def solve_nautilus_asf_problem(
self,
pareto_f: np.ndarray,
subset_indices: [int],
ref_point: np.ndarray,
ideal: np.ndarray,
nadir: np.ndarray,
) -> int:
"""Forms and solves the achievement scalarizing function to find the
closesto point on the Pareto optimal front to the given reference
point.
Args:
pareto_f (np.ndarray): The whole Pareto optimal front.
subset_indices ([type]): Indices of the currently reachable solutions.
ref_point (np.ndarray): The reference point indicating a decision
maker's preference.
ideal (np.ndarray): Ideal point.
nadir (np.ndarray): Nadir point.
Returns:
int: Index of the closest point according the minimized value of the ASF.
"""
asf = PointMethodASF(nadir, ideal)
scalarizer = DiscreteScalarizer(asf, {"reference_point": ref_point})
solver = DiscreteMinimizer(scalarizer)
tmp = np.copy(pareto_f)
mask = np.zeros(tmp.shape[0], dtype=bool)
mask[subset_indices] = True
tmp[~mask] = np.nan
res = solver.minimize(tmp)
return res
def test_discrete_solver_with_con():
ideal = np.array([0, 0, 0, 0])
nadir = np.array([1, 1, 1, 1])
asf = PointMethodASF(nadir, ideal)
con = lambda x: x[:, 0] > 0.2
dscalarizer = DiscreteScalarizer(asf, {"reference_point": nadir})
dminimizer = DiscreteMinimizer(dscalarizer, constraint_evaluator=con)
non_dominated_points = np.array([
[0.2, 0.4, 0.6, 0.8],
[0.4, 0.2, 0.6, 0.8],
[0.6, 0.4, 0.2, 0.8],
[0.4, 0.8, 0.6, 0.2],
])
# first occurrence with first point invalid
res_ind = dminimizer.minimize(non_dominated_points)
assert res_ind == 1
# first point as closest, but invalid
dscalarizer._scalarizer_args = {
"reference_point": np.array([0.2, 0.4, 0.6, 0.8])
}
res_ind = dminimizer.minimize(non_dominated_points)
assert res_ind == 1
# all points invalid
dminimizer._constraint_evaluator = lambda x: x[:, 0] > 1.0
with pytest.raises(ScalarSolverException):
_ = dminimizer.minimize(non_dominated_points)
def test_discrete_solver():
ideal = np.array([0, 0, 0, 0])
nadir = np.array([1, 1, 1, 1])
asf = PointMethodASF(nadir, ideal)
dscalarizer = DiscreteScalarizer(asf, {"reference_point": nadir})
dminimizer = DiscreteMinimizer(dscalarizer)
non_dominated_points = np.array([
[0.2, 0.4, 0.6, 0.8],
[0.4, 0.2, 0.6, 0.8],
[0.6, 0.4, 0.2, 0.8],
[0.4, 0.8, 0.6, 0.2],
])
# first occurrence
res_ind = dminimizer.minimize(non_dominated_points)
assert res_ind == 0
dscalarizer._scalarizer_args = {
"reference_point": np.array([0.6, 0.4, 0.2, 0.8])
}
res_ind = dminimizer.minimize(non_dominated_points)
assert res_ind == 2
def test_scalarizer_asf():
asf = PointMethodASF(np.array([10, 10, 10]), np.array([-10, -10, -10]))
ref = np.atleast_2d([1, 5, 2.5])
scalarizer = Scalarizer(
simple_vector_valued_fun, asf, scalarizer_args={"reference_point": ref}
)
res = scalarizer.evaluate(np.atleast_2d([2, 1, 1, 1]))
assert np.allclose(res, 0.1000002)
def solve_nautilus_asf_problem(
pareto_f: np.ndarray,
subset_indices: List[int],
ref_point: np.ndarray,
ideal: np.ndarray,
nadir: np.ndarray,
user_bounds: np.ndarray,
) -> int:
"""Forms and solves the achievement scalarizing function to find the
closest point on the Pareto optimal front to the given reference
point.
