# Source code for gemseo.algos.opt.lib_snopt

```
# 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: Damien Guenot
# OTHER AUTHORS - MACROSCOPIC CHANGES
# Francois Gallard : refactoring for v1, May 2016
"""SNOPT optimization library wrapper."""
from __future__ import annotations
import logging
from dataclasses import dataclass
from typing import Any
from typing import Callable
from typing import Optional
from typing import Tuple
from typing import Union
from numpy import append
from numpy import array
from numpy import concatenate
from numpy import float as np_float
from numpy import float64
from numpy import full
from numpy import hstack
from numpy import int as np_int
from numpy import isinf
from numpy import ndarray
from numpy import ones
from numpy import reshape
from numpy import str as np_str
from numpy import vstack
from numpy import where
from numpy import zeros
from optimize.snopt7 import SNOPT_solver
from gemseo.algos.opt.opt_lib import OptimizationAlgorithmDescription
from gemseo.algos.opt.opt_lib import OptimizationLibrary
from gemseo.algos.opt_result import OptimizationResult
LOGGER = logging.getLogger(__name__)
INFINITY = 1e30
OptionType = Optional[Union[str, int, float, bool, ndarray]]
SnOptPreprocessType = Tuple[
Callable[[int, int, int, int, ndarray, int], Any],
ndarray,
ndarray,
ndarray,
int,
]
[docs]@dataclass
class SNOPTAlgorithmDescription(OptimizationAlgorithmDescription):
"""The description of an optimization algorithm from the SNOPT library."""
library_name: str = "SNOPT"
[docs]class SnOpt(OptimizationLibrary):
"""SNOPT optimization library interface.
See OptimizationLibrary.
"""
LIB_COMPUTE_GRAD = False
OPTIONS_MAP = {"max_iter": "Iteration_limit"}
MESSAGES_DICT = {
1: "optimality conditions satisfied",
2: "feasible point found",
3: "requested accuracy could not be achieved",
11: "infeasible linear constraints",
12: "infeasible linear equalities",
13: "nonlinear infeasibilities minimized",
14: "infeasibilities minimized",
21: "unbounded objective",
22: "constraint violation limit reached",
31: "iteration limit reached",
32: "major iteration limit reached",
33: "the superbasics limit is too small",
41: "current point cannot be improved ",
42: "singular basis",
43: "cannot satisfy the general constraints",
44: "ill-conditioned null-space basis",
51: "incorrect objective derivatives",
52: "incorrect constraint derivatives",
61: "undefined function at the first feasible point",
62: "undefined function at the initial point",
63: "unable to proceed into undefined region",
72: "terminated during constraint evaluation",
73: "terminated during objective evaluation",
74: "terminated from monitor routine",
81: "work arrays must have at least 500 elements",
82: "not enough character storage",
83: "not enough integer storage",
84: "not enough real storage",
91: "invalid input argument",
92: "basis file dimensions do not match this problem",
141: "wrong number of basic variables",
142: "error in basis package",
}
LIBRARY_NAME = "SNOPT"
def __init__(self):
"""Constructor.
Generate the library dict, contains the list
of algorithms with their characteristics:
* does it require gradient,
* does it handle equality constraints,
* does it handle inequality constraints.
"""
super().__init__()
self.__n_ineq_constraints = 0
self.__n_eq_constraints = 0
self.descriptions = {
"SNOPTB": SNOPTAlgorithmDescription(
algorithm_name="SNOPT",
description="Sparse Nonlinear OPTimizer (SNOPT)",
handle_equality_constraints=True,
handle_inequality_constraints=True,
internal_algorithm_name="SNOPTB",
require_gradient=True,
website="https://ccom.ucsd.edu/~optimizers",
)
}
def _get_options(
self,
ftol_rel: float = 1e-9,
ftol_abs: float = 1e-9,
xtol_rel: float = 1e-9,
xtol_abs: float = 1e-9,
max_time: float = 0,
max_iter: int = 999, # pylint: disable=W0221
normalize_design_space: bool = True,
**kwargs: OptionType,
) -> dict[str, Any]:
"""Set the options.
Args:
ftol_rel: A stop criteria, the relative tolerance on the
objective function.
