def payoff_table_method_general(
objective_evaluator: Callable[[np.ndarray], np.ndarray],
n_of_objectives: int,
variable_bounds: np.ndarray,
constraint_evaluator: Optional[Callable[[np.ndarray], np.ndarray]] = None,
initial_guess: Optional[np.ndarray] = None,
solver_method: Optional[Union[ScalarMethod, str]] = "scipy_de",
) -> Tuple[np.ndarray, np.ndarray]:
"""Solves a representation for the nadir and ideal points for a
multiobjective minimization problem with objectives defined as the result
of some objective evaluator.
Args:
objective_evaluator (Callable[[np.ndarray], np.ndarray]): The
evaluator which returns the objective values given a set of
variabels.
n_of_objectives (int): Number of objectives returned by calling
objective_evaluator.
variable_bounds (np.ndarray): The lower and upper bounds of the
variables passed as argument to objective_evaluator. Should be a 2D
numpy array with the limits for each variable being on each row. The
first column should contain the lower bounds, and the second column
the upper bounds. Use np.inf to indicate no bounds.
constraint_evaluator (Optional[Callable[[np.ndarray], np.ndarray]], optional):
An evaluator accepting the same arguments as
objective_evaluator, which returns the constraint values of the
multiobjective minimization problem being solved. A negative
constraint value indicates a broken constraint. Defaults to None.
initial_guess (Optional[np.ndarray], optional): The initial guess
used for the variable values while solving the payoff table. The
relevancy of this parameter depends on the solver_method being used.
Defaults to None.
solver_method (Optional[Union[ScalarMethod, str]], optional): The
method to solve the scalarized problems in the payoff table method.
Defaults to "scipy_de", which ignores initial_guess.
Returns:
Tuple[np.ndarray, np.ndarray]: The representations computed using the
payoff table for the ideal and nadir points respectively.
"""
scalarizer = Scalarizer(
objective_evaluator,
weighted_scalarizer,
scalarizer_args={"ws": None},
)
solver = ScalarMinimizer(
scalarizer,
variable_bounds,
constraint_evaluator,
solver_method,
)
ws = np.eye(n_of_objectives)
po_table = np.zeros((n_of_objectives, n_of_objectives))
if initial_guess is None:
initial_guess = variable_bounds[:, 0]
for i in range(n_of_objectives):
scalarizer._scalarizer_args = {"ws": ws[i]}
opt_res = solver.minimize(initial_guess)
if not opt_res["success"]:
print(
"Unsuccessful optimization result encountered while computing a payoff table!"
)
po_table[i] = objective_evaluator(opt_res["x"])
ideal = np.diag(po_table)
nadir = np.max(po_table, axis=0)
return ideal, nadir
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)],
)