def __init__(self,
pop_size=None,
sampling=None,
selection=None,
crossover=None,
mutation=None,
survival=None,
n_offsprings=None,
eliminate_duplicates=DefaultDuplicateElimination(),
repair=None,
individual=Individual(),
**kwargs):
super().__init__(**kwargs)
# the population size used
self.pop_size = pop_size
# the survival for the genetic algorithm
self.survival = survival
# number of offsprings to generate through recombination
self.n_offsprings = n_offsprings
# if the number of offspring is not set - equal to population size
if self.n_offsprings is None:
self.n_offsprings = pop_size
# the object to be used to represent an individual - either individual or derived class
self.individual = individual
# set the duplicate detection class - a boolean value chooses the default duplicate detection
if isinstance(eliminate_duplicates, bool):
if eliminate_duplicates:
self.eliminate_duplicates = DefaultDuplicateElimination()
else:
self.eliminate_duplicates = NoDuplicateElimination()
else:
self.eliminate_duplicates = eliminate_duplicates
# simply set the no repair object if it is None
self.repair = repair if repair is not None else NoRepair()
self.initialization = Initialization(
sampling,
individual=individual,
repair=self.repair,
eliminate_duplicates=self.eliminate_duplicates)
self.mating = Mating(selection,
crossover,
mutation,
repair=self.repair,
eliminate_duplicates=self.eliminate_duplicates,
n_max_iterations=100)
# other run specific data updated whenever solve is called - to share them in all algorithms
self.n_gen = None
self.pop = None
self.off = None
def __init__(self,
display=CSDisplay(),
sampling=FloatRandomSampling(),
survival=FitnessSurvival(),
eliminate_duplicates=DefaultDuplicateElimination(),
termination=SingleObjectiveDefaultTermination(),
pop_size=100,
beta=1.5,
alfa=0.01,
pa=0.35,
**kwargs):
"""
Parameters
----------
display : {display}
sampling : {sampling}
survival : {survival}
eliminate_duplicates: This does not exists in the original paper/book.
Without this the solutions might get too biased to current global best solution,
because the global random walk use the global best solution as the reference.
termination : {termination}
pop_size : The number of nests (solutions)
beta : The input parameter of the Mantegna's Algorithm to simulate
sampling on Levy Distribution
alfa : alfa is the step size scaling factor and is usually
0.01, so that the step size will be scaled down to O(L/100) with L is
the scale (range of bounds) of the problem.
pa : The switch probability, pa fraction of the nests will be
abandoned on every iteration
"""
super().__init__(**kwargs)
self.initialization = Initialization(sampling)
self.survival = survival
self.display = display
self.pop_size = pop_size
self.default_termination = termination
self.eliminate_duplicates = eliminate_duplicates
#the scale will be multiplied by problem scale after problem given in setup
self.alfa = alfa
self.scale = alfa
self.pa = pa
self.beta = beta
a = math.gamma(1. + beta) * math.sin(math.pi * beta / 2.)
b = beta * math.gamma((1. + beta) / 2.) * 2**((beta - 1.) / 2)
self.sig = (a / b)**(1. / (2 * beta))
def __init__(self,
pop_size=200,
n_parallel=10,
sampling=LatinHypercubeSampling(),
display=SingleObjectiveDisplay(),
repair=None,
individual=Individual(),
**kwargs):
"""
Parameters
----------
pop_size : {pop_size}
sampling : {sampling}
selection : {selection}
crossover : {crossover}
mutation : {mutation}
eliminate_duplicates : {eliminate_duplicates}
n_offsprings : {n_offsprings}
"""
super().__init__(display=display, **kwargs)
self.initialization = Initialization(sampling,
individual=individual,
repair=repair)
self.pop_size = pop_size
self.n_parallel = n_parallel
self.each_pop_size = pop_size // n_parallel
self.solvers = None
self.niches = []
def cmaes(problem, x):
solver = CMAES(x0=x, tolfun=1e-11, tolx=1e-3, restarts=0)
solver.initialize(problem)
solver.next()
return solver
def nelder_mead(problem, x):
solver = NelderMead(X=x)
solver.initialize(problem)
solver._initialize()
solver.n_gen = 1
solver.next()
return solver
self.func_create_solver = nelder_mead
self.default_termination = SingleObjectiveDefaultTermination()
def __init__(self,
pop_size=None,
sampling=None,
eliminate_duplicates=DefaultDuplicateElimination(),
individual=Individual(),
**kwargs
):
super().__init__(**kwargs)
# the population size used
self.pop_size = pop_size
# number of offsprings
self.n_offsprings = pop_size
# the object to be used to represent an individual - either individual or derived class
self.individual = individual
# set the duplicate detection class - a boolean value chooses the default duplicate detection
if isinstance(eliminate_duplicates, bool):
if eliminate_duplicates:
self.eliminate_duplicates = DefaultDuplicateElimination()
else:
self.eliminate_duplicates = NoDuplicateElimination()
else:
self.eliminate_duplicates = eliminate_duplicates
# simply set the no repair object if it is None
self.repair = NoRepair()
self.initialization = Initialization(sampling,
individual=individual,
repair=self.repair,
eliminate_duplicates=self.eliminate_duplicates)
