import warnings
from scipy import optimize
from scipy.optimize import OptimizeWarning
import numpy as np
from CADETProcess import CADETProcessError
from CADETProcess.dataStructure import (
Bool, Switch, UnsignedInteger, UnsignedFloat
)
from CADETProcess.optimization import OptimizerBase, OptimizationProblem
class SciPyInterface(OptimizerBase):
"""Wrapper around scipy's optimization suite.
Defines the bounds and all constraints, saved in a constraint_object. Also
the jacobian matrix is defined for several solvers.
Parameters
----------
finite_diff_rel_step : None or array_like, optional
Relative step size to use for the numerical approximation of the jacobian.
The absolute step size `h` is computed as `h = rel_step * sign(x) * max(1, abs(x))`,
possibly adjusted to fit into the bounds. For `method='3-point'`,
the sign of `h` is ignored.
If `None` (default), the step size is selected automatically.
tol : float, optional
Tolerance for termination. When tol is specified, the selected minimization
algorithm sets some relevant solver-specific tolerance(s) equal to tol.
For detailed control, use solver-specific options.
jac : {'2-point', '3-point', 'cs'}
Method for computing the gradient vector. Only applicable to specific
solvers (CG, BFGS, Newton-CG, L-BFGS-B, TNC, SLSQP, dogleg, trust-ncg,
trust-krylov, trust-exact, and trust-constr).
The default is 2-point.
See Also
--------
COBYLA
TrustConstr
NelderMead
SLSQP
CADETProcess.optimization.OptimizationProblem.evaluate_objectives
options
scipy.optimize.minimize
"""
finite_diff_rel_step = UnsignedFloat()
tol = UnsignedFloat()
jac = Switch(valid=['2-point', '3-point', 'cs'], default='2-point')
def run(self, optimization_problem: OptimizationProblem, x0=None):
"""Solve the optimization problem using any of the scipy methods.
Returns
-------
results : OptimizationResults
Optimization results including optimization_problem and solver
configuration.
x0 : list, optional
Initial values of independent variables in untransformed space.
See Also
--------
COBYLA
TrustConstr
NelderMead
SLSQP
CADETProcess.optimization.OptimizationProblem.evaluate_objectives
options
scipy.optimize.minimize
"""
self.n_evals = 0
if optimization_problem.n_objectives > 1:
raise CADETProcessError("Can only handle single objective.")
def objective_function(x):
return optimization_problem.evaluate_objectives(
x, untransform=True, ensure_minimization=True,
)[0]
def callback_function(x, state=None):
"""Internal callback to report progress after evaluation.
Notes
-----
Currently, this evaluates all functions again. This should not be a problem
since objectives and constraints are automatically cached.
Unfortunately, only `trust-constr` returns a `state` which contains the
current best point. Hence, the internal pareto front is used.
"""
self.n_evals += 1
x = x.tolist()
f = optimization_problem.evaluate_objectives(
x,
untransform=True,
ensure_minimization=True,
)
g = optimization_problem.evaluate_nonlinear_constraints(
x, untransform=True
)
cv = optimization_problem.evaluate_nonlinear_constraints_violation(
x, untransform=True
)
self.run_post_processing(x, f, g, cv, self.n_evals)
return False
if x0 is None:
x0 = optimization_problem.create_initial_values(
1, include_dependent_variables=False
)[0]
x0_transformed = optimization_problem.transform(x0)
options = self.specific_options
if self.results.n_gen > 0:
x0 = self.results.population_last.x[0, :]
self.n_evals = self.results.n_evals
options['maxiter'] = self.maxiter - self.n_evals
if str(self) == 'COBYLA':
options['maxiter'] -= 1
with warnings.catch_warnings():
warnings.filterwarnings('ignore', category=OptimizeWarning)
warnings.filterwarnings('ignore', category=RuntimeWarning)
scipy_results = optimize.minimize(
objective_function,
x0=x0_transformed,
method=str(self),
tol=self.tol,
jac=self.jac,
constraints=self.get_constraint_objects(optimization_problem),
bounds=self.get_bounds(optimization_problem),
options=options,
callback=callback_function,
)
self.results.success = bool(scipy_results.success)
self.results.exit_flag = scipy_results.status
self.results.exit_message = scipy_results.message
def get_bounds(self, optimization_problem):
"""Returns the optimized bounds of a given optimization_problem as a
Bound object.
