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)