self.n_gen = None
self.pop = None
self.off = None
def __init__(self,
pop_size=20,
w=0.9,
c1=2.0,
c2=2.0,
sampling=LatinHypercubeSampling(),
adaptive=True,
pertube_best=True,
display=PSODisplay(),
repair=None,
individual=Individual(),
**kwargs):
"""
Parameters
----------
pop_size : {pop_size}
sampling : {sampling}
"""
super().__init__(display=display, **kwargs)
self.initialization = Initialization(sampling,
individual=individual,
repair=repair)
self.pop_size = pop_size
self.adaptive = adaptive
self.pertube_best = pertube_best
self.default_termination = SingleObjectiveDefaultTermination()
self.V_max = None
self.w = w
self.c1 = c1
self.c2 = c2
class GeneticAlgorithm(Algorithm):
def __init__(self,
pop_size=None,
sampling=None,
selection=None,
crossover=None,
mutation=None,
survival=None,
n_offsprings=None,
eliminate_duplicates=DefaultDuplicateElimination(),
repair=None,
individual=Individual(),
**kwargs
):
super().__init__(**kwargs)
# the population size used
self.pop_size = pop_size
# the survival for the genetic algorithm
self.survival = survival
# number of offsprings to generate through recombination
self.n_offsprings = n_offsprings
# if the number of offspring is not set - equal to population size
if self.n_offsprings is None:
self.n_offsprings = pop_size
# the object to be used to represent an individual - either individual or derived class
self.individual = individual
# set the duplicate detection class - a boolean value chooses the default duplicate detection
if isinstance(eliminate_duplicates, bool):
if eliminate_duplicates:
self.eliminate_duplicates = DefaultDuplicateElimination()
else:
self.eliminate_duplicates = None
else:
self.eliminate_duplicates = eliminate_duplicates
self.initialization = Initialization(sampling,
individual=individual,
repair=repair,
eliminate_duplicates=self.eliminate_duplicates)
self.mating = Mating(selection,
crossover,
mutation,
repair=repair,
eliminate_duplicates=self.eliminate_duplicates,
n_max_iterations=100)
# other run specific data updated whenever solve is called - to share them in all algorithms
self.n_gen = None
self.pop = None
self.off = None
def _initialize(self):
# create the initial population
pop = self.initialization.do(self.problem, self.pop_size, algorithm=self)
# then evaluate using the objective function
self.evaluator.eval(self.problem, pop, algorithm=self)
# that call is a dummy survival to set attributes that are necessary for the mating selection
if self.survival:
pop = self.survival.do(self.problem, pop, len(pop), algorithm=self)
self.pop = pop
def _next(self):
# do the mating using the current population
self.off = self.mating.do(self.problem, self.pop, n_offsprings=self.n_offsprings, algorithm=self)
# if the mating could not generate any new offspring (duplicate elimination might make that happen)
if len(self.off) == 0:
self.termination.force_termination = True
return
# if not the desired number of offspring could be created
elif len(self.off) < self.n_offsprings:
if self.verbose:
print("WARNING: Mating could not produce the required number of (unique) offsprings!")
# evaluate the offspring
self.evaluator.eval(self.problem, self.off, algorithm=self)
# merge the offsprings with the current population
self.pop = self.pop.merge(self.off)
# the do survival selection
if self.survival:
self.pop = self.survival.do(self.problem, self.pop, self.pop_size, algorithm=self)
def _finalize(self):
pass
def __init__(self,
pop_size=25,
sampling=LatinHypercubeSampling(),
w=0.9,
c1=2.0,
c2=2.0,
adaptive=True,
initial_velocity="random",
max_velocity_rate=0.20,
pertube_best=True,
display=PSODisplay(),
**kwargs):
"""
Parameters
----------
pop_size : The size of the swarm being used.
sampling : {sampling}
adaptive : bool
Whether w, c1, and c2 are changed dynamically over time. The update uses the spread from the global
optimum to determine suitable values.
w : float
The inertia weight to be used in each iteration for the velocity update. This can be interpreted
as the momentum term regarding the velocity. If `adaptive=True` this is only the
initially used value.
c1 : float
The cognitive impact (personal best) during the velocity update. If `adaptive=True` this is only the
initially used value.
c2 : float
The social impact (global best) during the velocity update. If `adaptive=True` this is only the
initially used value.
initial_velocity : str - ('random', or 'zero')
How the initial velocity of each particle should be assigned. Either 'random' which creates a
random velocity vector or 'zero' which makes the particles start to find the direction through the
velocity update equation.
max_velocity_rate : float
The maximum velocity rate. It is determined variable (and not vector) wise. We consider the rate here
since the value is normalized regarding the `xl` and `xu` defined in the problem.
pertube_best : bool
Some studies have proposed to mutate the global best because it has been found to converge better.
Which means the population size is reduced by one particle and one function evaluation is spend
additionally to permute the best found solution so far.
