Source code for openmdao.drivers.scipy_optimizer

"""
OpenMDAO Wrapper for the scipy.optimize.minimize family of local optimizers.
"""

from __future__ import print_function

import sys
from collections import OrderedDict
from distutils.version import LooseVersion

import numpy as np
from scipy import __version__ as scipy_version
from scipy.optimize import minimize
from six import itervalues, iteritems, reraise
from six.moves import range

import openmdao
import openmdao.utils.coloring as coloring_mod
from openmdao.core.driver import Driver, RecordingDebugging
from openmdao.utils.general_utils import warn_deprecation

# Optimizers in scipy.minimize
_optimizers = {'Nelder-Mead', 'Powell', 'CG', 'BFGS', 'Newton-CG', 'L-BFGS-B',
               'TNC', 'COBYLA', 'SLSQP'}
if LooseVersion(scipy_version) >= LooseVersion("1.1"):  # Only available in newer versions
    _optimizers.add('trust-constr')

# For 'basinhopping' and 'shgo' gradients are used only in the local minimization
_gradient_optimizers = {'CG', 'BFGS', 'Newton-CG', 'L-BFGS-B', 'TNC', 'SLSQP', 'dogleg',
                        'trust-ncg', 'trust-constr', 'basinhopping', 'shgo'}
_hessian_optimizers = {'trust-constr', 'trust-ncg'}
_bounds_optimizers = {'L-BFGS-B', 'TNC', 'SLSQP', 'trust-constr', 'dual_annealing', 'shgo',
                      'differential_evolution', 'basinhopping'}
_constraint_optimizers = {'COBYLA', 'SLSQP', 'trust-constr', 'shgo'}
_constraint_grad_optimizers = _gradient_optimizers & _constraint_optimizers
_eq_constraint_optimizers = {'SLSQP', 'trust-constr'}
_global_optimizers = {'differential_evolution', 'basinhopping'}
if LooseVersion(scipy_version) >= LooseVersion("1.2"):  # Only available in newer versions
    _global_optimizers |= {'shgo', 'dual_annealing'}

# Global optimizers and optimizers in minimize
_all_optimizers = _optimizers | _global_optimizers

# These require Hessian or Hessian-vector product, so they are not supported
# right now.
# dual-annealing and basinhopping not supported yet
_unsupported_optimizers = {'dogleg', 'trust-ncg'}

# With "old-style" a constraint is a dictionary, with "new-style" an object
# With "old-style" a bound is a tuple, with "new-style" a Bounds instance
# In principle now everything can work with "old-style"
# These settings have no effect to the optimizers implemented before SciPy 1.1
_supports_new_style = {'trust-constr'}
_use_new_style = True  # Recommended to set to True

CITATIONS = """
@article{Hwang_maud_2018
 author = {Hwang, John T. and Martins, Joaquim R.R.A.},
 title = "{A Computational Architecture for Coupling Heterogeneous
          Numerical Models and Computing Coupled Derivatives}",
 journal = "{ACM Trans. Math. Softw.}",
 volume = {44},
 number = {4},
 month = jun,
 year = {2018},
 pages = {37:1--37:39},
 articleno = {37},
 numpages = {39},
 doi = {10.1145/3182393},
 publisher = {ACM},
"""