Optimizes the bounds of the optimization_problem by calling the method
optimize.Bounds. Keep_feasible is set to True.
Returns
-------
bounds : Bounds
Returns the optimized bounds as an object called bounds.
"""
return optimize.Bounds(
optimization_problem.lower_bounds_independent_transformed,
optimization_problem.upper_bounds_independent_transformed,
keep_feasible=True
)
def get_constraint_objects(self, optimization_problem):
"""Return constraints as objets.
Returns
-------
constraint_objects : list
List containing lists of all constraint types of the optimization_problem.
If type of constraints is not defined, it is replaced with None.
See Also
--------
lincon_obj
lincon_obj
nonlincon_obj
"""
lincon = self.get_lincon_obj(optimization_problem)
lineqcon = self.get_lineqcon_obj(optimization_problem)
nonlincon = self.get_nonlincon_obj(optimization_problem)
constraints = [lincon, lineqcon, *nonlincon]
return [con for con in constraints if con is not None]
def get_lincon_obj(self, optimization_problem):
"""Return the linear constraints as an object.
Returns
-------
lincon_obj : LinearConstraint
Linear Constraint object with lower and upper bounds of b of the
optimization_problem.
See Also
--------
constraint_objects
A
b
"""
if optimization_problem.n_linear_constraints == 0:
return None
lb = [-np.inf]*len(optimization_problem.b)
ub = optimization_problem.b_transformed
return optimize.LinearConstraint(
optimization_problem.A_independent_transformed, lb, ub, keep_feasible=True
)
def get_lineqcon_obj(self, optimization_problem):
"""Return the linear equality constraints as an object.
Returns
-------
lineqcon_obj : LinearConstraint
Linear equality Constraint object with lower and upper bounds of beq of the
optimization_problem.
See Also
--------
constraint_objects
Aeq
beq
"""
if optimization_problem.n_linear_equality_constraints == 0:
return None
lb = optimization_problem.beq_transformed - optimization_problem.eps_eq
ub = optimization_problem.beq_transformed + optimization_problem.eps_eq
return optimize.LinearConstraint(
optimization_problem.Aeq_independent_transformed, lb, ub,
keep_feasible=True
)
def get_nonlincon_obj(self, optimization_problem):
"""Return the optimized nonlinear constraints as an object.
Returns
-------
nonlincon_obj : list
Nonlinear constraint violation objects with bounds the optimization_problem.
See Also
--------
constraint_objects
nonlinear_constraints
"""
if optimization_problem.n_nonlinear_constraints == 0:
return [None]
opt = optimization_problem
def makeConstraint(i):
"""Create optimize.NonlinearConstraint object.
Parameters
----------
i : int
Variable index
Returns
-------
constr : optimize.NonlinearConstraint
Constraint object.
Notes
-----
Note, this is necessary to avoid side effects when creating the function
in the main loop.
"""
constr = optimize.NonlinearConstraint(
lambda x: opt.evaluate_nonlinear_constraints_violation(x, untransform=True)[i],
lb=-np.inf, ub=0,
finite_diff_rel_step=self.finite_diff_rel_step,
keep_feasible=True
)
return constr
constraints = []
for i in range(opt.n_nonlinear_constraints):
constraints.append(makeConstraint(i))
return constraints
def __str__(self):
return self.__class__.__name__
[docs]
class TrustConstr(SciPyInterface):
"""Wrapper for the trust-constr optimization method from the scipy optimization suite.
It defines the solver options in the 'options' variable as a dictionary.
Supports:
- Linear constraints.
- Linear equality constraints.
- Nonlinear constraints.
- Bounds.
Parameters
----------
gtol : UnsignedFloat, optional
Tolerance for termination by the norm of the Lagrangian gradient.
The algorithm will terminate when both the infinity norm (i.e., max abs value)
of the Lagrangian gradient and the constraint violation are smaller than gtol.
Default is 1e-8.
xtol : UnsignedFloat, optional
Tolerance for termination by the change of the independent variable.
The algorithm will terminate when tr_radius < xtol,
where tr_radius is the radius of the trust region used in the algorithm.
Default is 1e-8.
barrier_tol : UnsignedFloat, optional
Threshold on the barrier parameter for the algorithm termination.
When inequality constraints are present, the algorithm will terminate only
when the barrier parameter is less than barrier_tol.
