def generate(image, label):
parent = [
candidate(int(np.random.uniform(0, 32)), int(np.random.uniform(0, 32)),
np.random.normal(128 / 256, 127 / 256),
np.random.normal(128 / 256, 127 / 256),
np.random.normal(128 / 256, 127 / 256)) for i in range(400)
]
iter_time = 1
for i in range(iter_time):
parent, child = DE(parent)
for j in range(len(parent)):
if score(image, label, parent[j]) > score(image, label, child[j]):
parent[j] = child[j]
final_index = 0
for i in range(len(parent)):
if score(image, label, parent[i]) < score(image, label,
parent[final_index]):
final_index = i
final_candi = parent[final_index]
final_image = copy.deepcopy(image)
final_x, final_y = final_candi.get_loc()
final_R, final_G, final_B = final_candi.get_perturbation()
final_image[0][0][final_x][final_y] = final_R
final_image[0][1][final_x][final_y] = final_G
final_image[0][2][final_x][final_y] = final_B
return final_image, final_candi
class Model(object):
"""
Differential Evolution Monte Carlo
...and so much more...
"""
param_names = property(lambda self: [p.name for p in self._params],
doc="""
List of parameter names.
""")
param_display_names = property(
lambda self: [p.display_name for p in self._params],
doc="""
List of parameter display names.
""")
particles = property(
lambda self: self.apply_param_transform(np.asarray(self._particles)),
doc="""
Particles as an array.
""")
log_likes = property(lambda self: np.asarray(self._log_likes),
doc="""
Log likelihoods as an array.
""")
weights = property(lambda self: np.asarray(self._weights),
doc="""
Weights as an array.
""")
times = property(lambda self: np.asarray(self._times),
doc="""
Times as an array.
""")
posts = property(lambda self: np.asarray(self._posts),
doc="""
Posts as an array.
""")
default_prop_gen = DE(gamma_best=0.0, rand_base=False)
default_burnin_prop_gen = DE(gamma_best=None, rand_base=True)
def __init__(self,
name,
params,
like_fun,
like_args=None,
num_chains=None,
proposal_gen=None,
burnin_proposal_gen=None,
initial_zeros_ok=False,
init_multiplier=1,
use_priors=True,
verbose=False,
partition=None,
parallel=None):
"""
DEMC
"""
# set the vars
self._name = name
self._params = params # can't be None
if num_chains is None:
num_chains = int(np.min([len(params) * 10, 100]))
self._num_chains = num_chains
self._initial_zeros_ok = initial_zeros_ok
self._init_multiplier = init_multiplier
self._use_priors = use_priors
self._verbose = verbose
if partition is None:
partition = len(self._params)
if partition > len(self._params):
partition = len(self._params)
self._partition = partition
self._parallel = parallel
# set up proposal generator
if proposal_gen is None:
proposal_gen = self.default_prop_gen
self._prop_gen = proposal_gen
if burnin_proposal_gen is None:
burnin_proposal_gen = self.default_burnin_prop_gen
self._burnin_prop_gen = burnin_proposal_gen
# set up the like function
# process the passed in like_fun
self._like_fun = like_fun
self._like_args = like_args
if self._like_args is None:
self._like_args = ()
# in some cases we will need to recalc the likes, but the user
# doesn't need to know about this
self._recalc_likes = False
# see if we need to apply a transform to any params
if np.any([p.transform for p in self._params]):
self._transform_needed = True
else:
self._transform_needed = False
# used for preprocessing
self._proposal = None
self._prop_log_likes = None
self._prop_posts = None
self._prev_log_likes = None
self._prev_posts = None
# we have not initialized
self._initialized = False
def _initialize(self, force=False, num_chains=None, partition=None):
if self._initialized and not force:
# already done
return
if self._verbose:
sys.stdout.write('Initializing: ')
sys.stdout.flush()
# time it
stime = time.time()
# initialize the particles and log_likes
self._num_params = len(self._params)
if num_chains is not None:
self._num_chains = num_chains
