def update(self, population):
"""Update the Pareto front hall of fame with the *population* by adding
the individuals from the population that are not dominated by the hall
of fame. If any individual in the hall of fame is dominated it is
removed.
:param population: A list of individual with a fitness attribute to
update the hall of fame with.
"""
added = 0
removed = 0
for ind in population:
is_dominated = False
has_twin = False
to_remove = []
for i, hofer in enumerate(self): # hofer = hall of famer
if isDominated(ind.fitness.wvalues, hofer.fitness.wvalues):
is_dominated = True
break
elif isDominated(hofer.fitness.wvalues, ind.fitness.wvalues):
to_remove.append(i)
elif ind.fitness == hofer.fitness and self.similar(ind, hofer):
has_twin = True
break
for i in reversed(to_remove): # Remove the dominated hofer
self.remove(i)
removed+=1
if not is_dominated and not has_twin:
self.insert(ind)
added+=1
return added, removed
def selSPEA2(individuals, k):
"""Apply SPEA-II selection operator on the *individuals*. Usually, the
size of *individuals* will be larger than *n* because any individual
present in *individuals* will appear in the returned list at most once.
Having the size of *individuals* equals to *n* will have no effect other
than sorting the population according to a strength Pareto scheme. The
list returned contains references to the input *individuals*. For more
details on the SPEA-II operator see [Zitzler2001]_.
:param individuals: A list of individuals to select from.
:param k: The number of individuals to select.
:returns: A list of selected individuals.
.. [Zitzler2001] Zitzler, Laumanns and Thiele, "SPEA 2: Improving the
strength Pareto evolutionary algorithm", 2001.
"""
N = len(individuals)
L = len(individuals[0].fitness.values)
K = math.sqrt(N)
strength_fits = [0] * N
fits = [0] * N
dominating_inds = [list() for i in xrange(N)]
for i in xrange(N):
for j in xrange(i + 1, N):
if tools.isDominated(individuals[i].fitness.wvalues, individuals[j].fitness.wvalues):
strength_fits[j] += 1
dominating_inds[i].append(j)
elif tools.isDominated(individuals[j].fitness.wvalues, individuals[i].fitness.wvalues):
strength_fits[i] += 1
dominating_inds[j].append(i)
for i in xrange(N):
for j in dominating_inds[i]:
fits[i] += strength_fits[j]
# Choose all non-dominated individuals
chosen_indices = [i for i in xrange(N) if fits[i] < 1]
if len(chosen_indices) < k: # The archive is too small
for i in xrange(N):
distances = [0.0] * N
for j in xrange(i + 1, N):
dist = 0.0
for l in xrange(L):
val = individuals[i].fitness.values[l] -\
individuals[j].fitness.values[l]
dist += val * val
distances[j] = dist
kth_dist = tools._randomizedSelect(distances, 0, N - 1, K)
density = 1.0 / (kth_dist + 2.0)
fits[i] += density
next_indices = [(fits[i], i) for i in xrange(N)\
if not i in chosen_indices]
next_indices.sort()
#print next_indices
chosen_indices += [i for _, i in next_indices[:k - len(chosen_indices)]]
elif len(chosen_indices) > k: # The archive is too large
N = len(chosen_indices)
distances = [[0.0] * N for i in xrange(N)]
sorted_indices = [[0] * N for i in xrange(N)]
for i in xrange(N):
for j in xrange(i + 1, N):
dist = 0.0
for l in xrange(L):
val = individuals[chosen_indices[i]].fitness.values[l] -\
individuals[chosen_indices[j]].fitness.values[l]
dist += val * val
distances[i][j] = dist
distances[j][i] = dist
distances[i][i] = -1
# Insert sort is faster than quick sort for short arrays
for i in xrange(N):
for j in xrange(1, N):
l = j
while l > 0 and distances[i][j] < distances[i][sorted_indices[i][l - 1]]:
sorted_indices[i][l] = sorted_indices[i][l - 1]
l -= 1
sorted_indices[i][l] = j
size = N
to_remove = []
while size > k:
# Search for minimal distance
min_pos = 0
for i in xrange(1, N):
for j in xrange(1, size):
dist_i_sorted_j = distances[i][sorted_indices[i][j]]
dist_min_sorted_j = distances[min_pos][sorted_indices[min_pos][j]]
if dist_i_sorted_j < dist_min_sorted_j:
min_pos = i
break
elif dist_i_sorted_j > dist_min_sorted_j:
break
# Remove minimal distance from sorted_indices
for i in xrange(N):
distances[i][min_pos] = float("inf")
distances[min_pos][i] = float("inf")
for j in xrange(1, size - 1):
if sorted_indices[i][j] == min_pos:
sorted_indices[i][j] = sorted_indices[i][j + 1]
sorted_indices[i][j + 1] = min_pos
# Remove corresponding individual from chosen_indices
to_remove.append(min_pos)
size -= 1
for index in reversed(sorted(to_remove)):
del chosen_indices[index]
return [individuals[i] for i in chosen_indices],[fits[i] for i in chosen_indices]