"""
super().__init__(display=display, **kwargs)
self.initialization = Initialization(sampling)
self.pop_size = pop_size
self.adaptive = adaptive
self.pertube_best = pertube_best
self.default_termination = SingleObjectiveDefaultTermination()
self.V_max = None
self.initial_velocity = initial_velocity
self.max_velocity_rate = max_velocity_rate
self.w = w
self.c1 = c1
self.c2 = c2
class PSO(Algorithm):
def __init__(self,
pop_size=25,
sampling=LatinHypercubeSampling(),
w=0.9,
c1=2.0,
c2=2.0,
adaptive=True,
initial_velocity="random",
max_velocity_rate=0.20,
pertube_best=True,
display=PSODisplay(),
**kwargs):
"""
Parameters
----------
pop_size : The size of the swarm being used.
sampling : {sampling}
adaptive : bool
Whether w, c1, and c2 are changed dynamically over time. The update uses the spread from the global
optimum to determine suitable values.
w : float
The inertia weight to be used in each iteration for the velocity update. This can be interpreted
as the momentum term regarding the velocity. If `adaptive=True` this is only the
initially used value.
c1 : float
The cognitive impact (personal best) during the velocity update. If `adaptive=True` this is only the
initially used value.
c2 : float
The social impact (global best) during the velocity update. If `adaptive=True` this is only the
initially used value.
initial_velocity : str - ('random', or 'zero')
How the initial velocity of each particle should be assigned. Either 'random' which creates a
random velocity vector or 'zero' which makes the particles start to find the direction through the
velocity update equation.
max_velocity_rate : float
The maximum velocity rate. It is determined variable (and not vector) wise. We consider the rate here
since the value is normalized regarding the `xl` and `xu` defined in the problem.
pertube_best : bool
Some studies have proposed to mutate the global best because it has been found to converge better.
Which means the population size is reduced by one particle and one function evaluation is spend
additionally to permute the best found solution so far.
"""
super().__init__(display=display, **kwargs)
self.initialization = Initialization(sampling)
self.pop_size = pop_size
self.adaptive = adaptive
self.pertube_best = pertube_best
self.default_termination = SingleObjectiveDefaultTermination()
self.V_max = None
self.initial_velocity = initial_velocity
self.max_velocity_rate = max_velocity_rate
self.w = w
self.c1 = c1
self.c2 = c2
def initialize(self, problem, **kwargs):
super().initialize(problem, **kwargs)
self.V_max = self.max_velocity_rate * (problem.xu - problem.xl)
def _initialize(self):
pop = self.initialization.do(self.problem,
self.pop_size,
algorithm=self)
self.evaluator.eval(self.problem, pop, algorithm=self)
if self.pertube_best:
pop = FitnessSurvival().do(self.problem, pop, self.pop_size - 1)
if self.initial_velocity == "random":
init_V = np.random.random(
(len(pop), self.problem.n_var)) * self.V_max[None, :]
elif self.initial_velocity == "zero":
init_V = np.zeros((len(pop), self.problem.n_var))
pop.set("V", init_V)
pop.set("pbest", pop)
self.pop, self.off = pop, pop
self.f = None
self.strategy = None
def _next(self):
self._step()
if self.adaptive:
self._adapt()
def _step(self):
pop = self.pop
X, F, V = pop.get("X", "F", "V")
# get the personal best of each particle
pbest = Population.create(*pop.get("pbest"))
P_X, P_F = pbest.get("X", "F")
# get the GLOBAL best solution - other variants such as local best can be implemented here too
best = self.opt.repeat(len(pop))
G_X = best.get("X")
# get the inertia weight of the individual
inerta = self.w * V
# calculate random values for the updates
r1 = np.random.random((len(pop), self.problem.n_var))
r2 = np.random.random((len(pop), self.problem.n_var))
cognitive = self.c1 * r1 * (P_X - X)
social = self.c2 * r2 * (G_X - X)
# calculate the velocity vector
_V = inerta + cognitive + social
_V = repair_out_of_bounds_manually(_V, -self.V_max, self.V_max)
# update the values of each particle
_X = X + _V
_X = repair_out_of_bounds(self.problem, _X)
# evaluate the offspring population
off = Population(len(pop)).set("X", _X, "V", _V, "pbest", pbest)
self.evaluator.eval(self.problem, off, algorithm=self)
# check whether a solution has improved or not - also consider constraints here
has_improved = ImprovementReplacement().do(self.problem,
pbest,
off,
return_indices=True)
# replace the personal best of each particle if it has improved
off[has_improved].set("pbest", off[has_improved])
off.set("best", best)
pop = off
# try to improve the current best with a pertubation
if self.pertube_best:
pbest = Population.create(*pop.get("pbest"))
k = FitnessSurvival().do(self.problem,
pbest,
1,
return_indices=True)[0]
eta = int(np.random.uniform(5, 30))
mutant = PolynomialMutation(eta).do(self.problem, pbest[[k]])[0]
self.evaluator.eval(self.problem, mutant, algorithm=self)
# if the mutant is in fact better - replace the personal best
if is_better(mutant, pop[k]):
pop[k].set("pbest", mutant)
self.pop = pop
def _adapt(self):
pop = self.pop
X, F, best = pop.get("X", "F", "best")
best = Population.create(*best)
w, c1, c2, = self.w, self.c1, self.c2
# get the average distance from one to another for normalization
D = norm_eucl_dist(self.problem, X, X)