[docs]class ScipyOptimizeDriver(Driver): """ Driver wrapper for the scipy.optimize.minimize family of local optimizers. Inequality constraints are supported by COBYLA and SLSQP, but equality constraints are only supported by SLSQP. None of the other optimizers support constraints. ScipyOptimizeDriver supports the following: equality_constraints inequality_constraints Attributes ---------- fail : bool Flag that indicates failure of most recent optimization. iter_count : int Counter for function evaluations. result : OptimizeResult Result returned from scipy.optimize call. opt_settings : dict Dictionary of solver-specific options. See the scipy.optimize.minimize documentation. _con_cache : OrderedDict Cached result of constraint evaluations because scipy asks for them in a separate function. _con_idx : dict Used for constraint bookkeeping in the presence of 2-sided constraints. _grad_cache : OrderedDict Cached result of nonlinear constraint derivatives because scipy asks for them in a separate function. _exc_info : 3 item tuple Storage for exception and traceback information. _obj_and_nlcons : list List of objective + nonlinear constraints. Used to compute total derivatives for all except linear constraints. _dvlist : list Copy of _designvars. _lincongrad_cache : np.ndarray Pre-calculated gradients of linear constraints. """
[docs] def __init__(self, **kwargs): """ Initialize the ScipyOptimizeDriver. Parameters ---------- **kwargs : dict of keyword arguments Keyword arguments that will be mapped into the Driver options. """ super(ScipyOptimizeDriver, self).__init__(**kwargs) # What we support self.supports['inequality_constraints'] = True self.supports['equality_constraints'] = True self.supports['two_sided_constraints'] = True self.supports['linear_constraints'] = True self.supports['simultaneous_derivatives'] = True # What we don't support self.supports['multiple_objectives'] = False self.supports['active_set'] = False self.supports['integer_design_vars'] = False # The user places optimizer-specific settings in here. self.opt_settings = OrderedDict() self.result = None self._grad_cache = None self._con_cache = None self._con_idx = {} self._obj_and_nlcons = None self._dvlist = None self._lincongrad_cache = None self.fail = False self.iter_count = 0 self._exc_info = None self.cite = CITATIONS
def _declare_options(self): """ Declare options before kwargs are processed in the init method. """ self.options.declare('optimizer', 'SLSQP', values=_all_optimizers, desc='Name of optimizer to use') self.options.declare('tol', 1.0e-6, lower=0.0, desc='Tolerance for termination. For detailed ' 'control, use solver-specific options.') self.options.declare('maxiter', 200, lower=0, desc='Maximum number of iterations.') self.options.declare('disp', True, types=bool, desc='Set to False to prevent printing of Scipy convergence messages') self.options.declare('dynamic_simul_derivs', default=False, types=bool, desc='Compute simultaneous derivative coloring dynamically if True ' '(deprecated)') self.options.declare('dynamic_derivs_repeats', default=3, types=int, desc='Number of compute_totals calls during dynamic computation of ' 'simultaneous derivative coloring') def _get_name(self): """ Get name of current optimizer. Returns ------- str The name of the current optimizer. """ return "ScipyOptimize_" + self.options['optimizer'] def _setup_driver(self, problem): """ Prepare the driver for execution. This is the final thing to run during setup. Parameters ---------- problem : <Problem> Pointer """ super(ScipyOptimizeDriver, self)._setup_driver(problem) opt = self.options['optimizer'] self.supports['gradients'] = opt in _gradient_optimizers self.supports['inequality_constraints'] = opt in _constraint_optimizers self.supports['two_sided_constraints'] = opt in _constraint_optimizers self.supports['equality_constraints'] = opt in _eq_constraint_optimizers # Raises error if multiple objectives are not supported, but more objectives were defined. if not self.supports['multiple_objectives'] and len(self._objs) > 1: msg = '{} currently does not support multiple objectives.' raise RuntimeError(msg.format(self.msginfo)) # Since COBYLA does not support bounds, we # need to add to the _cons metadata for any bounds that # need to be translated into a constraint if opt == 'COBYLA': for name, meta in iteritems(self._designvars): lower = meta['lower'] upper = meta['upper'] if isinstance(lower, np.ndarray) or lower >= -openmdao.INF_BOUND \ or isinstance(upper, np.ndarray) or upper <= openmdao.INF_BOUND: d = OrderedDict() d['lower'] = lower d['upper'] = upper d['equals'] = None d['indices'] = None d['adder'] = None d['scaler'] = None d['size'] = meta['size'] d['linear'] = True self._cons[name] = d
