def payoff_table_method(
problem: MOProblem,
initial_guess: Optional[np.ndarray] = None,
solver_method: Optional[Union[ScalarMethod, str]] = "scipy_de",
) -> Tuple[np.ndarray, np.ndarray]:
"""Uses the payoff table method to solve for the ideal and nadir points of a MOProblem.
Call through to payoff_table_method_general.
Args:
problem (MOProblem): The problem defined as a MOProblem class instance.
initial_guess (Optional[np.ndarray]): The initial guess of decision variables
to be used in the solver. If None, uses the lower bounds defined for
the variables in MOProblem. Defaults to None.
solver_method (Optional[Union[ScalarMethod, str]]): The method used to minimize the
invidual problems in the payoff table method. Defaults to 'scipy_de'.
Returns:
Tuple[np.ndarray, np.ndarray]: The ideal and nadir points
"""
if problem.n_of_constraints > 0:
constraints = lambda x: problem.evaluate(x).constraints.squeeze()
else:
constraints = None
return payoff_table_method_general(
lambda xs: problem.evaluate(xs).objectives,
problem.n_of_objectives,
problem.get_variable_bounds(),
constraints,
initial_guess,
solver_method,
)
def solve_pareto_front_representation(
problem: MOProblem,
step: Optional[Union[np.ndarray, float]] = 0.1,
eps: Optional[float] = 1e-6,
solver_method: Optional[Union[ScalarMethod, str]] = "scipy_de",
) -> Tuple[np.ndarray, np.ndarray]:
"""Pass through to solve_pareto_front_representation_general when the
problem for which the front is being calculated for is defined as an
MOProblem object.
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.
Args:
problem (MOProblem): The multiobjective minimization problem for which the front is to be solved for.
step (Optional[Union[np.ndarray, float]], optional): Either a 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.
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".
Returns:
Tuple[np.ndarray, np.ndarray]: A tuple containing representations of
the Pareto optimal variable values, and the corresponsing objective
values.
"""
if problem.n_of_constraints > 0:
constraints = lambda x: problem.evaluate(x).constraints.squeeze()
else:
constraints = None
var_values, obj_values = solve_pareto_front_representation_general(
lambda x: problem.evaluate(x).objectives,
problem.n_of_objectives,
problem.get_variable_bounds(),
step,
eps,
problem.ideal * problem._max_multiplier,
problem.nadir * problem._max_multiplier,
constraints,
solver_method,
)
return var_values, obj_values * problem._max_multiplier
def __init__( # parameters of the class
self,
problem: MOProblem,
scalarization_function: MOEADSF = Tchebycheff(),
n_neighbors: int = 20,
population_params: Dict = None,
initial_population: Population = None,
lattice_resolution: int = None,
use_repair: bool = True,
n_parents: int = 2,
a_priori: bool = False,
interact: bool = False,
use_surrogates: bool = False,
n_iterations: int = 10,
n_gen_per_iter: int = 100,
total_function_evaluations: int = 0,
):
super().__init__( # parameters for decomposition based approach
problem=problem,
population_size=None,
population_params=population_params,
initial_population=initial_population,
lattice_resolution=lattice_resolution,
a_priori=a_priori,
interact=interact,
use_surrogates=use_surrogates,
n_iterations=n_iterations,
n_gen_per_iter=n_gen_per_iter,
total_function_evaluations=total_function_evaluations,
)
self.population_size = self.population.pop_size
self.problem = problem
self.scalarization_function = scalarization_function
self.n_neighbors = n_neighbors
self.use_repair = use_repair
self.n_parents = n_parents
self.population.mutation = BP_mutation(
problem.get_variable_lower_bounds(),
problem.get_variable_upper_bounds(),
0.5,
20,
)
self.population.recombination = SBX_xover(1.0, 20)
selection_operator = MOEAD_select(self.population,
SF_type=self.scalarization_function)
self.selection_operator = selection_operator
# Compute the distance between each pair of reference vectors
distance_matrix_vectors = distance_matrix(
self.reference_vectors.values, self.reference_vectors.values)
# Get the closest vectors to obtain the neighborhoods
self.neighborhoods = np.argsort(distance_matrix_vectors,
axis=1,
kind="quicksort")[:, :n_neighbors]
self.population.update_ideal()
