# -*- 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
"""
Compute and display a Pareto Front
**********************************
"""
from __future__ import absolute_import, division, print_function, unicode_literals
from builtins import range, str
from itertools import combinations
import matplotlib.pyplot as plt
from future import standard_library
from numpy import all as np_all
from numpy import any as np_any
from numpy import full, vstack
standard_library.install_aliases()
[docs]def select_pareto_optimal(obj_values):
"""
Compute the Pareto front
Search for all non dominated points, ie there exists j such that
there is no lower value for obj_values[:,j] that does not degrade
at least one other objective obj_values[:,i]
:param obj_values: objective function array, of size (n_samples, n_objs)
:returns pareto_optimal: vector of booleans of size n_samples, True if
Pareto optimal
"""
pareto_optimal = full(obj_values.shape[0], True)
def any_ax1_all(arr):
return np_all(np_any(arr, axis=1))
for i, obj in enumerate(obj_values):
before_are_worse = any_ax1_all(obj_values[:i] > obj)
after_are_worse = any_ax1_all(obj_values[i + 1 :] > obj)
pareto_optimal[i] = before_are_worse and after_are_worse
return pareto_optimal
[docs]def plot_pareto_bi_obj(axe, obj_values, pareto_optimal, obj_names, all_pareto=None):
"""
Plot a 2D Pareto front
:param axe: matplotlib axe on which to be plotted
:param obj_values: objective function array, of size (n_samples, n_objs)
:param pareto_optimal: vector of booleans of size n_samples,
True if Pareto optimal.
:param obj_names: names of the objectives
:param all_pareto: indices of points that are pareto optimal wrt all
criteria.
"""
axe.scatter(obj_values[:, 0], obj_values[:, 1], color="b")
if all_pareto is not None:
axe.scatter(obj_values[all_pareto, 0], obj_values[all_pareto, 1], color="g")
axe.scatter(obj_values[pareto_optimal, 0], obj_values[pareto_optimal, 1], color="r")
axe.set_xlabel(obj_names[0])
axe.set_ylabel(obj_names[1])
[docs]def generate_pareto_plots(obj_values, obj_names, figsize=(10, 10)):
"""
Plot a 2D Pareto front
:param obj_values: objective function array, of size (n_samples, n_objs)
:param obj_names: names of the objectives
:param figsize: matplotlib figure size in inches
"""
n_obj = obj_values.shape[1]
if len(obj_names) != n_obj:
raise ValueError(
"Inconsistent objective values size and objective names!"
+ str(n_obj)
+ " !="
+ str(len(obj_names))
)
fig, axes = plt.subplots(n_obj - 1, n_obj - 1, figsize=figsize)
fig.suptitle("Pareto front")
pareto_opt_all = select_pareto_optimal(obj_values)
# 0 vs 1 0 vs 2 0 vs 3
# 1 vs 2 1 vs 3
# 2 vs 3
# i j+1 i=0...nobj-1
# j=1....nobj
for i, j in combinations(range(n_obj), 2): # no duplication, j!=j
if i == n_obj - 1:
continue
obj_loc = vstack((obj_values[:, i], obj_values[:, j])).T
pareto_opt_loc = select_pareto_optimal(obj_loc)
if n_obj == 2:
axe = axes
else:
axe = axes[i, j - 1]
plot_pareto_bi_obj(
axe, obj_loc, pareto_opt_loc, [obj_names[i], obj_names[j]], pareto_opt_all
)
if i != j - 1:
axes[j - 1, i].remove()
return fig