Args:
pareto_f (np.ndarray): The whole Pareto optimal front.
subset_indices ([type]): Indices of the currently reachable solutions.
ref_point (np.ndarray): The reference point indicating a decision
maker's preference.
ideal (np.ndarray): Ideal point.
nadir (np.ndarray): Nadir point.
user_bounds (np.ndarray): Bounds given by the user (the DM) for each objective,which should not be
exceeded. A 1D array where NaN's indicate 'no bound is given' for the respective objective value.
Returns:
int: Index of the closest point according the minimized value of the ASF.
"""
asf = PointMethodASF(nadir, ideal)
scalarizer = DiscreteScalarizer(asf, {"reference_point": ref_point})
solver = DiscreteMinimizer(scalarizer)
# Copy the front and filter out the reachable solutions.
# If user bounds are given, filter out solutions outside the those bounds.
# Infeasible solutions on the pareto font are set to be NaNs.
tmp = np.copy(pareto_f)
mask = np.zeros(tmp.shape[0], dtype=bool)
mask[subset_indices] = True
tmp[~mask] = np.nan
# indices of solutions with one or more objective value exceeding the user bounds.
bound_mask = np.any(tmp > user_bounds, axis=1)
tmp[bound_mask] = np.nan
res = solver.minimize(tmp)
return res["x"]
if np.all(bad_con_mask):
raise ScalarSolverException(
"None of the supplied vectors adhere to the given "
"constraint function.")
tmp = np.copy(vectors)
tmp[bad_con_mask] = np.nan
return np.nanargmin(self._scalarizer(tmp))
if __name__ == "__main__":
from desdeo_tools.scalarization.ASF import PointMethodASF
ideal = np.array([0, 0, 0, 0])
nadir = np.array([1, 1, 1, 1])
asf = PointMethodASF(nadir, ideal)
dscalarizer = DiscreteScalarizer(asf, {"reference_point": None})
dminimizer = DiscreteMinimizer(dscalarizer)
non_dominated_points = np.array([[0.2, 0.4, 0.6,
0.8], [0.4, 0.2, 0.6, 0.8],
[0.6, 0.4, 0.2, 0.8],
[0.4, 0.8, 0.6, 0.2]])
z = np.array([0.4, 0.2, 0.6, 0.8])
dscalarizer._scalarizer_args = {"reference_point": z}
print(asf(non_dominated_points, reference_point=z))
res = dminimizer.minimize(non_dominated_points)
def calculate_new_solutions(
self,
number_of_solutions: int,
levels: np.ndarray,
improve_inds: np.ndarray,
improve_until_inds: np.ndarray,
acceptable_inds: np.ndarray,
impaire_until_inds: np.ndarray,
free_inds: np.ndarray,
) -> Tuple[NimbusSaveRequest, SimplePlotRequest]:
"""Calcualtes new solutions based on classifications supplied by the decision maker by
solving ASF problems.
Args:
number_of_solutions (int): Number of solutions, should be between 1 and 4.
levels (np.ndarray): Aspiration and upper bounds relevant to the some of the classifications.
improve_inds (np.ndarray): Indices corresponding to the objectives which should be improved.
improve_until_inds (np.ndarray): Like above, but improved until an aspiration level is reached.
acceptable_inds (np.ndarray): Indices of objectives which are acceptable as they are now.
impaire_until_inds (np.ndarray): Indices of objectives which may be impaired until an upper limit is
reached.
free_inds (np.ndarray): Indices of objectives which may change freely.
Returns:
Tuple[NimbusSaveRequest, SimplePlotRequest]: A save request with the newly computed soutions, and
a plot request to visualize said solutions.
