# 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: Jean-Christophe Giret
# OTHER AUTHORS - MACROSCOPIC CHANGES
r"""Binh and Korn multi-objective problem.
This module implements the Binh and Korn multi-objective problem as defined in
:cite:`binh1997mobes`:
.. math::
\begin{aligned}
\text{minimize the objective function } & f_1(x, y) = 4x^2 + 4y^2 \\
& f_2(x, y) = (x-5)^2 + (y-5)^2 \\
\text{with respect to the design variables }&x,\,y \\
\text{subject to the general constraints }
& g_1(x,y) = (x-5)^2 + y^2 \leq 25.0\\
& g_2(x, y) = (x-8)^2 + (y+3)^2 \geq 7.7\\
\text{subject to the bound constraints }
& 0 \leq x \leq 5.0\\
& 0 \leq y \leq 3.0
\end{aligned}
"""
from __future__ import annotations
from typing import TYPE_CHECKING
from numpy import array
from numpy import ndarray
from numpy import zeros
from gemseo.algos.design_space import DesignSpace
from gemseo.algos.opt_problem import OptimizationProblem
from gemseo.core.mdofunctions.mdo_function import MDOFunction
if TYPE_CHECKING:
from gemseo.utils.matplotlib_figure import FigSizeType
[docs]
class BinhKorn(OptimizationProblem):
"""Binh and Korn optimization problem.
The constructor initializes the BinhKorn :class:`.OptimizationProblem` by defining
the :class:`.DesignSpace`, the objective function and the constraints.
"""
def __init__(self, initial_values: FigSizeType = (1.0, 1.0)) -> None:
"""
Args:
initial_values: Initial value of the design variables.
""" # noqa: D205 D212
design_space = DesignSpace()
design_space.add_variable("x", l_b=0.0, u_b=5.0, value=initial_values[0])
design_space.add_variable("y", l_b=0.0, u_b=3.0, value=initial_values[1])
super().__init__(design_space)
self.objective = MDOFunction(
self._compute_binhkorn,
name="compute_binhkorn",
f_type="obj",
jac=self._compute_binhkorn_jac,
expr="(4*x**2+ 4*y**2, (x-5.)**2 + (y-5.)**2)",
input_names=["x", "y"],
dim=2,
)
ineq1 = MDOFunction(
self._compute_ineq_constraint1,
name="ineq1",
f_type="ineq",
jac=self._compute_ineq_constraint1_jac,
expr="(x-5.)**2 + y**2 <= 25.",
input_names=["x", "y"],
)
self.add_ineq_constraint(ineq1)
ineq2 = MDOFunction(
self._compute_ineq_constraint2,
name="ineq2",
f_type="ineq",
jac=self._compute_ineq_constraint2_jac,
expr="(x-8.)**2 + (y+3)**2 >= 7.7",
input_names=["x", "y"],
)
self.add_ineq_constraint(ineq2)
@staticmethod
def _compute_binhkorn(
x_dv: ndarray,
) -> ndarray:
"""Compute the objective of the BinhKorn problem.
Args:
x_dv: The design variable vector.
Returns:
The objective function value.
"""
obj = array([0.0, 0.0])
obj[0] = 4 * x_dv[0] ** 2 + 4 * x_dv[1] ** 2
obj[1] = (x_dv[0] - 5.0) ** 2 + (x_dv[1] - 5.0) ** 2
return obj
@staticmethod
def _compute_ineq_constraint1(
x_dv: ndarray,
) -> ndarray:
"""Compute the first constraint.
Args:
x_dv: The design variable vector.
Returns:
The first constraint value.
"""
return array([(x_dv[0] - 5.0) ** 2 + x_dv[1] - 25.0])
@staticmethod
def _compute_ineq_constraint2(
x_dv: ndarray,
) -> ndarray:
"""Compute the second constraint.
Args:
x_dv: The design variable vector.
Returns:
The second constraint value.
"""
return array([-((x_dv[0] - 8.0) ** 2) - (x_dv[1] + 3) + 7.7])
@staticmethod
def _compute_binhkorn_jac(
x_dv: ndarray,
) -> ndarray:
"""Compute the gradient of the objective.
Args:
x_dv: The design variables vector.
Returns:
The gradient of the objective functions
w.r.t the design variables
"""
jac = zeros([2, 2])
jac[0, 0] = 8.0 * x_dv[0]
jac[0, 1] = 8.0 * x_dv[1]
jac[1, 0] = 2.0 * x_dv[0] - 10.0
jac[1, 1] = 2.0 * x_dv[1] - 10.0
return jac
@staticmethod
def _compute_ineq_constraint1_jac(
x_dv: ndarray,
): # (...) -> ndarray
"""Compute the first inequality constraint Jacobian.
Args:
x_dv: The design variables vector.
Returns:
The gradient of the first constraint function
w.r.t the design variables.
"""
jac = zeros([1, 2])
jac[0, 0] = 2.0 * x_dv[0] - 10.0
jac[0, 1] = 2.0 * x_dv[1]
return jac
@staticmethod
def _compute_ineq_constraint2_jac(
x_dv: ndarray,
): # (...) -> ndarray
"""Compute the second inequality constraint Jacobian.
Args:
x_dv: The design variables vector.
Returns:
The gradient of the second constraint function
w.r.t the design variables.
"""
jac = zeros([1, 2])
jac[0, 0] = -2.0 * x_dv[0] + 16.0
jac[0, 1] = -2.0 * x_dv[1] + 6.0
return jac