self._ideal_point = self.population.ideal_objective_vector
def __init__(self,
problem: MOProblem,
scalar_method: Optional[ScalarMethod] = None):
# check if ideal and nadir are defined
if problem.ideal is None or problem.nadir is None:
# TODO: use same method as defined in scalar_method
ideal, nadir = payoff_table_method(problem)
self._ideal = ideal
self._nadir = nadir
else:
self._ideal = problem.ideal
self._nadir = problem.nadir
self._scalar_method = scalar_method
# generate Pareto optimal starting point
asf = SimpleASF(np.ones(self._ideal.shape))
scalarizer = Scalarizer(
lambda x: problem.evaluate(x).objectives,
asf,
scalarizer_args={"reference_point": np.atleast_2d(self._ideal)},
)
if problem.n_of_constraints > 0:
_con_eval = lambda x: problem.evaluate(x).constraints.squeeze()
else:
_con_eval = None
solver = ScalarMinimizer(
scalarizer,
problem.get_variable_bounds(),
constraint_evaluator=_con_eval,
method=self._scalar_method,
)
# TODO: fix tools to check for scipy methods in general and delete me!
solver._use_scipy = True
res = solver.minimize(problem.get_variable_upper_bounds() / 2)
if res["success"]:
self._current_solution = res["x"]
self._current_objectives = problem.evaluate(
self._current_solution).objectives.squeeze()
self._archive_solutions = []
self._archive_objectives = []
self._state = "classify"
super().__init__(problem)
print(f"Loop {counter} of {total_count}")
counter += 1
# build problem
var_names = ["x" + str(i + 1) for i in range(n_var)]
obj_names = ["f" + str(i + 1) for i in range(n_obj)]
prob = wfg_problem(
name=problem_name, n_of_objectives=n_obj, n_of_variables=n_var
)
variables = variable_builder(
names=var_names,
initial_values=prob.lower,
lower_bounds=prob.lower,
upper_bounds=prob.upper,
)
objective = VectorObjective(name=obj_names, evaluator=prob.eval)
problem = MOProblem([objective], variables, None)
problem.ideal = prob.ideal
problem.nadir = (
abs(np.random.normal(size=n_obj, scale=0.15)) + 1
) * prob.nadir
true_nadir = prob.nadir
scalar = asf(ideal=problem.ideal, nadir=true_nadir)
# a posteriori
a_post_rvea = RVEA(
problem=problem, interact=False, n_gen_per_iter=gen, n_iterations=4
)
a_post_nsga = NSGAIII(
problem=problem, interact=False, n_gen_per_iter=gen, n_iterations=4
objkaikki = VectorObjective("obj", objectives)
# variables
var_names = ["x1", "x2"
] # Make sure that the variable names are meaningful to you.
initial_values = np.array([0.5, 0.5])
lower_bounds = [0.3, 0.3]
upper_bounds = [1.0, 1.0]
bounds = np.stack((lower_bounds, upper_bounds))
variables = variable_builder(var_names, initial_values, lower_bounds,
upper_bounds)
# problem
prob = MOProblem(objectives=[obj1, obj2, obj3, obj4],
variables=variables) # objectives "seperately"
# solved in Nautilus.py
ideal = np.array([-6.34, -3.44487179, -7.5, 0])
nadir = np.array([-4.751, -2.86054116, -0.32111111, 9.70666666])
# start solving
method = ReferencePointMethod(problem=prob, ideal=ideal, nadir=nadir)
# Pareto optimal solution: [-6.30, -3.26, -2.60, 3.63]
print("Let's start solving\n")
req = method.start()
rp = np.array([-5.0, -3.0, -3.0, 5.0])
req.response = {
"reference_point": rp,
return (x[0] + x[1]) - 0.5
f1 = _ScalarObjective(name="f1", evaluator=f_1)
f2 = _ScalarObjective(name="f2", evaluator=f_2)
f3 = _ScalarObjective(name="f3", evaluator=f_3)
f4 = _ScalarObjective(name="f4", evaluator=f_4)
f5 = _ScalarObjective(name="f5", evaluator=f_5)
varsl = variable_builder(
["x_1", "x_2"],
initial_values=[0.5, 0.5],
lower_bounds=[0.3, 0.3],
upper_bounds=[1.0, 1.0],
)
c1 = ScalarConstraint("c1", 2, 5, evaluator=c_1)
problem = MOProblem(variables=varsl,
objectives=[f1, f2, f3, f4, f5],
constraints=[c1])
method = NIMBUS(problem, scalar_method="scipy_de")
reqs = method.request_classification()[0]
response = {}
response["classifications"] = ["<", "<=", "=", ">=", "0"]
response["levels"] = [-6, -3, -5, 8, 0.349]
response["number_of_solutions"] = 3
reqs.response = response
res_1 = method.iterate(reqs)[0]
res_1.response = {"indices": []}
res_2 = method.iterate(res_1)[0]
response = {}
def test_problem_builder(name: str,
n_of_variables: int = None,
n_of_objectives: int = None) -> MOProblem:
"""Build test problems. Currently supported: ZDT1-4, ZDT6, and DTLZ1-7.