If abs(f(xk)-f(xk+1))/abs(f(xk))<= ftol_rel: stop.
ftol_abs: A stop criteria, the absolute tolerance on the objective
function. If abs(f(xk)-f(xk+1))<= ftol_rel: stop.
xtol_rel: A stop criteria, the relative tolerance on the
design variables. If norm(xk-xk+1)/norm(xk)<= xtol_rel: stop.
xtol_abs: A stop criteria, the absolute tolerance on the
design variables. If norm(xk-xk+1)<= xtol_abs: stop.
max_time: max_time: The maximum runtime in seconds,
disabled if 0.
max_iter: The maximum number of iterations,
i.e. unique calls to f(x).
normalize_design_space: If True, scales variables to [0, 1].
**kwargs: The additional options.
"""
nds = normalize_design_space
return self._process_options(
max_iter=max_iter,
normalize_design_space=nds,
ftol_rel=ftol_rel,
ftol_abs=ftol_abs,
xtol_rel=xtol_rel,
xtol_abs=xtol_abs,
max_time=max_time,
**kwargs,
)
@staticmethod
def __eval_func(
func: Callable[[ndarray], ndarray],
xn_vect: ndarray,
) -> tuple[ndarray, int]:
"""Evaluate a function at the given points.
Try to call it, if it fails, return a -1 status.
Args
func: The function to call.
xn_vect : The arguments for the function evaluation.
Returns:
The function value at `xn_vect` and the status of the evaluation.
"""
try:
val = func(xn_vect)
return val, 1
# SNOPT can handle non-computable points
except Exception as func_error:
LOGGER.error("SNOPT failed to evaluate the function !")
LOGGER.error(func_error.args[0])
return array([float("nan")]), -1
# cb_ means callback and avoids pylint to raise warnings
# about unused arguments
[docs] def cb_opt_objective_snoptb(
self,
mode: int,
nn_obj: int,
xn_vect: ndarray,
n_state: int = 0,
) -> tuple[int, ndarray, ndarray]:
r"""Evaluate the objective function and gradient.
Use the snOpt conventions for mode and status
(from web.stanford.edu/group/SOL/guides/sndoc7.pdf).
Args:
mode: Flag to indicate whether the obj, the gradient or both must
be assigned during the present call of the function
(0 :math:`\leq` mode :math:`\leq` 2).
mode = 2, assign the obj and the known components of the gradient.
mode = 1, assign the known components of gradient. obj is ignored.
mode = 0, only the obj needs to be assigned; the
gradient is ignored.
nn_obj: The number of design variables.
xn_vect: The normalized design vector.
n_state: An indicator for the first and last call to the current
function.
n_state = 0: NTR.
n_state = 1: first call to driver.cb_opt_objective_snoptb.
n_state > 1, snOptB is calling subroutine for the last time and:
n_state = 2 and the current x is optimal
n_state = 3, the problem appears to be infeasible
n_state = 4, the problem appears to be unbounded;
n_state = 5, an iterations limit was reached.
Returns:
The solution status, the evaluation of the objective function and its
gradient.
"""
obj_func = self.problem.objective
status = -1
if mode == 0:
obj_f, status = self.__eval_func(obj_func.func, xn_vect)
obj_df = full((xn_vect.shape[0],), 666.0)
if mode == 1:
obj_df, status = self.__eval_func(obj_func.jac, xn_vect)
obj_f = -666.0
if mode == 2:
obj_df, f_status = self.__eval_func(obj_func.jac, xn_vect)
obj_f, df_status = self.__eval_func(obj_func.func, xn_vect)
if f_status == 1 and df_status == 1:
status = 1
else:
status = -1
return status, obj_f, obj_df
def __snoptb_create_c(self, xn_vect: ndarray) -> tuple[ndarray, int]:
"""Return the evaluation of the constraints at the design vector.
Args:
xn_vect: The normalized design variables vector.
Returns:
The evaluation of the constraints at `xn_vect` and the status of
the evaluation.
"""
cstr = array([])
for constraint in self.problem.get_eq_constraints():
c_val, status = self.__eval_func(constraint, xn_vect)
if status == -1:
return c_val, -1
cstr = hstack((cstr, c_val))
for constraint in self.problem.get_ineq_constraints():
c_val, status = self.__eval_func(constraint, xn_vect)
if status == -1:
return c_val, -1
cstr = hstack((cstr, c_val))
return cstr, 1
def __snoptb_create_dc(self, xn_vect: ndarray) -> tuple[ndarray, int]:
"""Evaluate the constraints gradient at the design vector xn_vect.
