Source code for

# Copyright 2022 Airbus SAS
# Copyright 2021 IRT Saint Exupéry,
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
# License version 3 as published by the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# Lesser General Public License for more details.
# You should have received a copy of the GNU Lesser General Public License
# along with this program; if not, write to the Free Software Foundation,
# Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
# Contributors:
#    INITIAL AUTHORS - initial API and implementation and/or initial
#                           documentation
#        :author: Gabriel Max DE MENDONÇA ABRANTES
"""Scatter plot for multi-objective optimization problems."""

from __future__ import annotations

import logging
from math import degrees
from typing import TYPE_CHECKING
from typing import Any
from typing import ClassVar
from typing import Union

import matplotlib.pyplot as plt
from gemseo.algos.pareto import ParetoFront
from import OptPostProcessor
from matplotlib.patches import FancyArrowPatch
from matplotlib.text import Annotation
from numpy import arctan
from numpy import atleast_2d
from numpy import ndarray
from numpy import vstack
from numpy.linalg import norm as np_norm
from pymoo.visualization.scatter import Scatter as PymooScatter

from import Annotation3D
from import Arrow3D

    from import Sequence

LOGGER = logging.getLogger(__name__)

PlotPropertiesType = dict[str, Union[str, int, float, bool]]

[docs] class ScatterPareto(OptPostProcessor): """Scatter plot with pareto points and points of interest. See `Scatter <>`_. Note: This post-processor assumes the optimization has converged to a well-defined pareto front. """ fig_title: str = "Pareto" """The figure's title.""" fig_name_prefix: str = "scatter" """The figure's name prefix.""" font_size: int = 9 """The font size for the plot texts.""" prop_front: ClassVar[PlotPropertiesType] = { "color": "blue", "alpha": 0.2, "s": 10, "zorder": 1, } """The properties for the pareto points.""" prop_extra: ClassVar[PlotPropertiesType] = {"alpha": 0.8, "s": 30, "zorder": 2} """The properties for the extra points.""" prop_interest: ClassVar[PlotPropertiesType] = {"alpha": 1.0, "s": 30, "zorder": 3} """The properties for the points of interest.""" prop_arrow: ClassVar[PlotPropertiesType] = { "color": "black", "alpha": 0.5, "arrowstyle": "-|>", "mutation_scale": 12, } """The properties for the arrows.""" prop_annotation: ClassVar[PlotPropertiesType] = { "fontsize": font_size - 2, "ha": "center", "va": "bottom", "transform_rotates_text": True, "rotation_mode": "anchor", # Alignment occurs before rotation. } """The properties for the annotations.""" def _plot( self, points: ndarray | None = None, point_labels: Sequence[str] = "points", plot_extra: bool = True, plot_legend: bool = True, plot_arrow: bool = False, **scatter_options: Any, ) -> None: """Scatter plot of the pareto front along with the points of interest. Args: points: The points of interest to be plotted. If None, only the pareto front is plot along with extra point (depending on ``plot_extra`` value). point_labels: The label of the points of interest. If a list is provided, it must contain as many labels as the points of interest. Moreover, in the last case, each point will have a different color. plot_extra: Whether to plot the extra pareto related points, i.e. ``utopia``, ``nadir`` and ``anchor`` points. plot_legend: Whether to show the legend. plot_arrow: Whether to plot arrows connecting the utopia point to the compromise points. The arrows are annotated with the ``2-norm`` ( `Euclidian distance <>`_ ) of the vector represented by the arrow. **scatter_options: The keyword arguments for the class :class:`pymoo.visualization.scatter.Scatter`. Raises: ValueError: Either if the number of objectives is not 2 or 3, or if a list of labels is provided but its size does not match the number of points. """ # Objectives. n_obj = self.opt_problem.objective.dim obj_name = # Ensure right dimension. points = [] if points is None else atleast_2d(points) # Check post-processing suitability. if not 2 <= n_obj <= 3: msg = ( "This post-processing is only suitable for optimization " "problems with 2 or 3 objective functions!" ) raise ValueError(msg) # Check labels. if not isinstance(point_labels, str) and len(point_labels) != len(points): msg = ( "You must provide either a single label for all points " "or one label for each one!" ) raise ValueError(msg) # Create Pareto object. pareto = ParetoFront.from_optimization_problem(self.opt_problem) # Default plot options. plot_options = { "figsize": self.DEFAULT_FIG_SIZE, "title": self.fig_title, "tight_layout": False, "legend": (plot_legend, {"fontsize": self.font_size - 2, "loc": "best"}), "labels": [f"{obj_name} ({i + 1})" for i in range(n_obj)], # Axes' labels. "close_on_destroy": False, # Do not close figure when plot is destroyed. } # Update default options with user choices. plot_options.update(**scatter_options) # Create plot. plot = PymooScatter(**plot_options) # Change font family to ensure good alignment. plt.rc("font", family="monospace", size=self.font_size) # Plot pareto front. plot.add(pareto.f_optima, label="pareto front", **self.prop_front) # Plot extra pareto related points. if plot_extra: plot.add(pareto.f_anchors, label="anchor points", **self.prop_extra) utopia_label = f"utopia = {pareto.f_utopia.round(decimals=2)}" plot.add(pareto.f_utopia, label=utopia_label, **self.prop_extra) nadir_label = f" nadir = {pareto.f_anti_utopia.round(decimals=2)}" plot.add(pareto.f_anti_utopia, label=nadir_label, **self.prop_extra) # Plot points of interest. if len(points) > 0: if isinstance(point_labels, str): plot.add(points, label=point_labels, **self.prop_interest) else: for point, label in zip(points, point_labels): plot.add(point, label=label, **self.prop_interest) # Create arrows. if plot_arrow: for point in points: # Arrow vector. vect = point - pareto.f_utopia norm = np_norm(vect) if n_obj == 2: arr = FancyArrowPatch(pareto.f_utopia, point, **self.prop_arrow) rot = 90 if vect[0] == 0 else degrees(arctan(vect[1] / vect[0])) annot = Annotation( f"{norm:.2f}", (0.5 * (pareto.f_utopia + point)), rotation=rot, **self.prop_annotation, ) else: vect = vstack([pareto.f_utopia, point]) arr = Arrow3D(vect, **self.prop_arrow) annot = Annotation3D(f"{norm:.2f}", vect, **self.prop_annotation) # Plot arrow and text in axes. file_name = f"{self.fig_name_prefix}_{len(self.figures) + 1}" self._add_figure(plot.fig, file_name)