Args:
name (str): Name of the problem in all caps. For example: "ZDT1", "DTLZ4", etc.
n_of_variables (int, optional): Number of variables. Required for DTLZ problems,
but can be skipped for ZDT problems as they only support one variable value.
n_of_objectives (int, optional): Required for DTLZ problems,
but can be skipped for ZDT problems as they only support one variable value.
Raises:
ProblemError: When one of many issues occur while building the MOProblem
instance.
Returns:
MOProblem: The test problem object
"""
problems = {
"ZDT1": zdt.ZDT1,
"ZDT2": zdt.ZDT2,
"ZDT3": zdt.ZDT3,
"ZDT4": zdt.ZDT4,
"ZDT5": zdt.ZDT5,
"ZDT6": zdt.ZDT6,
"DTLZ1": dtlz.DTLZ1,
"DTLZ2": dtlz.DTLZ2,
"DTLZ3": dtlz.DTLZ3,
"DTLZ4": dtlz.DTLZ4,
"DTLZ5": dtlz.DTLZ5,
"DTLZ6": dtlz.DTLZ6,
"DTLZ7": dtlz.DTLZ7,
}
num_var = {"ZDT1": 30, "ZDT2": 30, "ZDT3": 30, "ZDT4": 10, "ZDT6": 10}
if not (name in problems.keys()):
msg = (
"Specified Problem not yet supported.\n The supported problems are:"
+ str(problems.keys()))
raise ProblemError(msg)
if "ZDT" in name:
if n_of_variables is None:
n_of_variables = num_var[name]
if n_of_objectives is None:
n_of_objectives = 2
if not (n_of_variables == num_var[name]):
msg = (name + " problem has been limited to " +
str(num_var[name]) +
" variables. Number of variables recieved = " +
str(n_of_variables))
raise ProblemError(msg)
if not (n_of_objectives == 2):
msg = ("ZDT problems can only have 2 objectives. " +
"Number of objectives recieved = " + str(n_of_objectives))
raise ProblemError(msg)
obj_func = problems[name]()
elif "DTLZ" in name:
if (n_of_variables is None) or (n_of_objectives is None):
msg = ("Please provide both number of variables and objectives" +
" for the DTLZ problems")
raise ProblemError(msg)
obj_func = problems[name](n_of_objectives, n_of_variables)
else:
msg = "How did you end up here?"