mD = D.sum(axis=1) / (len(pop) - 1)
_min, _max = mD.min(), mD.max()
# get the average distance to the global best
g_D = norm_euclidean_distance(self.problem)(best.get("X"), X).mean()
f = (g_D - _min) / (_max - _min + 1e-32)
S = np.array([
S1_exploration(f),
S2_exploitation(f),
S3_convergence(f),
S4_jumping_out(f)
])
strategy = S.argmax() + 1
delta = 0.05 + (np.random.random() * 0.05)
if strategy == 1:
c1 += delta
c2 -= delta
elif strategy == 2:
c1 += 0.5 * delta
c2 -= 0.5 * delta
elif strategy == 3:
c1 += 0.5 * delta
c2 += 0.5 * delta
elif strategy == 4:
c1 -= delta
c2 += delta
c1 = max(1.5, min(2.5, c1))
c2 = max(1.5, min(2.5, c2))
if c1 + c2 > 4.0:
c1 = 4.0 * (c1 / (c1 + c2))
c2 = 4.0 * (c2 / (c1 + c2))
w = 1 / (1 + 1.5 * np.exp(-2.6 * f))
self.f = f
self.strategy = strategy
self.c1 = c1
self.c2 = c2
self.w = w
def _set_optimum(self, force=False):
pbest = Population.create(*self.pop.get("pbest"))
self.opt = filter_optimum(pbest, least_infeasible=True)
def __init__(self,
pop_size=None,
sampling=None,
survival=None,
eliminate_duplicates=DefaultDuplicateElimination(),
repair=None,
individual=Individual(),
n_cell=None,
cell_size=10,
buffer_origin=None,
buffer_origin_constant=1e-2,
delta_b=0.2,
label_cost=10,
delta_p=10,
delta_s=0.3,
n_grid_sample=100,
n_process=cpu_count(),
**kwargs):
'''
Inputs (essential parameters):
pop_size: population size
sampling: initial sample data or sampling method to obtain initial population
n_cell: number of cells in performance buffer
cell_size: maximum number of samples inside each cell of performance buffer
buffer_origin: origin of performance buffer
buffer_origin_constant: when evaluted value surpasses the buffer origin, adjust the origin accordingly and subtract this constant
delta_b: unary energy normalization constant for sparse approximation, see section 6.4
label_cost: for reducing number of unique labels in sparse approximation, see section 6.4
delta_p: factor of perturbation in stochastic sampling, see section 6.2.2
delta_s: scaling factor for choosing reference point in local optimization, see section 6.2.3
n_grid_sample: number of samples on local manifold (grid), see section 6.3.1
n_process: number of processes for parallelization
'''
super().__init__(**kwargs)
self.pop_size = pop_size
self.survival = survival
self.individual = individual
if isinstance(eliminate_duplicates, bool):
if eliminate_duplicates:
self.eliminate_duplicates = DefaultDuplicateElimination()
else:
self.eliminate_duplicates = None
else:
self.eliminate_duplicates = eliminate_duplicates
self.initialization = Initialization(
sampling,
individual=individual,
repair=repair,
eliminate_duplicates=self.eliminate_duplicates)
self.n_gen = None
self.pop = None
self.off = None
self.approx_set = None
self.approx_front = None
self.fam_lbls = None
self.buffer = None
if n_cell is None:
n_cell = self.pop_size
self.buffer_args = {
'cell_num': n_cell,
'cell_size': cell_size,
'origin': buffer_origin,
'origin_constant': buffer_origin_constant,
'delta_b': delta_b,
'label_cost': label_cost
}
self.delta_p = delta_p
self.delta_s = delta_s
self.n_grid_sample = n_grid_sample
self.n_process = n_process
self.patch_id = 0
self.constr_func = None
class ParetoDiscovery(Algorithm):
'''
The Pareto discovery algorithm introduced by: Schulz, Adriana, et al. "Interactive exploration of design trade-offs." ACM Transactions on Graphics (TOG) 37.4 (2018): 1-14.
'''
def __init__(self,
pop_size=None,
sampling=None,
survival=None,
eliminate_duplicates=DefaultDuplicateElimination(),
repair=None,
individual=Individual(),
n_cell=None,
cell_size=10,
buffer_origin=None,
buffer_origin_constant=1e-2,
delta_b=0.2,
label_cost=10,
delta_p=10,
delta_s=0.3,
n_grid_sample=100,
n_process=cpu_count(),
**kwargs):
'''
Inputs (essential parameters):
pop_size: population size
sampling: initial sample data or sampling method to obtain initial population
n_cell: number of cells in performance buffer
cell_size: maximum number of samples inside each cell of performance buffer
buffer_origin: origin of performance buffer
buffer_origin_constant: when evaluted value surpasses the buffer origin, adjust the origin accordingly and subtract this constant
delta_b: unary energy normalization constant for sparse approximation, see section 6.4
label_cost: for reducing number of unique labels in sparse approximation, see section 6.4
delta_p: factor of perturbation in stochastic sampling, see section 6.2.2
delta_s: scaling factor for choosing reference point in local optimization, see section 6.2.3
n_grid_sample: number of samples on local manifold (grid), see section 6.3.1
n_process: number of processes for parallelization
'''
super().__init__(**kwargs)
self.pop_size = pop_size
self.survival = survival
self.individual = individual
if isinstance(eliminate_duplicates, bool):
if eliminate_duplicates:
self.eliminate_duplicates = DefaultDuplicateElimination()
else:
self.eliminate_duplicates = None
else:
self.eliminate_duplicates = eliminate_duplicates
self.initialization = Initialization(
sampling,
individual=individual,
repair=repair,
eliminate_duplicates=self.eliminate_duplicates)
self.n_gen = None
self.pop = None
self.off = None
self.approx_set = None
self.approx_front = None
self.fam_lbls = None
