# 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
r"""**Chankong and Haimes multi-objective problem**.
This module implements the Chankong and Haimes multi-objective problem:
.. math::
\begin{aligned}
\text{minimize the objective function }
& f_1(x, y) = 2 + (x - 2)^2 + (y - 1)^2 \\
& f_2(x, y) = 9x - (y - 1)^2 \\
\text{with respect to the design variables }&x,\,y \\
\text{subject to the general constraints }
& g_1(x, y) = x^2 + y^2 \leq 225.0\\
& g_2(x, y) = x - 3y + 10 \leq 0.0\\
\text{subject to the bound constraints }
& -20.0 \leq x \leq 20.\\
& -20.0 \leq y \leq 20.
\end{aligned}
Chankong, V., & Haimes, Y. Y. (2008).
Multiobjective decision making: theory and methodology.
Courier Dover Publications.
"""
from __future__ import annotations
import logging
from gemseo.algos.design_space import DesignSpace
from gemseo.algos.opt_problem import OptimizationProblem
from gemseo.core.mdofunctions.mdo_function import MDOFunction
from numpy import array
from numpy import ndarray
from numpy import zeros
LOGGER = logging.getLogger(__name__)
[docs]class ChankongHaimes(OptimizationProblem):
"""Chankong and Haimes optimization problem."""
def __init__(
self,
l_b: float = -20.0,
u_b: float = 20.0,
initial_guess: ndarray | None = None,
) -> None:
"""The constructor.
Initialize the ChankongHaimes
:class:`~gemseo.algos.opt_problem.OptimizationProblem` by defining the
:class:`~gemseo.algos.design_space.DesignSpace` and the objective and
constraints functions.
Args:
l_b: The lower bound (common value to all variables).
u_b: The upper bound (common value to all variables).
initial_guess: The initial guess for the optimal solution.
"""
design_space = DesignSpace()
design_space.add_variable("x", size=1, l_b=l_b, u_b=u_b)
design_space.add_variable("y", size=1, l_b=l_b, u_b=u_b)
if initial_guess is None:
design_space.set_current_value(zeros(2))
else:
design_space.set_current_value(initial_guess)
super().__init__(design_space)
# Set objective function.
self.objective = MDOFunction(
self.compute_objective,
name="changkong_haimes",
f_type=MDOFunction.TYPE_OBJ,
jac=self.compute_objective_jacobian,
expr="[2 + (x-2)**2 + (y-1)**2, 9*x - (y-1)**2]",
args=["x", "y"],
dim=2,
)
ineq1 = MDOFunction(
self.compute_constraint_1,
name="ineq1",
f_type=MDOFunction.TYPE_INEQ,
jac=self.compute_constraint_1_jacobian,
expr="x**2 + y**2 - 225",
args=["x", "y"],
dim=1,
)
self.add_ineq_constraint(ineq1)
ineq2 = MDOFunction(
self.compute_constraint_2,
name="ineq2",
f_type=MDOFunction.TYPE_INEQ,
jac=self.compute_constraint_2_jacobian,
expr="x - 3*y + 10",
args=["x", "y"],
dim=1,
)
self.add_ineq_constraint(ineq2)
[docs] @staticmethod
def compute_objective(design_variables: ndarray) -> ndarray:
"""Compute the objectives of the Chankong and Haimes function.
Args:
design_variables: The design variables vector.
Returns:
The objective function value.
"""
obj = zeros(2)
obj[0] = (
2.0 + (design_variables[0] - 2.0) ** 2 + (design_variables[1] - 1.0) ** 2
)
obj[1] = 9.0 * design_variables[0] - (design_variables[1] - 1.0) ** 2
return obj
[docs] @staticmethod
def compute_constraint_1(design_variables: ndarray) -> ndarray:
"""Compute the first constraint function.
Args:
design_variables: The design variables vector.
Returns:
The first constraint's value.
"""
return array([design_variables[0] ** 2 + design_variables[1] ** 2 - 225.0])
[docs] @staticmethod
def compute_constraint_2(design_variables: ndarray) -> ndarray:
"""Compute the second constraint function.
Args:
design_variables: The design variables vector.
Returns:
The second constraint's value.
"""
return array([design_variables[0] - 3 * design_variables[1] + 10.0])
[docs] @staticmethod
def compute_objective_jacobian(design_variables: ndarray) -> ndarray:
"""Compute the gradient of objective function.
Args:
design_variables: The design variables vector.
Returns:
The gradient of the objective functions wrt the design variables.
"""
jac = zeros([2, 2])
jac[0, 0] = 2.0 * (design_variables[0] - 2.0)
jac[0, 1] = 2.0 * (design_variables[1] - 1.0)
jac[1, 0] = 9.0
jac[1, 1] = -2.0 * (design_variables[1] - 1.0)
return jac
[docs] @staticmethod
def compute_constraint_1_jacobian(design_variables: ndarray) -> ndarray:
"""Compute the first inequality constraint jacobian.
Args:
design_variables: The design variables vector.
Returns:
The gradient of the first constraint function wrt the design variables.
"""
jac = zeros([1, 2])
jac[0, 0] = 2 * design_variables[0]
jac[0, 1] = 2 * design_variables[1]
return jac
[docs] @staticmethod
def compute_constraint_2_jacobian(design_variables: ndarray) -> ndarray:
"""Compute the second inequality constraint jacobian.
Args:
design_variables: The design variables vector.
Returns:
The gradient of the second constraint function wrt the design variables.
"""
jac = zeros([1, 2])
jac[0, 0] = 1.0
jac[0, 1] = -3.0
return jac