[docs] def run(self): """ Optimize the problem using selected Scipy optimizer. Returns ------- boolean Failure flag; True if failed to converge, False is successful. """ problem = self._problem opt = self.options['optimizer'] model = problem.model self.iter_count = 0 self._total_jac = None self._check_for_missing_objective() # Initial Run with RecordingDebugging(self._get_name(), self.iter_count, self) as rec: model.run_solve_nonlinear() self.iter_count += 1 self._con_cache = self.get_constraint_values() desvar_vals = self.get_design_var_values() self._dvlist = list(self._designvars) # maxiter and disp get passsed into scipy with all the other options. self.opt_settings['maxiter'] = self.options['maxiter'] self.opt_settings['disp'] = self.options['disp'] # Size Problem nparam = 0 for param in itervalues(self._designvars): nparam += param['size'] x_init = np.empty(nparam) # Initial Design Vars i = 0 use_bounds = (opt in _bounds_optimizers) if use_bounds: bounds = [] else: bounds = None for name, meta in iteritems(self._designvars): size = meta['size'] x_init[i:i + size] = desvar_vals[name] i += size # Bounds if our optimizer supports them if use_bounds: meta_low = meta['lower'] meta_high = meta['upper'] for j in range(size): if isinstance(meta_low, np.ndarray): p_low = meta_low[j] else: p_low = meta_low if isinstance(meta_high, np.ndarray): p_high = meta_high[j] else: p_high = meta_high bounds.append((p_low, p_high)) if use_bounds and (opt in _supports_new_style) and _use_new_style: # For 'trust-constr' it is better to use the new type bounds, because it seems to work # better (for the current examples in the tests) with the "keep_feasible" option try: from scipy.optimize import Bounds from scipy.optimize._constraints import old_bound_to_new except ImportError: msg = ('The "trust-constr" optimizer is supported for SciPy 1.1.0 and above. ' 'The installed version is {}') raise ImportError(msg.format(scipy_version)) # Convert "old-style" bounds to "new_style" bounds lower, upper = old_bound_to_new(bounds) # tuple, tuple keep_feasible = self.opt_settings.get('keep_feasible_bounds', True) bounds = Bounds(lb=lower, ub=upper, keep_feasible=keep_feasible) # Constraints constraints = [] i = 1 # start at 1 since row 0 is the objective. Constraints start at row 1. lin_i = 0 # counter for linear constraint jacobian lincons = [] # list of linear constraints self._obj_and_nlcons = list(self._objs) if opt in _constraint_optimizers: for name, meta in iteritems(self._cons): size = meta['size'] upper = meta['upper'] lower = meta['lower'] equals = meta['equals'] if 'linear' in meta and meta['linear']: lincons.append(name) self._con_idx[name] = lin_i lin_i += size else: self._obj_and_nlcons.append(name) self._con_idx[name] = i i += size # In scipy constraint optimizers take constraints in two separate formats # Type of constraints is list of NonlinearConstraint if opt in _supports_new_style and _use_new_style: try: from scipy.optimize import NonlinearConstraint except ImportError: msg = ('The "trust-constr" optimizer is supported for SciPy 1.1.0 and' 'above. The installed version is {}') raise ImportError(msg.format(scipy_version)) if equals is not None: lb = ub = equals else: lb = lower ub = upper # Loop over every index separately, # because scipy calls each constraint by index. for j in range(size): # Double-sided constraints are accepted by the algorithm args = [name, False, j] # TODO linear constraint if meta['linear'] # TODO add option for Hessian con = NonlinearConstraint(fun=signature_extender(self._con_val_func, args), lb=lb, ub=ub, jac=signature_extender(self._congradfunc, args)) constraints.append(con) else: # Type of constraints is list of dict # Loop over every index separately, # because scipy calls each constraint by index. for j in range(size): con_dict = {} if meta['equals'] is not None: con_dict['type'] = 'eq' else: con_dict['type'] = 'ineq' con_dict['fun'] = self._confunc if opt in _constraint_grad_optimizers: con_dict['jac'] = self._congradfunc con_dict['args'] = [name, False, j] constraints.append(con_dict) if isinstance(upper, np.ndarray): upper = upper[j] if isinstance(lower, np.ndarray): lower = lower[j] dblcon = (upper < openmdao.INF_BOUND) and (lower > -openmdao.INF_BOUND) # Add extra constraint if double-sided if dblcon: dcon_dict = {} dcon_dict['type'] = 'ineq' dcon_dict['fun'] = self._confunc if opt in _constraint_grad_optimizers: dcon_dict['jac'] = self._congradfunc dcon_dict['args'] = [name, True, j] constraints.append(dcon_dict) # precalculate gradients of linear constraints if lincons: self._lincongrad_cache = self._compute_totals(of=lincons, wrt=self._dvlist, return_format='array') else: self._lincongrad_cache = None # Provide gradients for optimizers that support it if opt in _gradient_optimizers: jac = self._gradfunc else: jac = None # Hessian calculation method for optimizers, which require it if opt in _hessian_optimizers: if 'hess' in self.opt_settings: