import pandas as pd
 import numpy as np
 
 
 class ValidationError(Exception):
-    """Raised when an error related to the validation is encountered.
-    """
+    """Raised when an error related to the validation is encountered."""
 
 
-def validate_ref_point_with_ideal_and_nadir(
-    dimensions_data: pd.DataFrame, reference_point: pd.DataFrame
-):
+def validate_ref_point_with_ideal_and_nadir(dimensions_data: pd.DataFrame, reference_point: pd.DataFrame):
     validate_ref_point_dimensions(dimensions_data, reference_point)
     validate_ref_point_data_type(reference_point)
     validate_ref_point_with_ideal(dimensions_data, reference_point)
     validate_with_ref_point_nadir(dimensions_data, reference_point)
 
 
-def validate_ref_point_with_ideal(
-    dimensions_data: pd.DataFrame, reference_point: pd.DataFrame
-):
+def validate_ref_point_with_ideal(dimensions_data: pd.DataFrame, reference_point: pd.DataFrame):
     validate_ref_point_dimensions(dimensions_data, reference_point)
     ideal_fitness = dimensions_data.loc["ideal"] * dimensions_data.loc["minimize"]
     ref_point_fitness = reference_point * dimensions_data.loc["minimize"]
     if not (ideal_fitness <= ref_point_fitness).all(axis=None):
-        problematic_columns = ideal_fitness.index[
-            (ideal_fitness > ref_point_fitness).values.tolist()[0]
-        ].values
+        problematic_columns = ideal_fitness.index[(ideal_fitness > ref_point_fitness).values.tolist()[0]].values
         msg = (
             f"Reference point should be worse than or equal to the ideal point\n"
             f"The following columns have problematic values: {problematic_columns}"
         )
         raise ValidationError(msg)
 
 
-def validate_with_ref_point_nadir(
-    dimensions_data: pd.DataFrame, reference_point: pd.DataFrame
-):
+def validate_with_ref_point_nadir(dimensions_data: pd.DataFrame, reference_point: pd.DataFrame):
     validate_ref_point_dimensions(dimensions_data, reference_point)
     nadir_fitness = dimensions_data.loc["nadir"] * dimensions_data.loc["minimize"]
     ref_point_fitness = reference_point * dimensions_data.loc["minimize"]
     if not (ref_point_fitness <= nadir_fitness).all(axis=None):
-        problematic_columns = nadir_fitness.index[
-            (nadir_fitness < ref_point_fitness).values.tolist()[0]
-        ].values
+        problematic_columns = nadir_fitness.index[(nadir_fitness < ref_point_fitness).values.tolist()[0]].values
         msg = (
             f"Reference point should be better than or equal to the nadir point\n"
             f"The following columns have problematic values: {problematic_columns}"
         )
         raise ValidationError(msg)
 
 
-def validate_ref_point_dimensions(
-    dimensions_data: pd.DataFrame, reference_point: pd.DataFrame
-):
+def validate_ref_point_dimensions(dimensions_data: pd.DataFrame, reference_point: pd.DataFrame):
     if not dimensions_data.shape[1] == reference_point.shape[1]:
         msg = (
             f"There is a mismatch in the number of columns of the dataframes.\n"
             f"Columns in dimensions data: {dimensions_data.columns}\n"
             f"Columns in the reference point provided: {reference_point.columns}"

 
 
 def validate_ref_point_data_type(reference_point: pd.DataFrame):
     for dtype in reference_point.dtypes:
         if not pd.api.types.is_numeric_dtype(dtype):
-            msg = (
-                f"Type of data in reference point dataframe should be numeric.\n"
-                f"Provided datatype: {dtype}"
-            )
+            msg = f"Type of data in reference point dataframe should be numeric.\n" f"Provided datatype: {dtype}"
             raise ValidationError(msg)
 
 
 def validate_specified_solutions(indices: np.ndarray, n_solutions: int) -> None:
     """Validate the Decision maker's choice of preferred/non-preferred solutions.