Args:
xn_vect: The normalized design variables vector.
Returns:
The evaluation of the constraints gradient at xn_vect and the status
of the computation.
"""
dcstr = array([])
# First equality constraints then inequality
for constraint in self.problem.get_eq_constraints():
dc_val, status = self.__eval_func(constraint.jac, xn_vect)
if status == -1:
return dc_val, status
if dcstr:
dcstr = vstack((dcstr, dc_val))
else:
dcstr = dc_val
for constraint in self.problem.get_ineq_constraints():
dc_val, status = self.__eval_func(constraint.jac, xn_vect)
if status == -1:
return dc_val, status
if dcstr.size > 0:
dcstr = vstack((dcstr, dc_val))
else:
dcstr = dc_val
if len(dcstr.shape) > 1:
dcstr = reshape(dcstr.T, dcstr.shape[0] * dcstr.shape[1])
return dcstr, 1
# cb_ means callback and avoids pylint to raise warnings
# about unused arguments
[docs] def cb_opt_constraints_snoptb(
self,
mode: int,
nn_con: int,
nn_jac: int,
ne_jac: int,
xn_vect: ndarray,
n_state: int,
) -> tuple[int, ndarray, ndarray]:
"""Evaluate the constraint functions and their gradient.
Use the snOpt conventions (from
web.stanford.edu/group/SOL/guides/sndoc7.pdf).
Args:
mode: A flag that indicates whether the obj, the gradient or both must
be assigned during the present call of function (0 ≤ mode ≤ 2).
mode = 2, assign obj and the known components of gradient.
mode = 1, assign the known components of gradient. obj is ignored.
mode = 0, only obj need be assigned; gradient is ignored.
nn_con: The number of non-linear constraints.
nn_jac: The number of dv involved in non-linear
constraint functions.
ne_jac: The number of non-zero elements in the constraints gradient.
If dcstr is 2D, then ne_jac = nn_con*nn_jac.
xn_vect: The normalized design vector.
n_state: An indicator for the first and last call to the current
function
n_state = 0: NTR.
n_state = 1: first call to driver.cb_opt_objective_snoptb.
n_state > 1, snOptB is calling subroutine for the last time and:
n_state = 2 and the current x is optimal
n_state = 3, the problem appears to be infeasible
n_state = 4, the problem appears to be unbounded;
n_state = 5, an iterations limit was reached.
Returns:
The solution status, the evaluation of the constraint function and
its gradient.
"""
if mode == 0:
cstr, status = self.__snoptb_create_c(xn_vect)
dcstr = full(
(self.__n_eq_constraints + self.__n_ineq_constraints)
* xn_vect.shape[0],
666.0,
)
status = 1
elif mode == 1:
dcstr, status = self.__snoptb_create_dc(xn_vect)
cstr = full((self.__n_eq_constraints + self.__n_ineq_constraints,), 666.0)
elif mode == 2:
cstr, c_status = self.__snoptb_create_c(xn_vect)
dcstr, dc_status = self.__snoptb_create_dc(xn_vect)
if c_status == 1 and dc_status == 1:
status = 1
else:
status = -1
return status, cstr, dcstr
# cb_ means callback and avoids pylint to raise warnings
# about unused arguments
[docs] @staticmethod
def cb_snopt_dummy_func(
mode: int,
nn_con: int,
nn_jac: int,
ne_jac: int,
xn_vect: ndarray,
n_state: int,
) -> float:
"""Return a dummy output for unconstrained problems.
Args:
mode: A flag that indicates whether the obj, the gradient or both must
be assigned during the present call of function (0 ≤ mode ≤ 2).
mode = 2, assign obj and the known components of gradient.
mode = 1, assign the known components of gradient. obj is ignored.
mode = 0, only obj need be assigned; gradient is ignored.
nn_con: The number of non-linear constraints.
nn_jac: The number of dv involved in non-linear
constraint functions.
ne_jac: The number of non-zero elements in the constraints gradient.
If dcstr is 2D, then ne_jac = nn_con*nn_jac.
xn_vect: The normalized design vector.
n_state: An indicator for the first and last call to the current
function
n_state = 0: NTR.
n_state = 1: first call to driver.cb_opt_objective_snoptb.
n_state > 1, snOptB is calling subroutine for the last time and:
n_state = 2 and the current x is optimal
n_state = 3, the problem appears to be infeasible
n_state = 4, the problem appears to be unbounded;
n_state = 5, an iterations limit was reached.