hess = self.opt_settings.pop('hess') else: # Defaults to BFGS, if not in opt_settings from scipy.optimize import BFGS hess = BFGS() else: hess = None # compute dynamic simul deriv coloring if option is set if coloring_mod._use_total_sparsity: if self._coloring_info['coloring'] is coloring_mod._DYN_COLORING: coloring_mod.dynamic_total_coloring(self, run_model=False, fname=self._get_total_coloring_fname()) elif self.options['dynamic_simul_derivs']: warn_deprecation("The 'dynamic_simul_derivs' option has been deprecated. Call " "the 'declare_coloring' function instead.") coloring_mod.dynamic_total_coloring(self, run_model=False, fname=self._get_total_coloring_fname()) # optimize try: if opt in _optimizers: result = minimize(self._objfunc, x_init, # args=(), method=opt, jac=jac, hess=hess, # hessp=None, bounds=bounds, constraints=constraints, tol=self.options['tol'], # callback=None, options=self.opt_settings) elif opt == 'basinhopping': from scipy.optimize import basinhopping def fun(x): return self._objfunc(x), jac(x) if 'minimizer_kwargs' not in self.opt_settings: self.opt_settings['minimizer_kwargs'] = {"method": "L-BFGS-B", "jac": True} self.opt_settings.pop('maxiter') # It does not have this argument def accept_test(f_new, x_new, f_old, x_old): # Used to implement bounds besides the original functionality if bounds is not None: bound_check = all([b[0] <= xi <= b[1] for xi, b in zip(x_new, bounds)]) user_test = self.opt_settings.pop('accept_test', None) # callable # has to satisfy both the bounds and the acceptance test defined by the # user if user_test is not None: test_res = user_test(f_new, x_new, f_old, x_old) if test_res == 'force accept': return test_res else: # result is boolean return bound_check and test_res else: # no user acceptance test, check only the bounds return bound_check else: return True result = basinhopping(fun, x_init, accept_test=accept_test, **self.opt_settings) elif opt == 'dual_annealing': from scipy.optimize import dual_annealing self.opt_settings.pop('disp') # It does not have this argument # There is no "options" param, so "opt_settings" can be used to set the (many) # keyword arguments result = dual_annealing(self._objfunc, bounds=bounds, **self.opt_settings) elif opt == 'differential_evolution': from scipy.optimize import differential_evolution # There is no "options" param, so "opt_settings" can be used to set the (many) # keyword arguments result = differential_evolution(self._objfunc, bounds=bounds, **self.opt_settings) elif opt == 'shgo': from scipy.optimize import shgo kwargs = dict() for param in ('minimizer_kwargs', 'sampling_method ', 'n', 'iters'): if param in self.opt_settings: kwargs[param] = self.opt_settings[param] # Set the Jacobian and the Hessian to the value calculated in OpenMDAO if 'minimizer_kwargs' not in kwargs or kwargs['minimizer_kwargs'] is None: kwargs['minimizer_kwargs'] = {} kwargs['minimizer_kwargs'].setdefault('jac', jac) kwargs['minimizer_kwargs'].setdefault('hess', hess) # Objective function tolerance self.opt_settings['f_tol'] = self.options['tol'] result = shgo(self._objfunc, bounds=bounds, constraints=constraints, options=self.opt_settings, **kwargs) else: msg = 'Optimizer "{}" is not implemented yet. Choose from: {}' raise NotImplementedError(msg.format(opt, _all_optimizers)) # If an exception was swallowed in one of our callbacks, we want to raise it # rather than the cryptic message from scipy. except Exception as msg: if self._exc_info is not None: self._reraise() else: raise if self._exc_info is not None: self._reraise() self.result = result if hasattr(result, 'success'): self.fail = False if result.success else True if self.fail: print('Optimization FAILED.') print(result.message) print('-' * 35) elif self.options['disp']: print('Optimization Complete') print('-' * 35) else: self.fail = True # It is not known, so the worst option is assumed print('Optimization Complete (success not known)') print(result.message) print('-' * 35) return self.fail
def _objfunc(self, x_new): """ Evaluate and return the objective function. Model is executed here. Parameters ---------- x_new : ndarray Array containing parameter values at new design point. Returns ------- float Value of the objective function evaluated at the new design point. """ model = self._problem.model try: # Pass in new parameters i = 0 for name, meta in iteritems(self._designvars): size = meta['size'] self.set_design_var(name, x_new[i:i + size]) i += size with RecordingDebugging(self._get_name(), self.iter_count, self) as rec: self.iter_count += 1 model.run_solve_nonlinear() # Get the objective function evaluations for obj in itervalues(self.get_objective_values()): f_new = obj break self._con_cache = self.get_constraint_values() except Exception as msg: self._exc_info = sys.exc_info() return 0 # print("Functions