 
     if indices.shape[0] < 1:
         raise ValidationError("Please specify at least one (non-)preferred solution.")
     if not isinstance(indices, (np.ndarray, list)):
         raise ValidationError(
-            "Please specify index/indices of (non-)preferred solutions in a list, even if there is only "
-            "one."
+            "Please specify index/indices of (non-)preferred solutions in a list, even if there is only " "one."
         )
     if not all(0 <= i <= (n_solutions - 1) for i in indices):
         msg = "indices of (non-)preferred solutions should be between 0 and {}. Current indices are {}.".format(
             n_solutions - 1, indices
         )
         raise ValidationError(msg)
 
 
-def validate_bounds(
-    dimensions_data: pd.DataFrame, bounds: np.ndarray, n_objectives: int
-) -> None:
+def validate_bounds(dimensions_data: pd.DataFrame, bounds: np.ndarray, n_objectives: int) -> None:
     """Validate the Decision maker's desired lower and upper bounds for objective values.
 
     Args:
         dimensions_data (pd.DataFrame): DataFrame including information whether an objective is minimized or
             maximized, for each objective. In addition, includes ideal and nadir vectors.

     Raises:
         ValidationError: In case desired bounds are invalid.
     """
 
     if not isinstance(bounds, np.ndarray):
-        msg = "Please specify bounds as a numpy array. Current type: {}.".format(
-            type(bounds)
-        )
+        msg = "Please specify bounds as a numpy array. Current type: {}.".format(type(bounds))
         raise ValidationError(msg)
     if len(bounds) != n_objectives:
-        msg = "Length of 'bounds' ({}) must be the same as number of objectives ({}).".format(
-            len(bounds), n_objectives
-        )
+        msg = "Length of 'bounds' ({}) must be the same as number of objectives ({}).".format(len(bounds), n_objectives)
         raise ValidationError(msg)
     if not all(isinstance(b, (np.ndarray, list)) for b in bounds):
         print(type(bounds[0]))
         msg = "Please give bounds for each objective in a list."
         raise ValidationError(msg)

         msg = "Lower bound cannot be greater than upper bound. Please specify lower bound first, then upper bound."
         raise ValidationError(msg)
 
     # check that bounds are within ideal and nadir points for each objective
     for i, b in enumerate(bounds):
-        if (
-            dimensions_data.loc["minimize"].values.tolist()[i] == 1
-        ):  # minimized objectives
+        if dimensions_data.loc["minimize"].values.tolist()[i] == 1:  # minimized objectives
             if dimensions_data.loc["ideal"].values.tolist()[i] is not None:
                 if b[0] < dimensions_data.loc["ideal"].values.tolist()[i]:
                     msg = "Lower bound cannot be lower than ideal value for objective. Ideal vector: {}.".format(
                         dimensions_data.loc["ideal"].values.tolist()
                     )

                 f"Mismatch in column names of data and dimensions_data.\n"
                 f"Column names in data: {data.columns}"
                 f"Column names in dimensions_data: {dimensions_data.columns}"
             )
             raise RequestError(msg)
-        rouge_indices = [
-            index
-            for index in dimensions_data.index
-            if index not in acceptable_dimensions_data_indices
-        ]
+        rouge_indices = [index for index in dimensions_data.index if index not in acceptable_dimensions_data_indices]
         if rouge_indices:
             msg = (
                 f"dimensions_data should only contain the following indices:\n"
                 f"{acceptable_dimensions_data_indices}\n"
                 f"The dataframe provided contains the following unsupported indices:\n"
                 f"{rouge_indices}"
             )
             raise RequestError(msg)
         if not isinstance(chart_title, (str, type(None))):
-            msg = (
-                f"Chart title should be a string. Provided chart type is:"
-                f"{type(chart_title)}"
-            )
+            msg = f"Chart title should be a string. Provided chart type is:" f"{type(chart_title)}"
             raise RequestError(msg)
         if not isinstance(message, str):
             if not isinstance(message, list):
                 msg = (
                     f"Message/s to be printed should be string or list of strings"

             msg = (
                 f"Dimensional data should be in a pandas dataframe.\n"
                 f"Provided data is of type: {type(dimensions_data)}"
             )
             raise RequestError(msg)
-        rouge_indices = [
-            index
-            for index in dimensions_data.index
-            if index not in acceptable_dimensions_data_indices
-        ]
+        rouge_indices = [index for index in dimensions_data.index if index not in acceptable_dimensions_data_indices]
         if rouge_indices:
             msg = (
                 f"dimensions_data should only contain the following indices:\n"
                 f"{acceptable_dimensions_data_indices}\n"
                 f"The dataframe provided contains the following unsupported indices:\n"