"""
results = []
# always computed
asf_1 = MaxOfTwoASF(self._nadir, self._ideal, improve_inds,
improve_until_inds)
def cons_1(
x: np.ndarray,
f_current: np.ndarray = self._current_objectives,
levels: np.ndarray = levels,
improve_until_inds: np.ndarray = improve_until_inds,
improve_inds: np.ndarray = improve_inds,
impaire_until_inds: np.ndarray = impaire_until_inds,
):
f = self._problem.evaluate(x).objectives.squeeze()
res_1 = f_current[improve_inds] - f[improve_inds]
res_2 = f_current[improve_until_inds] - f[improve_until_inds]
res_3 = levels[impaire_until_inds] - f_current[impaire_until_inds]
res = np.hstack((res_1, res_2, res_3))
if self._problem.n_of_constraints > 0:
res_prob = self._problem.evaluate(x).constraints.squeeze()
return np.hstack((res_prob, res))
else:
return res
scalarizer_1 = Scalarizer(
lambda x: self._problem.evaluate(x).objectives,
asf_1,
scalarizer_args={"reference_point": levels},
)
solver_1 = ScalarMinimizer(
scalarizer_1,
self._problem.get_variable_bounds(),
cons_1,
method=self._scalar_method,
)
res_1 = solver_1.minimize(self._current_solution)
results.append(res_1)
if number_of_solutions > 1:
# create the reference point needed in the rest of the ASFs
z_bar = np.zeros(self._problem.n_of_objectives)
z_bar[improve_inds] = self._ideal[improve_inds]
z_bar[improve_until_inds] = levels[improve_until_inds]
z_bar[acceptable_inds] = self._current_objectives[acceptable_inds]
z_bar[impaire_until_inds] = levels[impaire_until_inds]
z_bar[free_inds] = self._nadir[free_inds]
# second ASF
asf_2 = StomASF(self._ideal)
# cons_2 can be used in the rest of the ASF scalarizations, it's not a bug!
if self._problem.n_of_constraints > 0:
cons_2 = lambda x: self._problem.evaluate(
x).constraints.squeeze()
else:
cons_2 = None
scalarizer_2 = Scalarizer(
lambda x: self._problem.evaluate(x).objectives,
asf_2,
scalarizer_args={"reference_point": z_bar},
)
solver_2 = ScalarMinimizer(
scalarizer_2,
self._problem.get_variable_bounds(),
cons_2,
method=self._scalar_method,
)
res_2 = solver_2.minimize(self._current_solution)
results.append(res_2)
if number_of_solutions > 2:
# asf 3
asf_3 = PointMethodASF(self._nadir, self._ideal)
scalarizer_3 = Scalarizer(
lambda x: self._problem.evaluate(x).objectives,
asf_3,
scalarizer_args={"reference_point": z_bar},
)
solver_3 = ScalarMinimizer(
scalarizer_3,
self._problem.get_variable_bounds(),
cons_2,
method=self._scalar_method,
)
res_3 = solver_3.minimize(self._current_solution)
results.append(res_3)
if number_of_solutions > 3:
# asf 4
asf_4 = AugmentedGuessASF(self._nadir, self._ideal, free_inds)
scalarizer_4 = Scalarizer(
lambda x: self._problem.evaluate(x).objectives,
asf_4,
scalarizer_args={"reference_point": z_bar},
)
solver_4 = ScalarMinimizer(
scalarizer_4,
self._problem.get_variable_bounds(),
cons_2,
method=self._scalar_method,
)
res_4 = solver_4.minimize(self._current_solution)
results.append(res_4)
# create the save request
solutions = [res["x"] for res in results]
objectives = [
self._problem.evaluate(x).objectives.squeeze() for x in solutions
]
save_request = NimbusSaveRequest(solutions, objectives)
msg = "Computed new solutions."
plot_request = self.create_plot_request(objectives, msg)
return save_request, plot_request
def compute_intermediate_solutions(
self,
solutions: np.ndarray,
n_desired: int,
) -> Tuple[NimbusSaveRequest, SimplePlotRequest]:
"""Computs intermediate solution between two solutions computed earlier.
Args:
solutions (np.ndarray): The solutions between which the intermediat solutions should
be computed.
n_desired (int): The number of intermediate solutions desired.
Raises:
NimbusException
Returns:
Tuple[NimbusSaveRequest, SimplePlotRequest]: A save request with the compured intermediate
points, and a plot request to visualize said points.
