import numpy as np
from warnings import warn
from typing import List, Callable
from desdeo_emo.selection.SelectionBase import SelectionBase
from desdeo_emo.population.Population import Population
from desdeo_emo.utilities.ReferenceVectors import ReferenceVectors
[docs]class APD_Select(SelectionBase):
"""The selection operator for the RVEA algorithm. Read the following paper for more
details.
R. Cheng, Y. Jin, M. Olhofer and B. Sendhoff, A Reference Vector Guided
Evolutionary Algorithm for Many-objective Optimization, IEEE Transactions on
Evolutionary Computation, 2016
Parameters
----------
pop : Population
The population instance
time_penalty_function : Callable
A function that returns the time component in the penalty function.
alpha : float, optional
The RVEA alpha parameter, by default 2
"""
def __init__(
self, pop: Population, time_penalty_function: Callable, alpha: float = 2
):
self.time_penalty_function = time_penalty_function
self.alpha = alpha
self.n_of_objectives = pop.problem.n_of_objectives
[docs] def do(self, pop: Population, vectors: ReferenceVectors) -> List[int]:
"""Select individuals for mating on basis of Angle penalized distance.
Parameters
----------
pop : Population
The current population.
vectors : ReferenceVectors
Class instance containing reference vectors.
Returns
-------
List[int]
List of indices of the selected individuals
"""
partial_penalty_factor = self._partial_penalty_factor()
refV = vectors.neighbouring_angles_current
# Normalization - There may be problems here
if pop.ideal_fitness_val is not None:
fmin = pop.ideal_fitness_val
else:
fmin = np.amin(pop.fitness, axis=0)
translated_fitness = pop.fitness - fmin
fitness_norm = np.linalg.norm(translated_fitness, axis=1)
# TODO check if you need the next line
fitness_norm = np.repeat(fitness_norm, len(translated_fitness[0, :])).reshape(
len(pop.fitness), len(pop.fitness[0, :])
)
# Convert zeros to eps to avoid divide by zero.
# Has to be checked!
fitness_norm[fitness_norm == 0] = np.finfo(float).eps
normalized_fitness = np.divide(
translated_fitness, fitness_norm
) # Checked, works.
cosine = np.dot(normalized_fitness, np.transpose(vectors.values))
if cosine[np.where(cosine > 1)].size:
warn("RVEA.py line 60 cosine larger than 1 decreased to 1")
cosine[np.where(cosine > 1)] = 1
if cosine[np.where(cosine < 0)].size:
warn("RVEA.py line 64 cosine smaller than 0 increased to 0")
cosine[np.where(cosine < 0)] = 0
# Calculation of angles between reference vectors and solutions
theta = np.arccos(cosine)
# Reference vector asub_population_indexssignment
assigned_vectors = np.argmax(cosine, axis=1)
selection = np.array([], dtype=int)
# Selection
# Convert zeros to eps to avoid divide by zero.
# Has to be checked!
refV[refV == 0] = np.finfo(float).eps
for i in range(0, len(vectors.values)):
sub_population_index = np.atleast_1d(
np.squeeze(np.where(assigned_vectors == i))
)
sub_population_fitness = translated_fitness[sub_population_index]
if len(sub_population_fitness > 0):
# APD Calculation
angles = theta[sub_population_index, i]
angles = np.divide(angles, refV[i]) # This is correct.
# You have done this calculation before. Check with fitness_norm
# Remove this horrible line
sub_pop_fitness_magnitude = np.sqrt(
np.sum(np.power(sub_population_fitness, 2), axis=1)
)
apd = np.multiply(
np.transpose(sub_pop_fitness_magnitude),
(1 + np.dot(partial_penalty_factor, angles)),
)
minidx = np.where(apd == np.nanmin(apd))
if np.isnan(apd).all():
continue
selx = sub_population_index[minidx]
if selection.shape[0] == 0:
selection = np.hstack((selection, np.transpose(selx[0])))
else:
selection = np.vstack((selection, np.transpose(selx[0])))
return selection.squeeze()
[docs] def _partial_penalty_factor(self) -> float:
"""Calculate and return the partial penalty factor for APD calculation.
This calculation does not include the angle related terms, hence the name.
If the calculated penalty is outside [0, 1], it will round it up/down to 0/1
Returns
-------
float
The partial penalty value
"""
penalty = ((self.time_penalty_function()) ** self.alpha) * self.n_of_objectives
if penalty < 0:
penalty = 0
if penalty > 1:
penalty = 1
return penalty