self.buffer = None
if n_cell is None:
n_cell = self.pop_size
self.buffer_args = {
'cell_num': n_cell,
'cell_size': cell_size,
'origin': buffer_origin,
'origin_constant': buffer_origin_constant,
'delta_b': delta_b,
'label_cost': label_cost
}
self.delta_p = delta_p
self.delta_s = delta_s
self.n_grid_sample = n_grid_sample
self.n_process = n_process
self.patch_id = 0
self.constr_func = None
def _initialize(self):
# create the initial population
pop = self.initialization.do(self.problem,
self.pop_size,
algorithm=self)
pop_x = pop.get('X').copy()
# check if problem has constraints other than bounds
pop_constr = self.problem.evaluate_constraint(pop_x)
if pop_constr is not None:
self.constr_func = self.problem.evaluate_constraint
pop = pop[pop_constr <= 0]
while len(pop) < self.pop_size:
new_pop = self.initialization.do(self.problem,
self.pop_size,
algorithm=self)
new_pop_x = new_pop.get('X').copy()
new_pop = new_pop[
self.problem.evaluate_constraint(new_pop_x) <= 0]
pop = pop.merge(new_pop)
pop = pop[:self.pop_size]
pop_x = pop.get('X').copy()
pop_f = self.problem.evaluate(pop_x, return_values_of=['F'])
# initialize buffer
self.buffer = get_buffer(self.problem.n_obj, **self.buffer_args)
self.buffer.origin = self.problem.normalization.do(
y=self.buffer.origin.reshape(1, -1))[0]
patch_ids = np.full(
self.pop_size,
self.patch_id) # NOTE: patch_ids here might not make sense
self.patch_id += 1
self.buffer.insert(pop_x, pop_f, patch_ids)
# update population by the best samples in the buffer
pop = pop.new('X', self.buffer.sample(self.pop_size))
# evaluate population using the objective function
self.evaluator.eval(self.problem, pop, algorithm=self)
# NOTE: check if need survival here
if self.survival:
pop = self.survival.do(self.problem, pop, len(pop), algorithm=self)
self.pop = pop
# sys.stdout.write('ParetoDiscovery optimizing: generation %i' % self.n_gen)
# sys.stdout.flush()
def _next(self):
'''
Core algorithm part in each iteration, see algorithm 1.
--------------------------------------
xs = stochastic_sampling(B, F, X)
for x in xs:
D = select_direction(B, x)
x_opt = local_optimization(D, F, X)
M = first_order_approximation(x_opt, F, X)
update_buffer(B, F(M))
--------------------------------------
where F is problem evaluation, X is design constraints
'''
# update optimization progress
# sys.stdout.write('\b' * len(str(self.n_gen - 1)) + str(self.n_gen))
# sys.stdout.flush()
# stochastic sampling by adding local perturbance
xs = self._stochastic_sampling()
# parallelize core pareto discovery process by multiprocess, see _pareto_discover()
# including select_direction, local_optimization, first_order_approximation in above algorithm illustration
x_batch = np.array_split(xs, self.n_process)
queue = Queue()
process_count = 0
for x in x_batch:
if len(x) > 0:
p = Process(target=_pareto_discover,
args=(x, self.problem.evaluate,
[self.problem.xl,
self.problem.xu], self.constr_func,
self.delta_s, self.buffer.origin,
self.buffer.origin_constant,
self.n_grid_sample, queue))
p.start()
process_count += 1
# gather results (new samples, new patch ids, new origin of performance buffer) from parallel discovery
new_origin = self.buffer.origin
x_samples_all = []
patch_ids_all = []
for _ in range(process_count):
x_samples, patch_ids, sample_num, origin = queue.get()
if x_samples is not None:
x_samples_all.append(x_samples)
patch_ids_all.append(
np.array(patch_ids) + self.patch_id
) # assign corresponding global patch ids to samples
self.patch_id += sample_num
new_origin = np.minimum(new_origin, origin)
# evalaute all new samples and adjust the origin point of buffer
x_samples_all = np.vstack(x_samples_all)
y_samples_all = self.problem.evaluate(x_samples_all,
return_values_of=['F'])
new_origin = np.minimum(np.min(y_samples_all, axis=0), new_origin)
patch_ids_all = np.concatenate(patch_ids_all)
# update buffer
self.buffer.move_origin(new_origin)
self.buffer.insert(x_samples_all, y_samples_all, patch_ids_all)
# update population by the best samples in the buffer
self.pop = self.pop.new('X', self.buffer.sample(self.pop_size))
self.evaluator.eval(self.problem, self.pop, algorithm=self)
def _stochastic_sampling(self):
'''
Stochastic sampling around current population to initialize each iteration to avoid local minima, see section 6.2.2
'''
xs = self.pop.get('X').copy()
# sampling loop
num_target = xs.shape[0]
xs_final = np.zeros((0, xs.shape[1]), xs.dtype)
while xs_final.shape[0] < num_target:
# generate stochastic direction
d = np.random.random(xs.shape)
d /= np.expand_dims(np.linalg.norm(d, axis=1), axis=1)
# generate random scaling factor
delta = np.random.random() * self.delta_p
# generate new stochastic samples
xs_perturb = xs + 1.0 / (
2**delta
) * d # NOTE: is this scaling form reasonable? maybe better use relative scaling?
xs_perturb = np.clip(xs_perturb, self.problem.xl, self.problem.xu)
if self.constr_func is None:
xs_final = xs_perturb
else:
# check constraint values
constr = self.constr_func(xs_perturb)
flag = constr <= 0
if np.any(flag):
xs_final = np.vstack((xs_final, xs_perturb[flag]))
return xs_final[:num_target]
def propose_next_batch(self, curr_pfront, ref_point, batch_size,
normalization):
'''
Propose next batch to evaluate for active learning.