"""
# vector between the two solutions
between = solutions[0] - solutions[1]
norm = np.linalg.norm(between)
between_norm = between / norm
# the plus 2 assumes we are interested only in n_desired points BETWEEN the
# two supplied solutions
step_size = norm / (2 + n_desired)
intermediate_points = np.array([
solutions[1] + i * step_size * between_norm
for i in range(1, n_desired + 1)
])
# project each of the intermediate solutions to the Pareto front
intermediate_solutions = np.zeros(intermediate_points.shape)
intermediate_objectives = np.zeros(
(n_desired, self._problem.n_of_objectives))
asf = PointMethodASF(self._nadir, self._ideal)
for i in range(n_desired):
scalarizer = Scalarizer(
lambda x: self._problem.evaluate(x).objectives,
asf,
scalarizer_args={
"reference_point":
self._problem.evaluate(intermediate_points[i]).objectives
},
)
if self._problem.n_of_constraints > 0:
cons = lambda x: self._problem.evaluate(x).constraints.squeeze(
)
else:
cons = None
solver = ScalarMinimizer(
scalarizer,
self._problem.get_variable_bounds(),
cons,
method=self._scalar_method,
)
res = solver.minimize(self._current_solution)
intermediate_solutions[i] = res["x"]
intermediate_objectives[i] = self._problem.evaluate(
res["x"]).objectives
# create appropiate requests
save_request = NimbusSaveRequest(list(intermediate_solutions),
list(intermediate_objectives))
msg = "Computed intermediate solutions"
plot_request = self.create_plot_request(intermediate_objectives, msg)
return save_request, plot_request
def solve_pareto_front_representation_general(
objective_evaluator: Callable[[np.ndarray], np.ndarray],
n_of_objectives: int,
variable_bounds: np.ndarray,
step: Optional[Union[np.ndarray, float]] = 0.1,
eps: Optional[float] = 1e-6,
ideal: Optional[np.ndarray] = None,
nadir: Optional[np.ndarray] = None,
constraint_evaluator: Optional[Callable[[np.ndarray], np.ndarray]] = None,
solver_method: Optional[Union[ScalarMethod, str]] = "scipy_de",
) -> Tuple[np.ndarray, np.ndarray]:
"""Computes a representation of a Pareto efficient front from a
multiobjective minimizatino problem. Does so by generating an evenly spaced
set of reference points (in the objective space), in the space spanned by
the supplied ideal and nadir points. The generated reference points are
then used to formulate achievement scalaraization problems, which when
solved, yield a representation of a Pareto efficient solution. The result
is guaranteed to contain only non-dominated solutions.
Args:
objective_evaluator (Callable[[np.ndarray], np.ndarray]): A vector
valued function returning objective values given an array of decision
variables.
n_of_objectives (int): Numbr of objectives returned by
objective_evaluator.
variable_bounds (np.ndarray): The upper and lower bounds of the
decision variables. Bound for each variable should be on the rows,
with the first column containing lower bounds, and the second column
upper bounds. Use np.inf to indicate no bounds.
step (Optional[Union[np.ndarray, float]], optional): Etiher an float
or an array of floats. If a single float is given, generates
reference points with the objectives having values a step apart
between the ideal and nadir points. If an array of floats is given,
use the steps defined in the array for each objective's values.
Default to 0.1.
eps (Optional[float], optional): An offset to be added to the nadir
value to keep the nadir inside the range when generating reference
points. Defaults to 1e-6.
ideal (Optional[np.ndarray], optional): The ideal point of the
problem being solved. Defaults to None.
nadir (Optional[np.ndarray], optional): The nadir point of the
problem being solved. Defaults to None.
constraint_evaluator (Optional[Callable[[np.ndarray], np.ndarray]], optional):
An evaluator returning values for the constraints defined
for the problem. A negative value for a constraint indicates a breach
of that constraint. Defaults to None.
solver_method (Optional[Union[ScalarMethod, str]], optional): The
method used to minimize the achievement scalarization problems
arising when calculating Pareto efficient solutions. Defaults to
"scipy_de".
