# Source code for gemseo_pymoo.post.compromise

```
# Copyright 2022 Airbus SAS
# Copyright 2021 IRT Saint Exupéry, https://www.irt-saintexupery.com
#
# 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
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# 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
"""Compromise points for multi-criteria decision-making."""
from __future__ import annotations
import logging
from typing import Any
from typing import ClassVar
from numpy import atleast_2d
from numpy import ndarray
from numpy import vstack
from pymoo.factory import get_decomposition
from gemseo_pymoo.algos.opt_result_mo import Pareto
from gemseo_pymoo.post.scatter_pareto import ScatterPareto
LOGGER = logging.getLogger(__name__)
[docs]
class Compromise(ScatterPareto):
"""Scatter plot with pareto front and compromise points.
See
`Compromise Programming <https://pymoo.org/mcdm/index.html#Compromise-Programming>`_.
"""
fig_title = "Compromise Points"
fig_name_prefix = "compromise"
SCALARIZATION_FUNCTIONS: ClassVar[dict[str, str]] = {
"weighted-sum": "Weighted Sum",
"tchebi": "Tchebysheff",
"pbi": "PBI",
"asf": "Achievement Scalarization Function",
"aasf": "Augmented Achievement Scalarization Function",
"perp_dist": "Perpendicular Distance",
}
"""The alias and the corresponding name of the scalarization functions."""
def _plot(
self,
scalar_name: str = "weighted-sum",
weights: ndarray | None = None,
plot_extra: bool = True,
plot_legend: bool = True,
plot_arrow: bool = False,
**scalar_options: Any,
) -> None:
"""Scatter plot of the pareto front along with the compromise points.
The compromise points are calculated using a
`scalarization function <https://pymoo.org/misc/decomposition.html>`_).
Args:
scalar_name: The name of the scalarization function to use.
weights: The weights for the scalarization function. If None, a normalized
array is used, e.g. [1./n, 1./n, ..., 1./n] for an optimization problem
with n-objectives.
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 <https://en.wikipedia.org/wiki/Euclidean_distance>`_
) of the vector represented by the arrow.
**scalar_options: The keyword arguments for the scalarization function.
Raises:
ValueError: Either if the scalarization function name is unknown or if the
number of weights does not match the number of objectives.
"""
if scalar_name not in self.SCALARIZATION_FUNCTIONS:
raise ValueError(
"The scalarization function name must be one of the "
f"following: {self.SCALARIZATION_FUNCTIONS}"
)
# Objectives.
n_obj = self.opt_problem.objective.dim
# Default weights.
if weights is None:
weights = [1.0 / n_obj] * n_obj
# Ensure correct dimension and type.
weights = atleast_2d(weights).astype(float)
# Check weight's dimension.
if weights.shape[1] != n_obj:
raise ValueError(
"You must provide exactly one weight for each objective function!"
)
# Create Pareto object.
pareto = Pareto(self.opt_problem)
# Initialize decomposition function.
decomposition = get_decomposition(scalar_name, **scalar_options)
# Prepare points to plot.
points = [] # Points' coordinates.
point_labels = [] # Points' labels.
for weight in weights:
# Apply decomposition.
d_res = decomposition.do(
pareto.front,
weight,
utopian_point=pareto.utopia,
nadir_point=pareto.anti_utopia,
**scalar_options,
)
# Best value according to the scalarization function.
d_min = d_res.min()
# Index where the minimum value is located (at the pareto front).
d_idx = d_res.argmin()
# Point's coordinates.
points.append(pareto.front[d_idx])
# Point's label.
float_format = ".2e" if abs(d_min) > 1e3 else ".2f"
point_labels.append(f"s({weight}) = {d_min:{float_format}}")
# Concatenate points to plot.
points = vstack(points)
# Extra figure options.
self.fig_title = (
f"{self.fig_title}\n(s = {self.SCALARIZATION_FUNCTIONS[scalar_name]})"
)
# Update name's prefix with current decomposition function's name.
self.fig_name_prefix += f"_{scalar_name}"
super()._plot(points, point_labels, plot_extra, plot_legend, plot_arrow)
```