self._particles = []
self._log_likes = []
self._weights = []
self._times = []
self._posts = []
# set the partition
# see if we're modifying it
if partition is not None:
if partition > len(self._params):
partition = len(self._params)
self._partition = partition
self._parts = np.array([1] * self._partition + [0] *
(len(self._params) - self._partition),
dtype=np.bool)
# fill using init priors (for initialization)
init_parts = self._num_chains * self._init_multiplier
pop = np.hstack([
p.init_prior.rvs(
(init_parts, 1)) if hasattr(p.init_prior, "rvs") else np.ones(
(init_parts, 1)) * p.init_prior for p in self._params
])
if pop.ndim < 2:
pop = pop[:, np.newaxis]
# get the initial log_likes
if self._verbose:
sys.stdout.write('%d(%d) ' % (init_parts, self._num_chains))
sys.stdout.flush()
log_likes, posts = self._calc_log_likes(pop)
# make sure not zero
if not self._initial_zeros_ok:
ind = np.isinf(log_likes) | np.isnan(log_likes)
good_ind = ~ind
while good_ind.sum() < self._num_chains:
if self._verbose:
sys.stdout.write(
'%d(%d) ' %
(ind.sum(), self._num_chains - good_ind.sum()))
sys.stdout.flush()
npop = np.hstack([
p.init_prior.rvs(
(ind.sum(),
1)) if hasattr(p.init_prior, "rvs") else np.ones(
(ind.sum(), 1)) * p.init_prior
for p in self._params
])
if npop.ndim < 2:
npop = npop[:, np.newaxis]
pop[ind, :] = npop
# calc the log likes for those new pops
log_likes[ind], temp_posts = self._calc_log_likes(pop[ind])
if temp_posts is not None:
posts[ind] = temp_posts
ind = np.isinf(log_likes) | np.isnan(log_likes)
good_ind = ~ind
# save the good pop
good_ind = ~ind
pop = pop[good_ind]
if pop.ndim < 2:
pop = pop[:, np.newaxis]
log_likes = log_likes[good_ind]
if posts is not None:
posts = posts[good_ind]
if len(pop) > self._num_chains:
pop = pop[:self._num_chains]
log_likes = log_likes[:self._num_chains]
if posts is not None:
posts = posts[:self._num_chains]
# append the initial log_likes and particles
self._times.append(time.time() - stime)
self._log_likes.append(log_likes)
if self._use_priors:
# calc log_priors
log_priors = self.calc_log_prior(pop)
self._weights.append(log_likes + log_priors)
else:
self._weights.append(log_likes)
self._particles.append(pop)
if posts is not None:
self._posts.append(posts)
# say we've initialized
self._initialized = True
def apply_param_transform(self, pop):
if self._transform_needed:
pop = pop.copy()
for i, p in enumerate(self._params):
if p.transform:
pop[..., i] = p.transform(pop[..., i])
return pop
def _calc_log_likes(self, pop):
# apply transformation if necessary
pop = self.apply_param_transform(pop)
# first get the log likelihood for the pop
out = self._like_fun(pop, *(self._like_args))
if isinstance(out, tuple):
# split into likes and posts
log_likes, posts = out
else:
# just likes
log_likes = out
posts = None
return log_likes, posts
def _get_part_ind(self):
# grab the current partition indices
parts = self._parts.copy()
# roll them the size of the partition
self._parts = np.roll(self._parts, self._partition)
# return the pre-rolled value
return parts
def _crossover(self, burnin=False):
if burnin:
prop_gen = self._burnin_prop_gen
else:
prop_gen = self._prop_gen
# always pass params, though no longer using priors
proposal = prop_gen(self._particles[-1], self._weights[-1],
self._params)
# apply the partition by copying prev values back
parts = self._get_part_ind()
proposal[:, ~parts] = self._particles[-1][:, ~parts]
return proposal
def _migrate(self):
# pick which items will migrate
num_to_migrate = np.random.random_integers(2, self._num_chains)
to_migrate = random.sample(range(self._num_chains), num_to_migrate)
# do a circle swap
keepers = []
for f_ind in range(len(to_migrate)):
if f_ind == len(to_migrate) - 1:
# loop to beg
t_ind = 0
else:
# loop to next
t_ind = f_ind + 1
# set the from and to inds
i = to_migrate[f_ind]
j = to_migrate[t_ind]