Raises:
MCDMUtilityException: Mismatching sizes of the supplied ideal and
nadir points between the step, when step is an array. Or the type of
step is something else than np.ndarray of float.
Returns:
Tuple[np.ndarray, np.ndarray]: A tuple containing representationns of
the Pareto optimal variable values, and the corresponsing objective
values.
Note:
The objective evaluator should be defined such that minimization is
expected in each of the objectives.
"""
if ideal is None or nadir is None:
# compure ideal and nadir using payoff table
ideal, nadir = payoff_table_method_general(
objective_evaluator,
n_of_objectives,
variable_bounds,
constraint_evaluator,
)
# use ASF to (almost) guarantee Pareto optimality.
asf = PointMethodASF(nadir, ideal)
scalarizer = Scalarizer(objective_evaluator,
asf,
scalarizer_args={"reference_point": None})
solver = ScalarMinimizer(scalarizer,
bounds=variable_bounds,
method=solver_method)
# bounds to be used to compute slices
stacked = np.stack((ideal, nadir)).T
lower_slice_b, upper_slice_b = np.min(stacked, axis=1), np.max(stacked,
axis=1)
if type(step) is float:
slices = [
slice(start, stop + eps, step)
for (start, stop) in zip(lower_slice_b, upper_slice_b)
]
elif type(step) is np.ndarray:
if not ideal.shape == nadir.shape == step.shape:
raise MCDMUtilityException(
"The shapes of the supplied step array does not match the "
"shape of the ideal and nadir points.")
slices = [
slice(start, stop + eps, s)
for (start, stop, s) in zip(lower_slice_b, upper_slice_b, step)
]
else:
raise MCDMUtilityException(
"step must be either a numpy array or an float.")
z_mesh = np.mgrid[slices].reshape(len(ideal), -1).T
p_front_objectives = np.zeros(z_mesh.shape)
p_front_variables = np.zeros(
(len(p_front_objectives), len(variable_bounds.squeeze())))
for i, z in enumerate(z_mesh):
scalarizer._scalarizer_args = {"reference_point": z}
res = solver.minimize(None)
if not res["success"]:
print("Non successfull optimization")
p_front_objectives[i] = np.nan
p_front_variables[i] = np.nan
continue
# check for dominance, accept only non-dominated solutions
f_i = objective_evaluator(res["x"])
if not np.all(f_i > p_front_objectives[:i]
[~np.all(np.isnan(p_front_objectives[:i]), axis=1)]):
p_front_objectives[i] = f_i
p_front_variables[i] = res["x"]
elif i < 1:
p_front_objectives[i] = f_i
p_front_variables[i] = res["x"]
else:
p_front_objectives[i] = np.nan
p_front_variables[i] = np.nan
return (
p_front_variables[~np.all(np.isnan(p_front_variables), axis=1)],
p_front_objectives[~np.all(np.isnan(p_front_objectives), axis=1)],
)
dscalarizer = DiscreteScalarizer(lambda x: np.sum(x, axis=1))
res_1d = dscalarizer(vector)
assert np.array_equal(res_1d, [6.0])
def test_discrete_args():
vectors = np.array([[1, 1, 1], [2, 2, 2], [4, 5, 6.0]])
dscalarizer = DiscreteScalarizer(
lambda x, a=1: a * np.sum(x, axis=1), scalarizer_args={"a": 2}
)
res = dscalarizer(vectors)
assert np.array_equal(res, [6, 12, 30])
if __name__ == "__main__":
asf = PointMethodASF(np.array([10, 10, 10]), np.array([-10, -10, -10]))
ref = np.atleast_2d([2.5, 2.5, 2.5])
scalarizer = Scalarizer(
simple_vector_valued_fun, asf, scalarizer_args={"reference_point": ref}
)
res = scalarizer.evaluate(np.atleast_2d([2, 1, 1, 1]))
print(res)
asf.nadir = np.array([9, 9, 9])
res = scalarizer.evaluate(np.atleast_2d([2, 1, 1, 1]))
print(res)