raise ProblemError(msg)
lower_limits = obj_func.min_bounds
upper_limits = obj_func.max_bounds
var_names = ["x" + str(i + 1) for i in range(n_of_variables)]
obj_names = ["f" + str(i + 1) for i in range(n_of_objectives)]
variables = variable_builder(
names=var_names,
initial_values=lower_limits,
lower_bounds=lower_limits,
upper_bounds=upper_limits,
)
# Because optproblems can only handle one objective at a time
def modified_obj_func(x):
if isinstance(x, list):
if len(x) == n_of_variables:
return [obj_func(x)]
elif len(x[0]) == n_of_variables:
return list(map(obj_func, x))
else:
if x.ndim == 1:
return [obj_func(x)]
elif x.ndim == 2:
return list(map(obj_func, x))
raise TypeError("Unforseen problem, contact developer")
objective = VectorObjective(name=obj_names, evaluator=modified_obj_func)
problem = MOProblem([objective], variables, None)
return problem
def __init__(
self,
problem: MOProblem,
ideal: np.ndarray,
nadir: np.ndarray,
epsilon: float = 1e-6,
objective_names: Optional[List[str]] = None,
minimize: Optional[List[int]] = None,
):
if not ideal.shape == nadir.shape:
raise NautilusException(
"The dimensions of the ideal and nadir point do not match.")
if objective_names:
if not len(objective_names) == ideal.shape[0]:
raise NautilusException(
"The supplied objective names must have a length equal to "
"the numbr of objectives.")
self._objective_names = objective_names
else:
self._objective_names = [
f"f{i + 1}" for i in range(ideal.shape[0])
]
if minimize:
if not len(objective_names) == ideal.shape[0]:
raise NautilusException(
"The minimize list must have "
"as many elements as there are objectives.")
self._minimize = minimize
else:
self._minimize = [1 for _ in range(ideal.shape[0])]
# initialize method with problem
super().__init__(problem)
self._problem = problem
self._objectives: Callable = lambda x: self._problem.evaluate(
x).objectives
self._variable_bounds: Union[np.ndarray,
None] = problem.get_variable_bounds()
self._constraints: Optional[
Callable] = lambda x: self._problem.evaluate(x).constraints
# Used to calculate the utopian point from the ideal point
self._epsilon = epsilon
self._ideal = ideal
self._nadir = nadir
# calculate utopian vector
self._utopian = [ideal_i - self._epsilon for ideal_i in self._ideal]
# bounds of the reachable region
self._lower_bounds: List[np.ndarray] = []
self._upper_bounds: List[np.ndarray] = []
# current iteration step number
self._step_number = 1
# iteration points
self._zs: np.ndarray = []
# solutions, objectives, and distances for each iteration
self._xs: np.ndarray = []
self._fs: np.ndarray = []
self._ds: np.ndarray = []
# The current reference point
self._q: Union[None, np.ndarray] = None
# preference information
self._preference_method = None
self._preference_info = None
self._preferential_factors = None
# number of total iterations and iterations left
self._n_iterations = None
self._n_iterations_left = None
# flags for the iteration phase
# not utilized atm
self._use_previous_preference: bool = False
self._step_back: bool = False
self._short_step: bool = False
self._first_iteration: bool = True
# evolutionary method for minimizing
self._method_de: ScalarMethod = ScalarMethod(
lambda x, _, **y: differential_evolution(x, **y),
method_args={
"disp": False,
"polish": False,
"tol": 0.000001,
"popsize": 10,
"maxiter": 50000
},
use_scipy=True)
# define the variables, bounds -5 <= x_1 and x_2 <= 5
varsl = variable_builder(["x_1", "x_2", "x_3"],
initial_values=[0.5, 0.5, 0.5],
lower_bounds=[-5, -5, -5],
upper_bounds=[5, 5, 5])
# define constraints
def c_1(x, f=None):
x = x.squeeze()
# x_1 < 2
return x[0] + 2
# name of constraints, num variables, num objectives, evaluator
c1 = ScalarConstraint("c1", len(varsl), len(objl), evaluator=c_1)
problem = MOProblem(variables=varsl, objectives=objl, constraints=[c1])
max_bool = list(
map(lambda x: True if x < 0 else False, problem._max_multiplier))
max_multiplier = problem._max_multiplier
# define ideal and nadir
ideal = max_multiplier * np.array([-15, 15, 15])
nadir = max_multiplier * np.array([15, -15, -15])
problem.ideal = ideal
problem.nadir = nadir
# GLOBAL
global method
method = NIMBUS(problem, scalar_method="scipy_de")
f1 = _ScalarObjective(name="f1", evaluator=f_1, maximize=[True])
f2 = _ScalarObjective(name="f2", evaluator=f_2, maximize=[True])
f3 = _ScalarObjective(name="f3", evaluator=f_3, maximize=[True])
f4 = _ScalarObjective(name="f4", evaluator=f_4)
f5 = _ScalarObjective(name="f5", evaluator=f_5)
varsl = variable_builder(
["x_1", "x_2"],
initial_values=[0.5, 0.5],
lower_bounds=[0.3, 0.3],
upper_bounds=[1.0, 1.0],
)
problem = MOProblem(variables=varsl, objectives=[f1, f2, f3, f4, f5])
evolver = RVEA(problem, interact=True, n_iterations=10, n_gen_per_iter=100)
_, pref = evolver.iterate()
n_iteration = 1
sock = socket.socket(socket.AF_INET, socket.SOCK_STREAM)
sock.bind(("10.0.2.15", 5005))
# sock.bind(("127.0.0.1", 5005))
sock.listen(1)
print("Waiting for ComVis to connect...")