# do comparison and swap if necessary
log_diff = np.float64(self._weights[-1][i] - self._weights[-1][j])
# now exp so we can get the other probs
if log_diff > 0.0:
log_diff = 0.0
mh_prob = np.exp(log_diff)
if np.isnan(mh_prob):
mh_prob = 0.0
keep = (mh_prob - np.random.rand()) > 0.0
if keep:
keepers.append({
'ind': j,
'particle': self._particles[-1][i],
'weight': self._weights[-1][i],
'log_like': self._log_likes[-1][i]
})
for k in keepers:
# do the swap (i.e., replace j with i)
# replace the particle, weight, log_like
self._particles[-1][k['ind']] = k['particle']
self._weights[-1][k['ind']] = k['weight']
self._log_likes[-1][k['ind']] = k['log_like']
def _post_evolve(self, pop, kept):
pass
def _evolve(self, burnin=False):
# first generate new proposals
# loop over groups, making new proposal pops via mutation
# or crossover
if self._proposal is None:
proposal = self._crossover(burnin=burnin)
else:
proposal = self._proposal
# eval the population (this is separate from the proposals so
# that we can parallelize the entire operation)
if self._prop_log_likes is None:
prop_log_likes, prop_posts = self._calc_log_likes(proposal)
else:
prop_log_likes = self._prop_log_likes
prop_posts = self._prop_posts
# see if recalc prev_likes in case of HyperPrior
if self._recalc_likes:
if self._prev_log_likes is None:
prev_log_likes, prev_posts = self._calc_log_likes(
self._particles[-1])
else:
prev_log_likes = self._prev_log_likes
prev_posts = self._prev_posts
else:
prev_log_likes = self._log_likes[-1]
# decide whether to keep the new proposal or not
# keep with a MH step
log_diff = np.float64(prop_log_likes - prev_log_likes)
# next see if we need to include priors for each param
if self._use_priors:
prop_log_prior, prev_log_prior = self.calc_log_prior(
proposal, self._particles[-1])
weights = prop_log_likes + prop_log_prior
log_diff += np.float64(prop_log_prior - prev_log_prior)
prev_weights = prev_log_likes + prev_log_prior
else:
weights = prop_log_likes
prev_weights = prev_log_likes
# handle much greater than one
log_diff[log_diff > 0.0] = 0.0
# now exp so we can get the other probs
mh_prob = np.exp(log_diff)
mh_prob[np.isnan(mh_prob)] = 0.0
keep = (mh_prob - np.random.rand(len(mh_prob))) > 0.0
# set the not keepers from previous population
proposal[~keep] = self._particles[-1][~keep]
prop_log_likes[~keep] = prev_log_likes[~keep]
weights[~keep] = prev_weights[~keep]
#if self._use_priors:
# weights[~keep] += prev_log_prior[~keep]
if prop_posts is not None:
prop_posts[~keep] = self._posts[-1][~keep]
# append the new proposal
self._particles.append(proposal)
self._log_likes.append(prop_log_likes)
self._weights.append(weights)
if prop_posts is not None:
self._posts.append(prop_posts)
# call post_evolve hook
self._post_evolve(proposal, keep)
# clean up for next
self._proposal = None
self._prop_log_likes = None
self._prop_posts = None
self._prev_log_likes = None
self._prev_posts = None
pass
def __call__(self, num_iter, burnin=False, migration_prob=0.0):
# make sure we've initialized
self._initialize()
# loop over iterations
if self._verbose:
sys.stdout.write('Iterations (%d): ' % (num_iter))
times = []
for i in xrange(num_iter):
if np.random.rand() < migration_prob:
# migrate, which is deterministic and done in place
if self._verbose:
sys.stdout.write('x ')
self._migrate()
if self._verbose:
sys.stdout.write('%d ' % (i + 1))
sys.stdout.flush()
stime = time.time()
# evolve the population to the next generation
self._evolve(burnin=burnin)
times.append(time.time() - stime)
if self._verbose:
sys.stdout.write('\n')
self._times.extend(times)
return times
def calc_log_prior(self, *props):
# set starting log_priors
log_priors = [np.zeros(len(p)) for p in props]
# loop over params
for i, param in enumerate(self._params):
if hasattr(param.prior, "pdf"):