Greedely propose sample with max HV until all families ar visited. Allow only samples with max HV from unvisited family.
'''
approx_x, approx_y = normalization.undo(self.approx_set,
self.approx_front)
labels = self.fam_lbls
X_next = []
Y_next = []
family_lbls = []
if len(approx_x) >= batch_size:
# approximation result is enough to propose all candidates
curr_X_next, curr_Y_next, labels_next = propose_next_batch(
curr_pfront, ref_point, approx_y, approx_x, batch_size, labels)
X_next.append(curr_X_next)
Y_next.append(curr_Y_next)
family_lbls.append(labels_next)
else:
# approximation result is not enough to propose all candidates
# so propose all result as candidates, and propose others from buffer
# NOTE: may consider re-expanding manifolds to produce more approximation result, but may not be necessary
X_next.append(approx_x)
Y_next.append(approx_y)
family_lbls.extend(labels)
remain_batch_size = batch_size - len(approx_x)
buffer_xs, buffer_ys = self.buffer.flattened()
buffer_xs, buffer_ys = normalization.undo(buffer_xs, buffer_ys)
prop_X_next, prop_Y_next = propose_next_batch_without_label(
curr_pfront, ref_point, buffer_ys, buffer_xs,
remain_batch_size)
X_next.append(prop_X_next)
Y_next.append(prop_Y_next)
family_lbls.extend(np.full(remain_batch_size, -1))
X_next = np.vstack(X_next)
Y_next = np.vstack(Y_next)
return X_next, Y_next, family_lbls
def get_sparse_front(self, normalization):
'''
Get sparse approximation of Pareto front and set
'''
approx_x, approx_y = normalization.undo(self.approx_set,
self.approx_front)
labels = self.fam_lbls
return labels, approx_x, approx_y
def _finalize(self):
# set population as all samples in performance buffer
pop_x, pop_y = self.buffer.flattened()
self.pop = self.pop.new('X', pop_x, 'F', pop_y)
# get sparse front approximation
self.fam_lbls, self.approx_set, self.approx_front = self.buffer.sparse_approximation(
)
class PSO(Algorithm):
def __init__(self,
pop_size=20,
w=0.9,
c1=2.0,
c2=2.0,
sampling=LatinHypercubeSampling(),
adaptive=True,
pertube_best=True,
display=PSODisplay(),
repair=None,
individual=Individual(),
**kwargs):
"""
Parameters
----------
pop_size : {pop_size}
sampling : {sampling}
"""
super().__init__(display=display, **kwargs)
self.initialization = Initialization(sampling,
individual=individual,
repair=repair)
self.pop_size = pop_size
self.adaptive = adaptive
self.pertube_best = pertube_best
self.default_termination = SingleObjectiveDefaultTermination()
self.V_max = None
self.w = w
self.c1 = c1
self.c2 = c2
def initialize(self, problem, **kwargs):
super().initialize(problem, **kwargs)
self.V_max = 0.2 * (problem.xu - problem.xl)
def _initialize(self):
pop = self.initialization.do(self.problem,
self.pop_size,
algorithm=self)
self.evaluator.eval(self.problem, pop, algorithm=self)
if self.pertube_best:
pop = FitnessSurvival().do(self.problem, pop, self.pop_size - 1)
pop.set("V", np.zeros((len(pop), self.problem.n_var)))
pop.set("pbest", pop)
self.pop = pop
self.f = None
self.strategy = None
def _next(self):
self._step()
if self.adaptive:
self._adapt()
def _step(self):
pop = self.pop
X, F, V = pop.get("X", "F", "V")
# get the personal best of each particle
pbest = Population.create(*pop.get("pbest"))
P_X, P_F = pbest.get("X", "F")
# get the global best solution
best = self.opt.repeat(len(pop))
G_X = best.get("X")
# perform the pso equation
inerta = self.w * V
# calculate random values for the updates
r1 = np.random.random((len(pop), self.problem.n_var))
r2 = np.random.random((len(pop), self.problem.n_var))
cognitive = self.c1 * r1 * (P_X - X)
social = self.c2 * r2 * (G_X - X)
# calculate the velocity vector
_V = inerta + cognitive + social
_V = repair_out_of_bounds_manually(_V, -self.V_max, self.V_max)
# update the values of each particle
_X = X + _V
_X = repair_out_of_bounds(self.problem, _X)
# evaluate the offspring population
off = Population(len(pop)).set("X", _X, "V", _V, "pbest", pbest)
self.evaluator.eval(self.problem, off, algorithm=self)
# check whether a solution has improved or not - also consider constraints here
has_improved = ImprovementReplacement().do(self.problem,
pbest,
off,
return_indices=True)
# replace the personal best of each particle if it has improved
off[has_improved].set("pbest", off[has_improved])
off.set("best", best)
pop = off
# try to improve the current best with a pertubation
if self.pertube_best:
opt = FitnessSurvival().do(self.problem,
Population.create(*pop.get("pbest")), 1)
eta = int(np.random.uniform(5, 30))
mutant = PolynomialMutation(eta).do(self.problem, opt)
self.evaluator.eval(self.problem, mutant, algorithm=self)
if ImprovementReplacement().do(self.problem,
opt,
mutant,
return_indices=True)[0]:
k = [i for i, e in enumerate(pop.get("pbest")) if e == opt][0]
