# -*- coding: utf-8 -*-
# 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 - API and implementation and/or documentation
# :author: Francois Gallard
# :author: Damien Guenot
# OTHER AUTHORS - MACROSCOPIC CHANGES
"""A Pareto Front."""
from __future__ import division, unicode_literals
import logging
from typing import List, Optional, Sequence, Tuple
from numpy import full, ndarray
from gemseo.algos.pareto_front import generate_pareto_plots
from gemseo.post.opt_post_processor import OptPostProcessor
LOGGER = logging.getLogger(__name__)
[docs]class ParetoFront(OptPostProcessor):
"""Compute the Pareto front for a multi-objective problem.
The Pareto front of an optimization problem is the set of _non-dominated_ points of
the design space for which there is no other point that improves an objective
without damaging another.
This post-processing computes the Pareto front and generates a matrix of plots,
one per couple of objectives.
For a given plot, the red markers are the non-dominated points according to the
objectives of this plot and the green markers are the non-dominated points
according to all the objectives.
The latter are also called _Pareto optimal points_.
"""
DEFAULT_FIG_SIZE = (10.0, 10.0)
def _plot(
self,
objectives=None, # type: Optional[Sequence[str]]
objectives_labels=None, # type: Optional[Sequence[str]]
show_non_feasible=True, # type: bool
): # type: (...) -> None
"""
Args:
objectives: The functions names or design variables to plot.
If None, use the objective function (may be a vector).
objectives_labels: The labels of the objective components.
If None, use the objective name suffixed by an index.
show_non_feasible: If True, show the non feasible points in the plot.
Raises:
ValueError: If the numbers of objectives and objectives
labels are different.
"""
if objectives is None:
objectives = [self.opt_problem.objective.name]
all_funcs = self.opt_problem.get_all_functions_names()
all_dv_names = self.opt_problem.design_space.variables_names
sample_values, all_labels = self.__compute_names_and_values(
all_dv_names, all_funcs, objectives
)
non_feasible_samples = self.__compute_non_feasible_samples(sample_values)
if objectives_labels is not None:
if len(all_labels) != len(objectives_labels):
raise ValueError(
"objective_labels shall have the same dimension as the number"
" of objectives to plot."
)
all_labels = objectives_labels
fig = generate_pareto_plots(
sample_values,
all_labels,
figsize=self.DEFAULT_FIG_SIZE,
non_feasible_samples=non_feasible_samples,
show_non_feasible=show_non_feasible,
)
self._add_figure(fig)
def __compute_names_and_values(
self,
all_dv_names, # type: Sequence[str]
all_funcs, # type: Sequence[str]
objectives, # type: Sequence[str]
): # type: (...) -> Tuple[ndarray,List[str]]
"""Compute the names and values of the objective and design variables.
Args:
all_dv_names: The design variables names.
all_funcs: The function names.
objectives: The objective names.
Returns:
The sample values and the sample names.
"""
design_variables = []
for func in list(objectives):
self.__check_objective_name(all_dv_names, all_funcs, func, objectives)
self.__move_objective_to_design_variable(design_variables, func, objectives)
if not design_variables:
design_variables_labels = []
all_data_names = objectives
_, objective_labels, _ = self.database.get_history_array(
functions=objectives,
design_variables_names=None,
add_dv=False,
)
elif not objectives:
design_variables_labels = self._generate_x_names(variables=design_variables)
all_data_names = design_variables
objective_labels = []
else:
design_variables_labels = self._generate_x_names(variables=design_variables)
all_data_names = objectives + design_variables
_, objective_labels, _ = self.database.get_history_array(
functions=objectives,
design_variables_names=None,
add_dv=False,
)
all_data_names.sort()
all_labels = sorted(objective_labels + design_variables_labels)
sample_values = self.opt_problem.get_data_by_names(
names=all_data_names, as_dict=False, filter_non_feasible=False
)
return sample_values, all_labels
def __check_objective_name(
self,
all_dv_names, # type: Sequence[str]
all_funcs, # type: Sequence[str]
func, # type: str
objectives, # type: Sequence[str]
): # type: (...) -> None
"""Check that the objective name is valid.
Args:
all_dv_names: The design variables names.
all_funcs: The function names.
func: The function name.
objectives: The objectives names.
Raises:
ValueError: If the objective name is not valid.
"""
if func not in all_funcs and func not in all_dv_names:
min_f = "-" + func == self.opt_problem.objective.name
if min_f and not self.opt_problem.minimize_objective:
objectives[objectives.index(func)] = "-" + func
else:
msg = (
"Cannot build Pareto front,"
" Function {} is neither among"
" optimization problem functions: "
"{} nor design variables: {}."
)
msg = msg.format(func, str(all_funcs), str(all_dv_names))
raise ValueError(msg)
def __move_objective_to_design_variable(
self,
design_variables, # type: Sequence[str]
func, # type: str
objectives, # type: Sequence[str]
): # type: (...) -> None
"""Move an objective to a design variable.
If the given function is a design variable,
then move it from the objectives to the design_variables.
Args:
design_variables: The design variables.
func: The function name.
objectives: The objectives names.
"""
if func in self.opt_problem.design_space.variables_names:
objectives.remove(func)
design_variables.append(func)
def __compute_non_feasible_samples(
self, sample_values # type: ndarray
): # type: (...) -> ndarray
"""Compute the non-feasible indexes.
Args:
sample_values: The sample values.
Returns:
An array of size ``n_samples``, True if the point is non feasible
"""
x_feasible, _ = self.opt_problem.get_feasible_points()
feasible_indexes = [self.database.get_index_of(x) for x in x_feasible]
is_non_feasible = full(sample_values.shape[0], True)
is_non_feasible[feasible_indexes] = False
return is_non_feasible