# it's not a fixed value
# pick props and make sure to pass all
# into pdf at the same time
# to ensure using the same prior dist
p = np.hstack(
[props[j][:, i][:, np.newaxis] for j in range(len(props))])
log_pdf = np.log(param.prior.pdf(p))
for j in range(len(props)):
log_priors[j] += log_pdf[:, j]
# just pick singular column if there's only one passed in
if len(log_priors) == 1:
log_priors = log_priors[0]
return log_priors
def __init__(self, model, **settings): O.__init__(self) self.model = model self.settings = default().update(**settings) self.de = DE(model, gens = self.settings.k1) self.mutator = Mutator(model.get_tree())
from de import DE
from problem_data import ProblemData
from config import Config
def test(self):
print('%6.2f %6.2f' % (self.score, self.config.population.best_score))
if __name__ == "__main__":
config = Config()
config.size = 100
config.dimensions = 5
config.set_function_evaluations_budget(10000)
problem_data = ProblemData(pname='Rosenbrock',
n_dimensions=config.dimensions)
config.problem = problem_data
de = DE(config=config)
de.set_before_eval_callback(test)
de.run()
print(de.population.best_score)
class Star1(O):
def __init__(self, model, **settings):
O.__init__(self)
self.model = model
self.settings = default().update(**settings)
self.de = DE(model, gens = self.settings.k1)
self.mutator = Mutator(model.get_tree())
# def sample(self, sub_folder):
# stat = self.de.run()
# self.to_csv(stat, "csv/"+sub_folder+"/"+self.model.get_tree().name+".csv")
# stat.settings.gen_step = self.settings.gen_step
# stat.tiles()
# population = set()
# for point in stat.generations[0]:
# population.add(point)
# for point in stat.generations[-1]:
# population.add(point)
# best_size = int(len(population) * self.settings.best_percent/100)
# best = sel_nsga2(self.model, list(population), best_size)
# rest = population - set(best)
# return best, list(rest)
def sample(self, sub_folder):
stat = self.de.run()
self.to_csv(stat, "csv/"+sub_folder+"/"+self.model.get_tree().name+".csv")
stat.settings.gen_step = self.settings.gen_step
stat.tiles()
best = set()
population = set()
for point in stat.generations[0]:
population.add(point)
for point in stat.generations[-1]:
population.add(point)
for obj_index in range(len(self.de.settings.better)):
sorted_pop = sorted(list(population), key=lambda x: x.objectives[obj_index], reverse=True)[:len(stat.generations[-1])//5]
best.update(sorted_pop)
rest = population - best
return list(best), list(rest)
def rank(self, best, rest):
best_size = len(best)
rest_size = len(rest)
p_best = best_size / (best_size + rest_size)
p_rest = rest_size / (best_size + rest_size)
decisions = []
for dec_node in self.model.bases:
f_best, pos_count, neg_count = 0, 0, 0
for point in best:
if point.decisions[dec_node.id] > 0:
pos_count += 1
elif point.decisions[dec_node.id] < 0:
neg_count += 1
f_pos_best = pos_count / best_size
l_pos_best = f_pos_best * p_best
f_neg_best = neg_count / best_size
l_neg_best = f_neg_best * p_best
f_pos_rest, f_neg_rest = 0, 0
for point in rest:
if point.decisions[dec_node.id] > 0:
f_pos_rest += 1
else:
f_neg_rest += 1
f_pos_rest /= rest_size
f_neg_rest /= rest_size
l_pos_rest = f_pos_rest * p_rest
l_neg_rest = f_neg_rest * p_rest
if l_pos_best == 0 and l_pos_rest == 0:
sup_pos = 0
else:
sup_pos = l_pos_best ** 2 / (l_pos_best + l_pos_rest)
if l_neg_best == 0 and l_neg_rest == 0:
sup_neg = 0
else:
sup_neg = l_neg_best ** 2 / (l_neg_best + l_neg_rest)
decisions.append(Decision(id = dec_node.id, name = dec_node.name,
support=sup_pos, value = 1,
type = dec_node.type, container=dec_node.container,
cost = dec_node.base_cost, benefit = dec_node.base_benefit))
decisions.append(Decision(id = dec_node.id, name = dec_node.name,
support=sup_neg, value = -1,
type = dec_node.type, container=dec_node.container,
cost = dec_node.base_cost, benefit = dec_node.base_benefit))