             RequestError: If reference point is not provided in a pandas DataFrame.
         """
         if not isinstance(value, pd.DataFrame):
             msg = "Reference should be provided in a pandas dataframe format"
             raise RequestError(msg)
-        self.content["validator"](
-            reference_point=value, dimensions_data=self.content["dimensions_data"]
-        )
+        self.content["validator"](reference_point=value, dimensions_data=self.content["dimensions_data"])
         self._response = value
 
 
 class PreferredSolutionPreference(BaseRequest):
     """Methods can use this class to ask the Decision maker to provide their preferences

 
 from typing import Type, List, Union, Dict
 
 
 class PreferenceIncorporatedSpaceError(Exception):
-    """Raised when an error related to the preference incorporated space is encountered.
-    """
+    """Raised when an error related to the preference incorporated space is encountered."""
 
 
 class PreferenceIncorporatedSpace:
     def __init__(
         self,

         if utopian is not None:
             self.utopian = utopian
         if nadir is not None:
             self.nadir = nadir
 
-        self.initialized_scalarizers = [
-            scalarizer(utopian=utopian, nadir=nadir, rho=rho)
-            for scalarizer in scalarizers
-        ]
+        self.initialized_scalarizers = [scalarizer(utopian=utopian, nadir=nadir, rho=rho) for scalarizer in scalarizers]
 
         self.has_additional_constraints = False
         self.constrained_scalarizers = []
 
         for scalarizer in self.initialized_scalarizers:
             # self.required_keys = scalarizer.required_keys.keys()
 
             self.constrained_scalarizers.append(scalarizer.has_additional_constraints)
-            self.has_additional_constraints = (
-                self.has_additional_constraints or scalarizer.has_additional_constraints
-            )
+            self.has_additional_constraints = self.has_additional_constraints or scalarizer.has_additional_constraints
 
     def __call__(self, objective_vector: np.ndarray):
-        mapped_vectors = np.zeros(
-            (len(objective_vector), len(self.initialized_scalarizers))
-        )
+        mapped_vectors = np.zeros((len(objective_vector), len(self.initialized_scalarizers)))
         for i, scalarizer in enumerate(self.initialized_scalarizers):
             mapped_vectors[:, i] = scalarizer(objective_vector, self.preferences[i])
         return mapped_vectors
 
     def evaluate_constraints(self, objective_vector: np.ndarray):

             if not has_constraints:
                 continue
             constraints = np.hstack(
                 (
                     constraints,
-                    scalarizer.evaluate_constraints(
-                        objective_vector, self.preferences[i]
-                    ),
+                    scalarizer.evaluate_constraints(objective_vector, self.preferences[i]),
                 )
             )
 
 
 class classificationPIS:

             self.nadir = nadir
 
         self.nimbus = NIMBUS_GLIDE(utopian=utopian, nadir=nadir)
         self.nimbus_copycat = reference_point_method_GLIDE(utopian=utopian, nadir=nadir)
 
-        self.initialized_scalarizers = [
-            scalarizer(utopian=utopian, nadir=nadir, rho=rho)
-            for scalarizer in scalarizers
-        ]
+        self.initialized_scalarizers = [scalarizer(utopian=utopian, nadir=nadir, rho=rho) for scalarizer in scalarizers]
         self.has_additional_constraints = False
 
     def update_preference(self, preference: dict):
-
         self.preference = preference
         if "classifications" in preference.keys():
             self.classification_preference = preference
-            self.RP_preference = classification_to_reference_point(
-                preference, ideal=self.utopian, nadir=self.nadir
-            )
+            self.RP_preference = classification_to_reference_point(preference, ideal=self.utopian, nadir=self.nadir)
         else:
-            raise PreferenceIncorporatedSpaceError(
-                "Classification preference expected."
-            )
+            raise PreferenceIncorporatedSpaceError("Classification preference expected.")
 