pop[k].set("pbest", mutant)
self.pop = pop
def _adapt(self):
pop = self.pop
X, F, best = pop.get("X", "F", "best")
best = Population.create(*best)
w, c1, c2, = self.w, self.c1, self.c2
# get the average distance from one to another for normalization
D = norm_eucl_dist(self.problem, X, X)
mD = D.sum(axis=1) / (len(pop) - 1)
_min, _max = mD.min(), mD.max()
# get the average distance to the global best
g_D = norm_euclidean_distance(self.problem)(best.get("X"), X).mean()
f = (g_D - _min) / (_max - _min + 1e-32)
S = np.array([
S1_exploration(f),
S2_exploitation(f),
S3_convergence(f),
S4_jumping_out(f)
])
strategy = S.argmax() + 1
delta = 0.05 + (np.random.random() * 0.05)
if strategy == 1:
c1 += delta
c2 -= delta
elif strategy == 2:
c1 += 0.5 * delta
c2 -= 0.5 * delta
elif strategy == 3:
c1 += 0.5 * delta
c2 += 0.5 * delta
elif strategy == 4:
c1 -= delta
c2 += delta
c1 = max(1.5, min(2.5, c1))
c2 = max(1.5, min(2.5, c2))
if c1 + c2 > 4.0:
c1 = 4.0 * (c1 / (c1 + c2))
c2 = 4.0 * (c2 / (c1 + c2))
w = 1 / (1 + 1.5 * np.exp(-2.6 * f))
self.f = f
self.strategy = strategy
self.c1 = c1
self.c2 = c2
self.w = w
def _set_optimum(self, force=False):
pbest = Population.create(*self.pop.get("pbest"))
self.opt = filter_optimum(pbest, least_infeasible=True)
class CuckooSearch(Algorithm):
def __init__(self,
display=CSDisplay(),
sampling=FloatRandomSampling(),
survival=FitnessSurvival(),
eliminate_duplicates=DefaultDuplicateElimination(),
termination=SingleObjectiveDefaultTermination(),
pop_size=100,
beta=1.5,
alfa=0.01,
pa=0.35,
**kwargs):
"""
Parameters
----------
display : {display}
sampling : {sampling}
survival : {survival}
eliminate_duplicates: This does not exists in the original paper/book.
Without this the solutions might get too biased to current global best solution,
because the global random walk use the global best solution as the reference.
termination : {termination}
pop_size : The number of nests (solutions)
beta : The input parameter of the Mantegna's Algorithm to simulate
sampling on Levy Distribution
alfa : alfa is the step size scaling factor and is usually
0.01, so that the step size will be scaled down to O(L/100) with L is
the scale (range of bounds) of the problem.
pa : The switch probability, pa fraction of the nests will be
abandoned on every iteration
"""
super().__init__(**kwargs)
self.initialization = Initialization(sampling)
self.survival = survival
self.display = display
self.pop_size = pop_size
self.default_termination = termination
self.eliminate_duplicates = eliminate_duplicates
#the scale will be multiplied by problem scale after problem given in setup
self.alfa = alfa
self.scale = alfa
self.pa = pa
self.beta = beta
a = math.gamma(1. + beta) * math.sin(math.pi * beta / 2.)
b = beta * math.gamma((1. + beta) / 2.) * 2**((beta - 1.) / 2)
self.sig = (a / b)**(1. / (2 * beta))
def setup(self, problem, **kwargs):
super().setup(problem, **kwargs)
x_lower, x_upper = self.problem.bounds()
if x_lower is not None and x_upper is not None:
self.scale = self.alfa * (x_upper - x_lower)
else:
self.scale = self.alfa
def _initialize(self):
pop = self.initialization.do(
self.problem,
self.pop_size,
algorithm=self,
eliminate_duplicates=self.eliminate_duplicates)
self.evaluator.eval(self.problem, pop, algorithm=self)
if self.survival:
pop = self.survival.do(self.problem, pop, len(pop), algorithm=self)
self.pop = pop
def _next(self):
self._step()
def _get_levy_step(self, shape):
#Mantegna's algorithm simulating levy sampling
U = np.random.normal(0, self.sig, shape)
V = abs(np.random.normal(0, 1, shape))**(1. / self.beta)
return U / V
def _get_global_step_size(self, X):
step = self._get_levy_step(X.shape)
step_size = self.scale * step
return step_size
def _get_local_directional_vector(self, X):
#local random walk (abandon nest) for pa fraction of the nests
#find 2 random different solution for the local random walk (nest_i ~ nest_i+ (nest_j - nest_k))
Xjk_idx = np.random.rand(len(X), len(X)).argpartition(2, axis=1)[:, :2]
Xj_idx = Xjk_idx[:, 0]
Xk_idx = Xjk_idx[:, 1]
Xj = X[Xj_idx]
Xk = X[Xk_idx]
#calculate Heaviside function (or wether local search will be done with nest_i or not)
#then duplicate H coloumn as many as the number of decision variable
H = (np.random.rand(len(X)) < self.pa).astype(np.float)
H = np.tile(H, (self.problem.n_var, 1)).transpose()
#calculate d (scale*(X_j - X_k)) , however XS Yang implementation in mathworks differ from the book
#replacing the scale with a random number [0,1], we use the book version here (a0)
dir_vec = np.random.rand(*X.shape) * (Xj - Xk) * H
return dir_vec
def _step(self):
pop = self.pop
X = pop.get("X")
F = pop.get("F")
#Levy Flight
best = self.opt
G_X = best.get("X")
step_size = self._get_global_step_size(X)
