotation_matrix, x - shift_vector)
y = base_functions.levy_montalvo(x)
return y
[docs]def michalewicz(x, shift_vector=None, rotation_matrix=None):
"""**Michalewicz** test function.
Parameters
----------
x : ndarray
input vector.
shift_vector : array_like
shift vector with the same size as `x`.
rotation_matrix : ndarray
rotation matrix of size [`len(x)` * `len(x)`].
Returns
-------
y : float
scalar fitness.
"""
shift_vector, rotation_matrix = load_shift_and_rotation(michalewicz, x, shift_vector, rotation_matrix)
x = np.dot(rotation_matrix, x - shift_vector)
y = base_functions.michalewicz(x)
return y
[docs]def salomon(x, shift_vector=None, rotation_matrix=None):
"""**Salomon** test function.
Parameters
----------
x : ndarray
input vector.
shift_vector : array_like
shift vector with the same size as `x`.
rotation_matrix : ndarray
rotation matrix of size [`len(x)` * `len(x)`].
Returns
-------
y : float
scalar fitness.
"""
shift_vector, rotation_matrix = load_shift_and_rotation(salomon, x, shift_vector, rotation_matrix)
x = np.dot(rotation_matrix, x - shift_vector)
y = base_functions.salomon(x)
return y
[docs]def shubert(x, shift_vector=None, rotation_matrix=None):
"""**Shubert** test function.
Parameters
----------
x : ndarray
input vector.
shift_vector : array_like
shift vector with the same size as `x`.
rotation_matrix : ndarray
rotation matrix of size [`len(x)` * `len(x)`].
Returns
-------
y : float
scalar fitness.
"""
shift_vector, rotation_matrix = load_shift_and_rotation(shubert, x, shift_vector, rotation_matrix)
x = np.dot(rotation_matrix, x - shift_vector)
y = base_functions.shubert(x)
return y
[docs]def schaffer(x, shift_vector=None, rotation_matrix=None):
"""**Schaffer** test function.
Parameters
----------
x : ndarray
input vector.
shift_vector : array_like
shift vector with the same size as `x`.
rotation_matrix : ndarray
rotation matrix of size [`len(x)` * `len(x)`].
Returns
-------
y : float
scalar fitness.
"""
shift_vector, rotation_matrix = load_shift_and_rotation(schaffer, x, shift_vector, rotation_matrix)
x = np.dot(rotation_matrix, x - shift_vector)
y = base_functions.schaffer(x)
return y