     def __call__(self, objective_vector: np.ndarray):
-
         # IOPIS/NIMBUS logic
-        nimbus_obj = self.nimbus(
-            objective_vector=objective_vector, preference=self.classification_preference
-        )
-        nimbus_constraint = self.nimbus.evaluate_constraints(
-            objective_vector, self.classification_preference
-        )
+        nimbus_obj = self.nimbus(objective_vector=objective_vector, preference=self.classification_preference)
+        nimbus_constraint = self.nimbus.evaluate_constraints(objective_vector, self.classification_preference)
         feasible = np.all(nimbus_constraint > 0, axis=1)
 
         if not feasible.any():
             nimbus_optimal = objective_vector[nimbus_constraint.max(axis=1).argmax()]
         else:
             nimbus_obj[~feasible] = np.inf
             nimbus_optimal = objective_vector[nimbus_obj.argmin()]
 
         # IOPIS mapping
-        mapped_vectors = np.zeros(
-            (len(objective_vector), len(self.initialized_scalarizers) + 1)
-        )
+        mapped_vectors = np.zeros((len(objective_vector), len(self.initialized_scalarizers) + 1))
 
         mapped_vectors[:, 0] = self.nimbus_copycat(
             objective_vector=objective_vector,
             preference={"reference point": nimbus_optimal},
         )

         num_DM: int = 2,
         scalarizer: Type[GLIDEBase] = AUG_STOM_GLIDE,
         nadir: np.ndarray = None,
         rho: float = 1e-6,
     ):
-        super().__init__(
-            scalarizers=[scalarizer] * num_DM, utopian=utopian, nadir=nadir, rho=rho
-        )
+        super().__init__(scalarizers=[scalarizer] * num_DM, utopian=utopian, nadir=nadir, rho=rho)
 
     def update_preference(self, preference: List[Dict]):
         self.preferences = preference
 
 

 from desdeo_tools.solver.ScalarSolver import ScalarMinimizer
 from typing import Optional, Callable, Union
 
 
 class ECMError(Exception):
-    """Raised when an error related to the Epsilon Constraint Method is encountered.
-    """
+    """Raised when an error related to the Epsilon Constraint Method is encountered."""
 
 
 class EpsilonConstraintMethod:
     """A class to represent a class for scalarizing MOO problems using the epsilon
         constraint method.

                 if ival != self._to_be_minimized
             ]
         )
 
         if len(epsilon_left_side) != len(self.epsilons):
-            msg = (
-                "The lenght of the epsilons array ({}) must match the total number of objectives - 1 ({})."
-            ).format(len(self.epsilons), len(self.objectives(xs)) - 1)
+            msg = ("The lenght of the epsilons array ({}) must match the total number of objectives - 1 ({}).").format(
+                len(self.epsilons), len(self.objectives(xs)) - 1
+            )
             raise ECMError(msg)
 
         # evaluate values of epsilon constraint functions
-        e: np.ndarray = np.array(
-            [-(f - v) for f, v in zip(epsilon_left_side, self.epsilons)]
-        )
+        e: np.ndarray = np.array([-(f - v) for f, v in zip(epsilon_left_side, self.epsilons)])
 
         if self.constraints(xs) is not None:
             c = self.constraints(xs)
-            return np.concatenate(
-                [c, e], axis=None
-            )  # does it work with multiple constraints?
+            return np.concatenate([c, e], axis=None)  # does it work with multiple constraints?
         else:
             return e
 
     def __call__(self, objective_vector: np.ndarray) -> Union[float, np.ndarray]:
         """

 
         Returns:
             Value of objective function to be minimized.
         """
         if np.shape(objective_vector)[0] > 1:  # more rows than one
-            return np.array(
-                [
-                    objective_vector[i][self._to_be_minimized]
-                    for i, _ in enumerate(objective_vector)
-                ]
-            )
+            return np.array([objective_vector[i][self._to_be_minimized] for i, _ in enumerate(objective_vector)])
         else:
             return objective_vector[0][self._to_be_minimized]
 