_X = X + np.random.rand(*X.shape) * step_size * (G_X - X)
_X = set_to_bounds_if_outside_by_problem(self.problem, _X)
#Evaluate
off = Population(len(pop)).set("X", _X)
self.evaluator.eval(self.problem, off, algorithm=self)
# replace the worse pop with better off per index
# this method includes replacement with less constraints violation
# which the original paper doesn't have
ImprovementReplacement().do(self.problem, pop, off, inplace=True)
#Local Random Walk
dir_vec = self._get_local_directional_vector(X)
_X = X + dir_vec
_X = set_to_bounds_if_outside_by_problem(self.problem, _X)
off = Population(len(pop)).set("X", _X)
self.evaluator.eval(self.problem, off, algorithm=self)
#append offspring to population and then sort for elitism (survival)
self.pop = Population.merge(pop, off)
self.pop = self.survival.do(self.problem,
self.pop,
self.pop_size,
algorithm=self)
class MMGA(Algorithm):
def __init__(self,
pop_size=200,
n_parallel=10,
sampling=LatinHypercubeSampling(),
display=SingleObjectiveDisplay(),
repair=None,
individual=Individual(),
**kwargs):
"""
Parameters
----------
pop_size : {pop_size}
sampling : {sampling}
selection : {selection}
crossover : {crossover}
mutation : {mutation}
eliminate_duplicates : {eliminate_duplicates}
n_offsprings : {n_offsprings}
"""
super().__init__(display=display, **kwargs)
self.initialization = Initialization(sampling,
individual=individual,
repair=repair)
self.pop_size = pop_size
self.n_parallel = n_parallel
self.each_pop_size = pop_size // n_parallel
self.solvers = None
self.niches = []
def cmaes(problem, x):
solver = CMAES(x0=x, tolfun=1e-11, tolx=1e-3, restarts=0)
solver.initialize(problem)
solver.next()
return solver
def nelder_mead(problem, x):
solver = NelderMead(X=x)
solver.initialize(problem)
solver._initialize()
solver.n_gen = 1
solver.next()
return solver
self.func_create_solver = nelder_mead
self.default_termination = SingleObjectiveDefaultTermination()
def _initialize(self):
self.pop = self.initialization.do(self.problem,
self.pop_size,
algorithm=self)
self.evaluator.eval(self.problem, self.pop, algorithm=self)
X = self.pop.get("X")
D = norm_eucl_dist(self.problem, X, X)
S = select_by_clearing(self.pop, D, self.n_parallel,
func_select_by_objective)
self.solvers = []
for s in S:
solver = self.func_create_solver(self.problem, self.pop[s].X)
self.solvers.append(solver)
def _next(self):
n_evals = np.array(
[solver.evaluator.n_eval for solver in self.solvers])
ranks = np.array([solver.opt[0].F[0]
for solver in self.solvers]).argsort() + 1
rws = RouletteWheelSelection(ranks, larger_is_better=False)
S = rws.next()
self.solvers[S].next()
print(n_evals.sum(), n_evals)
if self.solvers[S].termination.force_termination or self.solvers[
S].termination.has_terminated(self.solvers[S]):
self.niches.append(self.solvers[S])
print(self.solvers[S].opt.get("F"), self.solvers[S].opt.get("X"))
self.solvers[S] = None
for k in range(self.n_parallel):
if self.solvers[k] is None:
x = FloatRandomSampling().do(self.problem, 1)[0].get("X")
self.solvers[S] = self.func_create_solver(self.problem, x)
def _set_optimum(self, force=False):
self.opt = Population()
for solver in self.niches:
self.opt = Population.merge(self.opt, solver.opt)
class RandomAlgorithm(Algorithm):
def __init__(self,
pop_size=None,
sampling=None,
eliminate_duplicates=DefaultDuplicateElimination(),
individual=Individual(),
**kwargs
):
super().__init__(**kwargs)
# the population size used
self.pop_size = pop_size
# number of offsprings
self.n_offsprings = pop_size
# the object to be used to represent an individual - either individual or derived class
self.individual = individual
# set the duplicate detection class - a boolean value chooses the default duplicate detection
if isinstance(eliminate_duplicates, bool):
if eliminate_duplicates:
self.eliminate_duplicates = DefaultDuplicateElimination()
else:
self.eliminate_duplicates = NoDuplicateElimination()
else:
self.eliminate_duplicates = eliminate_duplicates
# simply set the no repair object if it is None
self.repair = NoRepair()
self.initialization = Initialization(sampling,
individual=individual,
repair=self.repair,
eliminate_duplicates=self.eliminate_duplicates)
self.n_gen = None
self.pop = None
self.off = None
def _initialize(self):
# create the initial population
pop = self.initialization.do(self.problem, self.pop_size, algorithm=self)
pop.set("n_gen", self.n_gen)
# then evaluate using the objective function
self.evaluator.eval(self.problem, pop, algorithm=self)
self.pop, self.off = pop, pop
def _next(self):
# sampling again
self.off = self.initialization.do(self.problem, self.pop_size, algorithm=self)
self.off.set("n_gen", self.n_gen)
# evaluate the offspring
self.evaluator.eval(self.problem, self.off, algorithm=self)
self.pop = self.off