connection, client_addr = sock.accept()
print("Connection estabilished!")
lower_bounds=[-5, -5, -5],
upper_bounds=[5, 5, 5],
)
f1 = _ScalarObjective(name="f1", evaluator=f_1)
f2 = _ScalarObjective(name="f2", evaluator=f_2)
#For AI_DM ranges are always defined as IDEAL, NADIR.
f1_range = [-20, -14]
f2_range = [-14, 0.5]
x1 = np.linspace(min(f1_range), max(f1_range), 1000)
x2 = np.linspace(min(f2_range), max(f2_range), 1000)
y = np.linspace(0, 0, 1000)
problem = MOProblem(variables=varsl,
objectives=[f1, f2],
ideal=np.array([-20, -12]),
nadir=np.array([-14, 0.5]))
from desdeo_mcdm.interactive.NIMBUS import NIMBUS
from scipy.optimize import minimize, differential_evolution
scalar_method = ScalarMethod(
lambda x, _, **y: differential_evolution(x, **y),
use_scipy=True,
method_args={
"polish": True,
"disp": True
})
method = NIMBUS(problem, scalar_method)
def __init__(
self,
problem: MOProblem,
ideal: np.ndarray,
nadir: np.ndarray,
epsilon: float = 1e-6,
objective_names: Optional[List[str]] = None,
minimize: Optional[List[int]] = None,
):
if not ideal.shape == nadir.shape:
raise RPMException(
"The dimensions of the ideal and nadir point do not match.")
if objective_names:
if not len(objective_names) == ideal.shape[0]:
raise RPMException(
"The supplied objective names must have a leangth equal to "
"the number of objectives.")
self._objective_names = objective_names
else:
self._objective_names = [
f"f{i + 1}" for i in range(ideal.shape[0])
]
if minimize:
if not len(objective_names) == ideal.shape[0]:
raise RPMException("The minimize list must have "
"as many elements as there are objectives.")
self._minimize = minimize
else:
self._minimize = [1 for _ in range(ideal.shape[0])]
# initialize method with problem
super().__init__(problem)
self._problem = problem
self._objectives: Callable = lambda x: self._problem.evaluate(
x).objectives
self._variable_bounds: Union[np.ndarray,
None] = problem.get_variable_bounds()
self._constraints: Optional[
Callable] = lambda x: self._problem.evaluate(x).constraints
self._ideal = ideal
self._nadir = nadir
self._utopian = ideal - epsilon
self._n_objectives = self._ideal.shape[0]
# current iteration step number
self._h = 1
# solutions in decision and objective space, distances and referation points for each iteration
self._xs = [None] * 10
self._fs = [None] * 10
self._ds = [None] * 10
self._qs = [None] * 10
# perturbed reference points
self._pqs = [None] * 10
# additional solutions
self._axs = [None] * 10
self._afs = [None] * 10
# current reference point
self._q: Union[None, np.ndarray] = None
# weighting vector for achievement function
self._w: np.ndarray = []
# evolutionary method for minimizing
self._method_de: ScalarMethod = ScalarMethod(
lambda x, _, **y: differential_evolution(x, **y),
method_args={
"disp": False,
"polish": False,
"tol": 0.000001,
"popsize": 10,
"maxiter": 50000
},
use_scipy=True,
)
def __init__(self,
problem: MOProblem,
assign_type: str = "RandomDesign",
pop_size=None,
recombination_type=None,
crossover_type="simulated_binary_crossover",
mutation_type="bounded_polynomial_mutation",
*args):
"""Initialize the population.