 
 # Testing the method
 if __name__ == "__main__":
     # 1. Define objective functions, bounds and constraints
 
     def volume(r, h):
-        return np.pi * r ** 2 * h
+        return np.pi * r**2 * h
 
     def area(r, h):
-        return 2 * np.pi ** 2 + np.pi * r * h
+        return 2 * np.pi**2 + np.pi * r * h
 
     # add third objective
 
     def weight(v):
         return 0.01 * v

     # index of which objective function to minimize
     obj_min = 2
 
     # set upper bound(s) for the other objectives, in the same order than which corresponding objective functions
     # are defined
-    epsil = np.array(
-        [2000, -100]
-    )  # multiply the epsilons with -1, if the constraint is of form f_i(x) >= e_i
+    epsil = np.array([2000, -100])  # multiply the epsilons with -1, if the constraint is of form f_i(x) >= e_i
 
     # create an instance of EpsilonConstraintMethod-class for given problem
     eps = EpsilonConstraintMethod(objective, obj_min, epsil, constraints=con_golden)
 
     # constraint evaluator, used by the solver

 
     # 3. Solve
 
     # starting point
     x0 = np.array([2, 11])
-    minimizer = ScalarMinimizer(
-        scalarized_objective, bounds, constraint_evaluator=cons_evaluate, method=None
-    )
+    minimizer = ScalarMinimizer(scalarized_objective, bounds, constraint_evaluator=cons_evaluate, method=None)
 
     # minimize
     res = minimizer.minimize(x0)
     final_r, final_h = res["x"][0], res["x"][1]
     final_obj = objective(res["x"]).squeeze()
     final_V, final_A, final_W = final_obj[0], final_obj[1], final_obj[2]
 
     print(f"Final cake specs: radius: {final_r}cm, height: {final_h}cm.")
-    print(
-        f"Final cake dimensions: volume: {final_V}, area: {-final_A}, weight: {final_W}."
-    )
+    print(f"Final cake dimensions: volume: {final_V}, area: {-final_A}, weight: {final_W}.")
     print(final_r / final_h)
     print(res)

     Instances of the implementations of this class should function as
     function.
     """
 
     @abstractmethod
-    def __call__(
-        self, objective_vector: np.ndarray, reference_point: np.ndarray
-    ) -> Union[float, np.ndarray]:
+    def __call__(self, objective_vector: np.ndarray, reference_point: np.ndarray) -> Union[float, np.ndarray]:
         """Evaluate the ASF.
 
         Args:
             objective_vectors (np.ndarray): The objective vectors to calculate
                 the values.

     """
 
     def __init__(self, weights: np.ndarray):
         self.weights = weights
 
-    def __call__(
-        self, objective_vector: np.ndarray, reference_point: np.ndarray
-    ) -> Union[float, np.ndarray]:
+    def __call__(self, objective_vector: np.ndarray, reference_point: np.ndarray) -> Union[float, np.ndarray]:
         """Evaluate the simple order-representing ASF.
 
         Args:
             objective_vector (np.ndarray): A vector representing a solution in
                 the solution space.

         self.preferential_factors = preferential_factors
         self.nadir = nadir
         self.utopian_point = utopian_point
         self.rho = rho
 
-    def __call__(
-        self, objective_vector: np.ndarray, reference_point: np.ndarray
-    ) -> Union[float, np.ndarray]:
+    def __call__(self, objective_vector: np.ndarray, reference_point: np.ndarray) -> Union[float, np.ndarray]:
         mu = self.preferential_factors
         f = objective_vector
         q = reference_point
         rho = self.rho
         z_nad = self.nadir

         self.lt_inds = lt_inds
         self.lte_inds = lte_inds
         self.rho = rho
         self.rho_sum = rho_sum
 
-    def __call__(
-        self, objective_vector: np.ndarray, reference_point: np.ndarray
-    ) -> Union[float, np.ndarray]:
+    def __call__(self, objective_vector: np.ndarray, reference_point: np.ndarray) -> Union[float, np.ndarray]:
         # assure this function works with single objective vectors
         if objective_vector.ndim == 1:
             f = objective_vector.reshape((1, -1))
         else:
             f = objective_vector

     def __init__(self, ideal: np.ndarray, rho: float = 1e-6, rho_sum: float = 1e-6):
         self.ideal = ideal
         self.rho = rho
         self.rho_sum = rho_sum
 