decisions.sort(key=lambda x:x.support, reverse=True)
sorted_decs = []
aux = set()
for dec in decisions:
if dec.id not in aux:
sorted_decs.append(dec)
aux.add(dec.id)
assert len(sorted_decs) == len(self.model.bases), "Mismatch after sorting support"
return sorted_decs
def generate(self, presets = None, check_validity = False):
population = list()
while len(population) < self.settings.k2:
point = Point(self.mutator.generate())
if not point in population:
for preset in presets:
point.decisions[preset.id] = preset.value
if check_validity:
self.model.reset_nodes(point.decisions)
self.model.eval(self.model.get_tree().root)
if self.model.get_tree().root.value != 1:
continue
population.append(point)
return population
@staticmethod
def objective_stats(generations):
stats = []
obj_len = len(generations[0][0].objectives)
objective_map = {}
for i in range(obj_len):
objectives = []
data_map = {}
meds = []
iqrs = []
for gen, pop in enumerate(generations):
objs = [pt.objectives[i] for pt in pop]
objectives.append(objs)
med, iqr = median_iqr(objs)
meds.append(med)
iqrs.append(iqr)
objective_map[i] = objectives
data_map["meds"] = meds
data_map["iqrs"] = iqrs
stats.append(data_map)
return stats, objective_map
def evaluate(self, point, decisions):
model = self.model
if not point.objectives:
model.reset_nodes(point.decisions)
self.model.eval(self.model.get_tree().root)
point.objectives = self.model.get_tree().evaluate(model, point)
point.objectives.append(sum(decision.cost for decision in decisions if decision.value > 0))
point._nodes = [node.clone() for node in model.get_tree().nodes.values()]
point.objectives = [0 if one is None else one for one in point.objectives]
return point.objectives
def prune(self, support, check_validity):
gens = []
for i in range(len(support)):
decisions = support[:i]
population = self.generate(decisions, check_validity=check_validity)
for point in population:
self.evaluate(point, decisions)
gens.append(population)
obj_stats, objective_map = self.objective_stats(gens)
return obj_stats, gens, objective_map
def report(self, stats, sub_folder, fig_name):
#headers = [obj.__name__.split("_")[-1] for obj in self.de.settings.obj_funcs]
headers = ["root cost", "root benefit", "softgoals", "preset decisions cost"]
headers = ["root cost", "root benefit", "softgoals"]
med_spread_plot(stats, headers, fig_name="img/"+sub_folder+"/"+fig_name+".png")
return "img/"+sub_folder+"/"+fig_name+".png"
def to_csv(self, stats, fname):
directory = fname.rsplit("/", 1)[0]
mkdir(directory)
last_gen = sorted(stats.generations[-1], key=lambda x:x.objectives[1]-x.objectives[0], reverse=True)
self.plot_objectives(last_gen, directory)
ids = self.model.get_tree().nodes.keys()
names = [self.model.get_tree().nodes[key].name for key in ids] + ["?cost", "?benefit", "?softgoals"]
table = [names]
max_cost, max_benefit = -1, -1
for point in last_gen:
row = [point.get_nodes()[key].value for key in ids] + point.objectives
max_cost = max(point.objectives[0], max_cost)
max_benefit = max(point.objectives[1], max_benefit)
table.append(row)
with open(fname, "wb") as file_obj:
writer = csv.writer(file_obj)
writer.writerows(table)
def plot_objectives(self, points, directory):
directory = directory.replace("csv/", "img/")
objectives = []
for point in points:
dec_lens = sum([1 if dec == 1 else 0 for dec in point.decisions.values()])
obj = [dec_lens]
for o in point.objectives[:2]:
obj.append(o)
objectives.append(obj)
zipped = zip(*objectives)
x = zipped[0]
costs = zipped[1]
benefits = zipped[2]
tree_name = self.model.get_tree().name
mkdir(directory)
point_plot(x, {"cost":costs}, ['ro'], "%s/%s_costs.png"%(directory, tree_name))
point_plot(x, {"benefit":benefits}, ['bx'], "%s/%s_benefits.png"%(directory, tree_name))
point_plot_3d(x, costs, benefits, 'r', 'x', "%s/%s_3d.png"%(directory, tree_name),
"Number of Decisions", "Costs", "Benefits")