Default is 1e-8.
initial_tr_radius : float, optional
Initial trust radius. The trust radius gives the maximum distance between solution points
in consecutive iterations. It reflects the trust the algorithm puts in the local approximation
of the optimization problem. For an accurate local approximation, the trust-region should be large,
and for an approximation valid only close to the current point, it should be a small one.
The trust radius is automatically updated throughout the optimization process,
with initial_tr_radius being its initial value. Default is 1.
initial_constr_penalty : float, optional
Initial constraints penalty parameter. The penalty parameter is used for balancing
the requirements of decreasing the objective function and satisfying the constraints.
It is used for defining the merit function: merit_function(x) = fun(x)
+ constr_penalty * constr_norm_l2(x), where constr_norm_l2(x) is the l2 norm of a vector
containing all the constraints. The merit function is used for accepting or rejecting trial points,
and constr_penalty weights the two conflicting goals of reducing the objective function and constraints.
The penalty is automatically updated throughout the optimization process,
with initial_constr_penalty being its initial value. Default is 1.
initial_barrier_parameter : float, optional
Initial barrier parameter. Used only when inequality constraints are present.
For dealing with optimization problems min_x f(x) subject to inequality constraints c(x) <= 0,
the algorithm introduces slack variables, solving the problem
min_(x, s) f(x) + barrier_parameter * sum(ln(s)) subject to the equality constraints c(x) + s = 0
instead of the original problem. This subproblem is solved for decreasing values of barrier_parameter
and with decreasing tolerances for the termination, starting with initial_barrier_parameter for the barrier parameter.
Default is 0.1.
initial_barrier_tolerance : float, optional
Initial tolerance for the barrier subproblem. Used only when inequality constraints are present.
For dealing with optimization problems min_x f(x) subject to inequality constraints c(x) <= 0,
the algorithm introduces slack variables, solving the problem
min_(x, s) f(x) + barrier_parameter * sum(ln(s)) subject to the equality constraints c(x) + s = 0
instead of the original problem. This subproblem is solved for decreasing values of barrier_parameter
and with decreasing tolerances for the termination, starting with initial_barrier_tolerance for the barrier tolerance.
Default is 0.1.
factorization_method : str or None, optional
Method to factorize the Jacobian of the constraints.
Use None (default) for auto selection or one of:
- 'NormalEquation'
- 'AugmentedSystem'
- 'QRFactorization'
- 'SVDFactorization'.
The methods 'NormalEquation' and 'AugmentedSystem' can be used only with sparse
constraints. The methods 'QRFactorization' and 'SVDFactorization' can be used
only with dense constraints.
Default is None.
maxiter : UnsignedInteger, optional
Maximum number of algorithm iterations. Default is 1000.
verbose : UnsignedInteger, optional
Level of algorithm's verbosity:
- 0 (default) for silent
- 1 for a termination report
- 2 for progress during iterations
- 3 for more complete progress report.
disp : Bool, optional
If True, then verbose will be set to 1 if it was 0. Default is False.
"""
supports_linear_constraints = True
supports_linear_equality_constraints = True
supports_nonlinear_constraints = True
supports_bounds = True
gtol = UnsignedFloat(default=1e-8)
xtol = UnsignedFloat(default=1e-8)
barrier_tol = UnsignedFloat(default=1e-8)
initial_tr_radius = UnsignedFloat(default=1.0)
initial_constr_penalty = UnsignedFloat(default=1.0)
initial_barrier_parameter = UnsignedFloat(default=0.1)
initial_barrier_tolerance = UnsignedFloat(default=0.1)
factorization_method = Switch(valid=[
'NormalEquation', 'AugmentedSystem', 'QRFactorization', 'SVDFactorization'
])
maxiter = UnsignedInteger(default=1000)
verbose = UnsignedInteger(default=0)
disp = Bool(default=False)
x_tol = xtol # Alias for uniform interface
cv_tol = gtol # Alias for uniform interface
n_max_evals = maxiter # Alias for uniform interface
n_max_iter = maxiter # Alias for uniform interface
_specific_options = [
'gtol', 'xtol', 'barrier_tol', 'finite_diff_rel_step',
'initial_constr_penalty', 'initial_tr_radius', 'initial_barrier_parameter',
'initial_barrier_tolerance', 'factorization_method', 'maxiter', 'verbose', 'disp'
]
def __str__(self):
return 'trust-constr'
[docs]
class COBYLA(SciPyInterface):
"""Wrapper for the COBYLA optimization method from the scipy optimization suite.
