Source code for gemseo.problems.analytical.power_2

# Copyright 2021 IRT Saint Exupéry, https://www.irt-saintexupery.com
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# Lesser General Public License for more details.
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# You should have received a copy of the GNU Lesser General Public License
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# Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
# Contributors:
#    INITIAL AUTHORS - API and implementation and/or documentation
#        :author: Damien Guenot
#        :author: Francois Gallard
#    OTHER AUTHORS   - MACROSCOPIC CHANGES
"""
A quadratic analytical problem
******************************
"""
from __future__ import annotations

import logging

from numpy import array
from numpy import ndarray
from numpy import sum as np_sum

from gemseo.algos.design_space import DesignSpace
from gemseo.algos.opt_problem import OptimizationProblem
from gemseo.core.mdofunctions.mdo_function import MDOFunction

LOGGER = logging.getLogger(__name__)


[docs]class Power2(OptimizationProblem): """**Power2** is a very basic quadratic analytical :class:`.OptimizationProblem`: - Objective to minimize: :math:`x_{dv,0}^2+x_1^2+x_2^2` - Inequality constraint 1: :math:`x_{dv,0}^3 - 0.5 > 0` - Inequality constraint 2: :math:`x_{dv,1}^3 - 0.5 > 0` - Equality constraint: :math:`x_{dv,2}^3 - 0.9 = 0` - Analytical optimum: :math:`(0.5^{1/3}, 0.5^{1/3}, 0.9^{1/3})` """ def __init__( self, exception_error: bool = False, initial_value: float = 1.0 ) -> None: """ Args: exception_error: Whether to raise an error when calling the objective; useful for tests. initial_value: The initial design value of the problem. """ design_space = DesignSpace() design_space.add_variable("x", 3, l_b=-1.0, u_b=1.0, value=initial_value) super().__init__(design_space) self.objective = MDOFunction( self.pow2, name="pow2", f_type="obj", jac=self.pow2_jac, expr="x[0]**2+x[1]**2+x[2]**2", args=["x"], ) self.add_ineq_constraint( MDOFunction( self.ineq_constraint1, name="ineq1", f_type="ineq", jac=self.ineq_constraint1_jac, expr="0.5 -x[0] ** 3", args=["x"], ) ) self.add_ineq_constraint( MDOFunction( self.ineq_constraint2, name="ineq2", f_type="ineq", jac=self.ineq_constraint2_jac, expr="0.5 -x[1] ** 3", args=["x"], ) ) self.add_eq_constraint( MDOFunction( self.eq_constraint, name="eq", f_type="eq", jac=self.eq_constraint_jac, expr="x[2] ** 3 - 0.9", args=["x"], ) ) self.iter_error = 0 self.exception_error = exception_error
[docs] def pow2(self, x_dv: ndarray) -> ndarray: """Compute the objective :math:`x_{dv,0}^2+x_1^2+x_2^2`. Args: x_dv: The design variable vector. Returns: The objective value. Raises: ValueError: When :attr:`.exception_error` is ``True`` and the method has already been called three times. """ if self.exception_error: if self.iter_error >= 3: raise ValueError("pow2() has already been called three times.") self.iter_error += 1 return np_sum(x_dv**2)
[docs] @staticmethod def pow2_jac(x_dv: ndarray) -> ndarray: """Compute the gradient of the objective. Args: x_dv: The design variable vector. Returns: The value of the objective gradient. """ return 2 * x_dv
[docs] @staticmethod def ineq_constraint1(x_dv: ndarray) -> ndarray: """Compute the first inequality constraint :math:`x_{dv,0}^3 - 0.5 > 0`. Args: x_dv: The design variable vector. Returns: The value of the first inequality constraint. """ return -x_dv[[0]] ** 3 + 0.5
[docs] @staticmethod def ineq_constraint2(x_dv: ndarray) -> ndarray: """Compute the second inequality constraint :math:`x_{dv,1}^3 - 0.5 > 0`. Args: x_dv: The design variable vector. Returns: The value of the second inequality constraint. """ return -x_dv[[1]] ** 3 + 0.5
[docs] @staticmethod def eq_constraint(x_dv: ndarray) -> ndarray: """Compute the equality constraint :math:`x_{dv,2}^3 - 0.9 = 0`. Args: x_dv: The design variable vector. Returns: The value of the equality constraint. """ return -x_dv[[2]] ** 3 + 0.9
[docs] @staticmethod def ineq_constraint1_jac(x_dv: ndarray) -> ndarray: """Compute the gradient of the first inequality constraint. Args: x_dv: The design variable vector. Returns: The value of the gradient of the first inequality constraint. """ return -array([3 * x_dv[0] * x_dv[0], 0.0, 0.0])
[docs] @staticmethod def ineq_constraint2_jac(x_dv: ndarray) -> ndarray: """Compute the gradient of the second inequality constraint. Args: x_dv: The design variable vector. Returns: The value of the gradient of the second inequality constraint. """ return -array([0, 3 * x_dv[1] * x_dv[1], 0.0])
[docs] @staticmethod def eq_constraint_jac(x_dv: ndarray) -> ndarray: """Compute the gradient of the equality constraint. Args: x_dv: The design variable vector. Returns: The value of the gradient of the equality constraint. """ return -array([0.0, 0.0, 3 * x_dv[2] * x_dv[2]])
[docs] @staticmethod def get_solution() -> tuple[ndarray, ndarray]: """Return the analytical solution of the problem. Returns: The theoretical optimum of the problem. """ x_opt = array([0.5 ** (1.0 / 3.0), 0.5 ** (1.0 / 3.0), 0.9 ** (1.0 / 3.0)]) f_opt = np_sum(x_opt**2) return x_opt, f_opt