def visualize(self, decisions):
tracks = []
for i in range(len(decisions)):
pos_decs, neg_decs = [], []
for j in range(len(decisions)):
if j < i:
pos_decs.append(Decision(id = decisions[j].id, value = decisions[j].value,
cost = decisions[j].cost, benefit = decisions[j].benefit))
neg_decs.append(Decision(id = decisions[j].id, value = decisions[j].value,
cost = decisions[j].cost, benefit = decisions[j].benefit))
elif j == i:
pos_decs.append(Decision(id = decisions[j].id, value = +1,
cost = decisions[j].cost, benefit = decisions[j].benefit))
neg_decs.append(Decision(id = decisions[j].id, value = -1,
cost = decisions[j].cost, benefit = decisions[j].benefit))
# else:
# pos_decs.append(Decision(id = decisions[j].id, value = -1 * decisions[j].value))
# neg_decs.append(Decision(id = decisions[j].id, value = -1 * decisions[j].value))
if decisions[i].value == 1:
pos_pop = self.generate(pos_decs, check_validity=True)
neg_pop = self.generate(neg_decs, check_validity=False)
else:
pos_pop = self.generate(pos_decs, check_validity=False)
neg_pop = self.generate(neg_decs, check_validity=True)
for pos, neg in zip(pos_pop, neg_pop):
self.evaluate(pos, pos_decs)
self.evaluate(neg, neg_decs)
p_meds, p_iqrs = [], []
n_meds, n_iqrs = [], []
for o_i in range(len(pos_pop[0].objectives)):
p_objs = [pt.objectives[o_i] for pt in pos_pop]
n_objs = [pt.objectives[o_i] for pt in neg_pop]
med, iqr = median_iqr(p_objs)
p_meds.append(med)
p_iqrs.append(iqr)
med, iqr = median_iqr(n_objs)
n_meds.append(med)
n_iqrs.append(iqr)
tracks.append(O(id = decisions[i].id, name = decisions[i].name,
pos_meds = p_meds, pos_iqrs = p_iqrs,
neg_meds = n_meds, neg_iqrs = n_iqrs,
prefered_value = decisions[i].value,
cost = decisions[i].cost, benefit = decisions[i].benefit))
return tracks
@staticmethod
def get_elbow(gens, index, obj_index=None):
pop = gens[index]
pop = sorted(pop, key=lambda x: x.objectives[obj_index])
point = pop[len(pop)//2]
return point
def run_de(graph):
model = Model(graph)
de = DE(model)
stat = de.run()
stat.tiles()
def run_de(graph):
model = Model(graph)
de = DE(model)
stat = de.run()
stat.tiles()
% (median(fbest_r)))
if runs > 1:
results.write('Gbest Standard Deviation: %.4f\n\n' %
(stdev(fbest_r)))
results.write('Elappsed Time Average: %.4f\n' %
(sum(elapTime_r) / len(elapTime_r)))
if runs > 1:
results.write('Elappsed Time Standard Deviation: %.4f\n' %
(stdev(elapTime_r)))
results.write(
'=================================================================================================================\n'
)
if __name__ == '__main__':
from de import DE
max_iterations = 100
pop_size = 20
dim = 2
runs = 10
bounds = ((-5.12, 5.12), (-5.12, 5.12))
p = DE()
p.diferentialEvolution(pop_size,
dim,
bounds,
max_iterations,
runs,
maximize=False,
operator=0)
import benchmark_functions as bf
import matplotlib.pyplot as plt
from ga import GA
from de import DE
# Select function for minimization
f = bf.Sphere(dim=2)
# View 3d plot of the function
if f.dim == 2:
bf.plot3d(function=f, show_contour=True)
plt.show()
# Create algorithm, Differential evolution or Genetic algorithm
de = DE(obj_function=f, F=0.8, Cr=0.3, gen_max=10000)
ga = GA(obj_function=f, k=70, pm=0.5, gen_max=10000, sigma=2)
# Find solution
de_solution, de_gen = de.search(show_progress=False, error_tolerance=f.epsilon)
ga_solution, ga_gen = ga.search(show_progress=False,
error_tolerance=f.epsilon,
c=0.9,
msc=50)
# Print results
print("============== Differential evolution ==============")
print(
"Solution {:f} found in {:d} generations. Optimal value is {:f}. Error is: {:f}."
.format(f.value(de_solution), de_gen, f.optimum,
f.value(de_solution) - f.optimum))
print("============== Genetic algorithm ==============")
print(
"Solution {:f} found in {:d} generations. Optimal value is {:f}. Error is: {:f}."
.format(f.value(ga_solution), ga_gen, f.optimum,