It defines the solver options in the 'options' variable as a dictionary.
Supports:
- Linear constraints
- Linear equality constraints
- Nonlinear constraints
Parameters
----------
rhobeg : float, default 1
Reasonable initial changes to the variables.
tol : float, default 0.0002
Final accuracy in the optimization (not precisely guaranteed).
This is a lower bound on the size of the trust region.
disp : bool, default False
Set to True to print convergence messages.
If False, verbosity is ignored and set to 0.
maxiter : int, default 10000
Maximum number of function evaluations.
catol : float, default 2e-4
Absolute tolerance for constraint violations.
"""
supports_linear_constraints = True
supports_linear_equality_constraints = True
supports_nonlinear_constraints = True
supports_bounds = True
rhobeg = UnsignedFloat(default=1)
tol = UnsignedFloat(default=0.0002)
maxiter = UnsignedInteger(default=10000)
disp = Bool(default=False)
catol = UnsignedFloat(default=0.0002)
f_tol = tol # Alias for uniform interface
cv_tol = catol # Alias for uniform interface
n_max_evals = maxiter # Alias for uniform interface
n_max_iter = maxiter # Alias for uniform interface
_specific_options = ['rhobeg', 'tol', 'maxiter', 'disp', 'catol']
[docs]
class NelderMead(SciPyInterface):
"""Wrapper for the Nelder-Mead optimization method from the scipy optimization suite.
It defines the solver options in the 'options' variable as a dictionary.
Parameters
----------
maxiter : UnsignedInteger
Maximum allowed number of iterations. The default = 1000.
initial_simplex : None or array_like, optional
Initial simplex. If given, it overrides x0.
initial_simplex[j, :] should contain the coordinates of the jth vertex of the
N+1 vertices in the simplex, where N is the dimension.
xatol : UnsignedFloat, optional
Absolute error in xopt between iterations that is acceptable for convergence.
fatol : UnsignedFloat, optional
Absolute error in f(xopt) between iterations that is acceptable for convergence.
adaptive : Bool, optional
Adapt algorithm parameters to dimensionality of the problem.
Useful for high-dimensional minimization.
disp : Bool, optional
Set to True to print convergence messages.
"""
maxiter = UnsignedInteger(default=1000)
initial_simplex = None
xatol = UnsignedFloat(default=1e-3)
fatol = UnsignedFloat(default=1e-3)
adaptive = Bool(default=True)
disp = Bool(default=False)
x_tol = xatol # Alias for uniform interface
f_tol = fatol # Alias for uniform interface
n_max_evals = maxiter # Alias for uniform interface
n_max_iter = maxiter # Alias for uniform interface
_specific_options = [
'maxiter', 'initial_simplex', 'xatol', 'fatol', 'adaptive', 'disp'
]
def __str__(self):
return 'Nelder-Mead'
[docs]
class SLSQP(SciPyInterface):
"""Wrapper for the SLSQP optimization method from the scipy optimization suite.
It defines the solver options in the 'options' variable as a dictionary.
Supports:
- Linear constraints
- Linear equality constraints
- Nonlinear constraints
- Bounds
Parameters
----------
ftol : float, default 1e-2
Precision goal for the value of f in the stopping criterion.
eps : float, default 1e-6
Step size used for numerical approximation of the Jacobian.
disp : bool, default False
Set to True to print convergence messages.
If False, verbosity is ignored and set to 0.
maxiter : int, default 1000
Maximum number of iterations.
iprint: int, optional
The verbosity of fmin_slsqp :
iprint <= 0 : Silent operation
iprint == 1 : Print summary upon completion (default)
iprint >= 2 : Print status of each iterate and summary
"""
supports_linear_constraints = True
supports_linear_equality_constraints = True
supports_nonlinear_constraints = True
supports_bounds = True
ftol = UnsignedFloat(default=1e-2)
eps = UnsignedFloat(default=1e-6)
disp = Bool(default=False)
maxiter = UnsignedInteger(default=1000)
iprint = UnsignedInteger(ub=2, default=1)
f_tol = ftol # Alias for uniform interface
n_max_evals = maxiter # Alias for uniform interface
n_max_iter = maxiter # Alias for uniform interface
_specific_options = [
'ftol', 'eps', 'disp', 'maxiter', 'finite_diff_rel_step', 'iprint'
]