Parameters
----------
problem : BaseProblem
An object of the class Problem
assign_type : str, optional
Define the method of creation of population.
If 'assign_type' is 'RandomDesign' the population is generated
randomly. If 'assign_type' is 'LHSDesign', the population is
generated via Latin Hypercube Sampling. If 'assign_type' is
'custom', the population is imported from file. If assign_type
is 'empty', create blank population.
'EvoNN' and 'EvoDN2' will create neural networks or deep neural networks,
respectively,
for population .
plotting : bool, optional
(the default is True, which creates the plots)
pop_size : int
Population size
recombination_type, crossover_type, mutation_type : str
Recombination functions. If recombination_type is specified, crossover and
mutation
will be handled by the same function. If None, they are done separately.
"""
self.assign_type = assign_type
self.num_var = problem.n_of_variables
self.lower_limits = np.asarray(problem.get_variable_lower_bounds())
self.upper_limits = np.asarray(problem.get_variable_upper_bounds())
self.hyp = 0
self.non_dom = 0
self.pop_size = pop_size
# Fix to remove the following assumptions
self.recombination_funcs = {
"biogp_xover": biogp_xover,
"biogp_mut": biogp_mutation,
"evodn2_xover_mutation": evodn2_xover_mutation,
"evonn_xover_mutation": evonn_xover_mutation,
"bounded_polynomial_mutation": bounded_polynomial_mutation,
"simulated_binary_crossover": simulated_binary_crossover,
}
self.crossover_type = crossover_type
self.mutation_type = mutation_type
self.recombination = self.recombination_funcs.get(
recombination_type, None)
if recombination_type is None:
self.crossover = self.recombination_funcs.get(crossover_type, None)
self.mutation = self.recombination_funcs.get(mutation_type, None)
self.problem = problem
self.filename = (problem.name + "_" + str(problem.n_of_objectives)
) # Used for plotting
self.plotting = plotting
self.individuals = []
self.objectives = np.empty((0, self.problem.n_of_objectives), float)
if problem.minimize is not None:
self.fitness = self.objectives[:, self.problem.minimize]
self.ideal_fitness = np.full((1, self.fitness.shape[1]), np.inf)
self.worst_fitness = -1 * self.ideal_fitness
else:
self.fitness = np.empty((0, self.problem.num_of_objectives), float)
self.ideal_fitness = np.full((1, self.problem.num_of_objectives),
np.inf)
self.worst_fitness = -1 * self.ideal_fitness
self.constraint_violation = np.empty(
(0, self.problem.num_of_constraints), float)
self.archive = pd.DataFrame(
columns=["generation", "decision_variables", "objective_values"])
if not assign_type == "empty":
individuals = create_new_individuals(assign_type,
problem,
pop_size=self.pop_size)
self.add(individuals)
if self.plotting:
self.figure = []
self.plot_init_()
return -0.5 + (x[:, 0] - 0.5)**2 + (x[:, 1] - 0.5)**2
list_vars = variable_builder(["x", "y"],
initial_values=[0, 0],
lower_bounds=[0, 0],
upper_bounds=[np.pi, np.pi])
f1 = _ScalarObjective(name="f1", evaluator=f_1)
f2 = _ScalarObjective(name="f2", evaluator=f_2)
c1 = ScalarConstraint("c1", 2, 2, c_1)
c2 = ScalarConstraint("c2", 2, 2, c_2)
problem = MOProblem(variables=list_vars,
objectives=[f1, f2],
constraints=[c1, c2])
evolver = RVEA(problem)
"""
figure = animate_init_(evolver.population.objectives, filename="MOPC4.html")
"""
while evolver.continue_evolution():
evolver.iterate()
"""figure = animate_next_(
evolver.population.objectives,
figure,
filename="MOPC4.html",
generation=evolver._iteration_counter,
)
"""