-    def __call__(
-        self, objective_vectors: np.ndarray, reference_point: np.ndarray
-    ) -> Union[float, np.ndarray]:
+    def __call__(self, objective_vectors: np.ndarray, reference_point: np.ndarray) -> Union[float, np.ndarray]:
         # assure this function works with single objective vectors
         if objective_vectors.ndim == 1:
             f = objective_vectors.reshape((1, -1))
         else:
             f = objective_vectors

         nad = self.nadir
         uto = self.ideal - self.rho
         ex_mask = np.full((f.shape[1]), True, dtype=bool)
         ex_mask[self.index_to_exclude] = False
 
-        max_term = np.max(
-            (f[:, ex_mask] - nad[ex_mask]) / (nad[ex_mask] - z[ex_mask]), axis=1
-        )
-        sum_term_1 = self.rho_sum * np.sum(
-            (f[:, ex_mask]) / (nad[ex_mask] - z[ex_mask]), axis=1
-        )
+        max_term = np.max((f[:, ex_mask] - nad[ex_mask]) / (nad[ex_mask] - z[ex_mask]), axis=1)
+        sum_term_1 = self.rho_sum * np.sum((f[:, ex_mask]) / (nad[ex_mask] - z[ex_mask]), axis=1)
         # avoid division by zeros
-        sum_term_2 = self.rho_sum * np.sum(
-            (f[:, ~ex_mask]) / (nad[~ex_mask] - uto[~ex_mask]), axis=1
-        )
+        sum_term_2 = self.rho_sum * np.sum((f[:, ~ex_mask]) / (nad[~ex_mask] - uto[~ex_mask]), axis=1)
 
         return max_term + sum_term_1 + sum_term_2
 
 
 class GuessASF(ASFBase):

 
         max_term = np.max((f - nad) / (nad - z), axis=1)
 
         return max_term
 
-    
+
 class AspResASF(ASFBase):
     """Implementation of an ASF using both aspiration and reservation levels.
-       directly consider both upper and lower bounds of the preferred ranges within the solution 
-       generation process, the variant of ASF utilizing both aspirations and reservations levels. 
+       directly consider both upper and lower bounds of the preferred ranges within the solution
+       generation process, the variant of ASF utilizing both aspirations and reservations levels.
        Originally proposed by Wierzbicki (1986), and also used in the PIE method (Sindhya et al. (2011)).
-    
+
     Args:
         nadir (np.ndarray): The nadir point.
         ideal (np.ndarray): The ideal point.
         rho  A small number to form the utopian point.
         rho_sum (float): A small number to be used as a weight for the sum term.
         alpha (float): An extricly positive number.
         beta(float): An extricly positive number.
-    
+
     References:
         Wierzbicki, A. P.
-        On the completeness and constructiveness of parametric characterizations to vector optimization 
-        problems, 
+        On the completeness and constructiveness of parametric characterizations to vector optimization
+        problems,
         OR Spektrum, 1986, 8(2), 73–87.
-        
+
         Sindhya, K., Ruiz, A. B. and Miettinen, K.
         A preference based interactive evolutionary algorithm for multi-objective optimization: PIE
-        in H. Takahashi, K. Deb, E. Wanner and S. Greco, eds, ‘Evolutionary Multi-Criterion Optimization: 
+        in H. Takahashi, K. Deb, E. Wanner and S. Greco, eds, ‘Evolutionary Multi-Criterion Optimization:
         6th International Conference’, Proceedings, Springer-Verlag, Berlin, Heidelberg, 2011, pp. 212–225.
     """
 
-    def __init__(self, nadir: np.ndarray, ideal: np.ndarray, rho: float = 1e-6, rho_sum: float = 1e-6,
-                alpha: float = 1e-1, beta: float = 1e-1,):
+    def __init__(
+        self,
+        nadir: np.ndarray,
+        ideal: np.ndarray,
+        rho: float = 1e-6,
+        rho_sum: float = 1e-6,
+        alpha: float = 1e-1,
+        beta: float = 1e-1,
+    ):
         self.nadir = nadir
         self.ideal = ideal
         self.rho = rho
         self.rho_sum = rho_sum
         self.alpha = alpha