Source code for gemseo.problems.analytical.power_2

# -*- 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.
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# 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: Damien Guenot
#        :author: Francois Gallard
#    OTHER AUTHORS   - MACROSCOPIC CHANGES
"""
A quadratic analytical problem
******************************
"""
from __future__ import division, unicode_literals

import logging

from numpy import array
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=False, initial_value=1.0): """The constructor initializes the Power2 :class:`.OptimizationProblem` by defining the :class:`.DesignSpace`, the objective function and the constraints. :param exception_error: if True, call to the objective raises errors useful for tests :type exception_error: bool """ design_space = DesignSpace() design_space.add_variable("x", 3, l_b=-1.0, u_b=1.0, value=initial_value) super(Power2, self).__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"], ) ineq1 = 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(ineq1) ineq2 = MDOFunction( self.ineq_constraint2, name="ineq2", f_type="ineq", jac=self.ineq_constraint2_jac, expr="0.5 -x[1] ** 3", args=["x"], ) self.add_ineq_constraint(ineq2) eq_c = MDOFunction( self.eq_constraint, name="eq", f_type="eq", jac=self.eq_constraint_jac, expr="x[2] ** 3 - 0.9", args=["x"], ) self.add_eq_constraint(eq_c) self.iter_error = 0 self.exception_error = exception_error
[docs] def pow2(self, x_dv): """Compute the objective of analytical function. :param x_dv: design variable vector :type x_dv: numpy array :returns: objective value :rtype: float """ if self.exception_error: if self.iter_error < 3: self.iter_error += 1 obj = np_sum(x_dv ** 2) else: raise ValueError else: obj = np_sum(x_dv ** 2) return obj
[docs] @staticmethod def pow2_jac(x_dv): """Compute the gradient of objective. :param x_dv: design variable vector :type x_dv: numpy array :returns: value of the objective gradient :rtype: numpy array """ return 2 * x_dv
[docs] @staticmethod def ineq_constraint1(x_dv): """Compute the first inequality constraint. :param x_dv: design variable vector :type x_dv: numpy array :returns: value of the first inequality constraint :rtype: numpy array """ return -array([(x_dv[0] ** 3 - 0.5)])
[docs] @staticmethod def ineq_constraint2(x_dv): """Compute the second inequality constraint. :param x_dv: design variable vector :type x_dv: numpy array :returns: value of the second inequality constraint :rtype: numpy array """ return -array([(x_dv[1] ** 3 - 0.5)])
[docs] @staticmethod def eq_constraint(x_dv): """Compute the equality constraint. :param x_dv: design variable vector :type x_dv: numpy array :returns: value of the equality constraint :rtype: numpy array """ return -array([x_dv[2] ** 3 - 0.9])
[docs] @staticmethod def ineq_constraint1_jac(x_dv): """Compute the first inequality constraint gradient. :param x_dv: design variable vector :type x_dv: numpy array :returns: value of the first inequality constraint gradient :rtype: numpy array """ return -array([3 * x_dv[0] * x_dv[0], 0.0, 0.0])
[docs] @staticmethod def ineq_constraint2_jac(x_dv): """Compute the second inequality constraint gradient. :param x_dv: design variable vector :type x_dv: numpy array :returns: value of the second inequality constraint gradient :rtype: numpy array """ return -array([0, 3 * x_dv[1] * x_dv[1], 0.0])
[docs] @staticmethod def eq_constraint_jac(x_dv): """Compute the equality constraint gradient. :param x_dv: design variable vector :type x_dv: numpy array :returns: value of the equality constraint gradient :rtype: numpy array """ return -array([0.0, 0.0, 3 * x_dv[2] * x_dv[2]])
[docs] @staticmethod def get_solution(): """Return analytical result of optimization. :returns: theoretical optimum :rtype: numpy array """ x_opt = array([0.5 ** (1.0 / 3.0), 0.5 ** (1.0 / 3.0), 0.9 ** (1.0 / 3.0)]) f_opt = Power2().pow2(x_opt) return x_opt, f_opt