Returns:
A dummy output.
"""
return 1.0
def __preprocess_snopt_constraints(
self, names: ndarray(dtype=np_str)
) -> SnOptPreprocessType:
"""Set the snopt parameters according to the constraints.
Args:
names: The names of the design variables and constraints to
be stored in the snopt internal process.
Returns:
The pointer to the constraint value & gradient,
the array of lower bound constraints,
the array of upper bound constraints,
the design variable names and constraint names,
and the number of constraints.
"""
blc = array(())
buc = array(())
if self.__n_eq_constraints > 0:
blc = zeros((self.__n_eq_constraints,))
buc = zeros((self.__n_eq_constraints,))
ceqlist = ["c_eq" + str(i) for i in range(self.__n_eq_constraints)]
names = append(names, array(ceqlist, dtype=str))
if self.__n_ineq_constraints > 0:
min_inf = full(self.__n_ineq_constraints, -INFINITY)
blc = append(blc, min_inf)
buc = append(buc, zeros(self.__n_ineq_constraints))
cieqlist = ["c_ie" + str(i) for i in range(self.__n_ineq_constraints)]
names = append(names, array(cieqlist, dtype=str))
# Mandatory dummy free row if unconstrained
n_constraints = self.__n_ineq_constraints + self.__n_eq_constraints
if n_constraints == 0:
n_constraints = 1
funcon = self.cb_snopt_dummy_func
blc = append(blc, full((1,), -INFINITY))
buc = append(buc, full((1,), INFINITY))
names = append(names, array(["dummy"], dtype=np_str))
else:
funcon = self.cb_opt_constraints_snoptb
return funcon, blc, buc, names, n_constraints
def _run(self, **options: OptionType) -> OptimizationResult:
"""Run the algorithm, to be overloaded by subclasses.
Args:
**options: The options for the algorithm,
see the associated JSON file.
Returns:
The optimization result.
Raises:
KeyError: If an unknown option or incorrect type is provided.
"""
normalize_ds = options.pop(self.NORMALIZE_DESIGN_SPACE_OPTION, True)
# Get the bounds anx x0
x_0, l_b, u_b = self.get_x0_and_bounds_vects(normalize_ds)
self.__n_ineq_constraints = self.problem.get_ineq_cstr_total_dim()
self.__n_eq_constraints = self.problem.get_eq_cstr_total_dim()
snopt_problem = SNOPT_solver(name="SNOPTB")
for (key, value) in options.items():
try:
snopt_problem.setOption(key.replace("_", " "), value)
except RuntimeError:
raise KeyError(
"Unknown option or incorrect type :" + str(key) + ":" + str(value)
)
snopt_problem.setOption("Verbose", True)
snopt_problem.setOption("Solution print", True)
# n_nonlinear_constraints = n_ineq_constraints + n_eq_constraints
# It is assumed that all constraints provided to optimizer are not
# inear
# n_linear_constraints = 0
# n_nonlinear_constraints = n_ineq_constraints + n_eq_constraints
n_design_variables = x_0.shape[0]
# Get the normalized bounds:
l_b = where(isinf(l_b), -INFINITY, l_b)
u_b = where(isinf(u_b), INFINITY, u_b)
names = array(["dv" + str(i) for i in range(n_design_variables)], dtype=str)
i_obj = array([0], np_int)
funcon, blc, buc, names, n_constraints = self.__preprocess_snopt_constraints(
names
)
n_nl_func = n_constraints
x0_snopt = append(x_0, zeros((n_constraints,), dtype=float64))
lower_bounds = concatenate((l_b, blc))
upper_bounds = concatenate((u_b, buc))
jacobian = ones((n_nl_func, x_0.shape[0]))
obj_add = array([0.0], np_float)
snopt_problem.snoptb(
# name='SNOPTB',
m=n_nl_func,
x0=x0_snopt,
n=n_design_variables,
nnCon=n_constraints,
nnObj=n_design_variables,
nnJac=n_design_variables,
iObj=i_obj,
bl=lower_bounds,
bu=upper_bounds,
J=jacobian,
ObjAdd=obj_add,
funcon=funcon,
Names=names,
funobj=self.cb_opt_objective_snoptb,
)
message = self.MESSAGES_DICT[snopt_problem.info]
status = snopt_problem.info
return self.get_optimum_from_database(message, status)
```