calculated") # print(x_new) # print(f_new) return f_new def _con_val_func(self, x_new, name, dbl, idx): """ Return the value of the constraint function requested in args. The lower or upper bound is **not** subtracted from the value. Used for optimizers, which take the bounds of the constraints (e.g. trust-constr) Parameters ---------- x_new : ndarray Array containing parameter values at new design point. name : string Name of the constraint to be evaluated. dbl : bool True if double sided constraint. idx : float Contains index into the constraint array. Returns ------- float Value of the constraint function. """ return self._con_cache[name][idx] def _confunc(self, x_new, name, dbl, idx): """ Return the value of the constraint function requested in args. Note that this function is called for each constraint, so the model is only run when the objective is evaluated. Parameters ---------- x_new : ndarray Array containing parameter values at new design point. name : string Name of the constraint to be evaluated. dbl : bool True if double sided constraint. idx : float Contains index into the constraint array. Returns ------- float Value of the constraint function. """ if self._exc_info is not None: self._reraise() cons = self._con_cache meta = self._cons[name] # Equality constraints equals = meta['equals'] if equals is not None: if isinstance(equals, np.ndarray): equals = equals[idx] return cons[name][idx] - equals # Note, scipy defines constraints to be satisfied when positive, # which is the opposite of OpenMDAO. upper = meta['upper'] if isinstance(upper, np.ndarray): upper = upper[idx] lower = meta['lower'] if isinstance(lower, np.ndarray): lower = lower[idx] if dbl or (lower <= -openmdao.INF_BOUND): return upper - cons[name][idx] else: return cons[name][idx] - lower def _gradfunc(self, x_new): """ Evaluate and return the gradient for the objective. Gradients for the constraints are also calculated and cached here. Parameters ---------- x_new : ndarray Array containing parameter values at new design point. Returns ------- ndarray Gradient of objective with respect to parameter array. """ try: grad = self._compute_totals(of=self._obj_and_nlcons, wrt=self._dvlist, return_format='array') self._grad_cache = grad except Exception as msg: self._exc_info = sys.exc_info() return np.array([[]]) # print("Gradients calculated") # print(x_new) # print(grad[0, :]) return grad[0, :] def _congradfunc(self, x_new, name, dbl, idx): """ Return the cached gradient of the constraint function. Note, scipy calls the constraints one at a time, so the gradient is cached when the objective gradient is called. Parameters ---------- x_new : ndarray Array containing parameter values at new design point. name : string Name of the constraint to be evaluated. dbl : bool Denotes if a constraint is double-sided or not. idx : float Contains index into the constraint array. Returns ------- float Gradient of the constraint function wrt all params. """ if self._exc_info is not None: self._reraise() meta = self._cons[name] if meta['linear']: grad = self._lincongrad_cache else: grad = self._grad_cache grad_idx = self._con_idx[name] + idx # print("Constraint Gradient returned") # print(x_new) # print(name, idx, grad[grad_idx, :]) # Equality constraints if meta['equals'] is not None: return grad[grad_idx, :] # Note, scipy defines constraints to be satisfied when positive, # which is the opposite of OpenMDAO. lower = meta['lower'] if isinstance(lower, np.ndarray): lower = lower[idx] if dbl or (lower <= -openmdao.INF_BOUND): return -grad[grad_idx, :] else: return grad[grad_idx, :] def _reraise(self): """ Reraise any exception encountered when scipy calls back into our method. """ exc = self._exc_info self._exc_info = None reraise(*exc)
[docs]def signature_extender(fcn, extra_args): """ Closure function, which appends extra arguments to the original function call. The first argument is the design vector. The possible extra arguments from the callback of :func:`scipy.optimize.minimize` are not passed to the function. Some algorithms take a sequence of :class:`~scipy.optimize.NonlinearConstraint` as input for the constraints. For this class it is not possible to pass additional arguments. With this function the signature will be correct for both scipy and the driver. Parameters ---------- fcn : callable Function, which takes the design vector as the first argument. extra_args : tuple or list Extra arguments for the function Returns ------- callable The function with the signature expected by the driver. """ def closure(x, *args): return fcn(x, *extra_args) return closure
[docs]class ScipyOptimizer(ScipyOptimizeDriver): """ Deprecated. Use ScipyOptimizeDriver. """
[docs] def __init__(self, **kwargs): """ Initialize attributes. Parameters ---------- **kwargs : dict Named args. """ super(ScipyOptimizer, self).__init__(**kwargs) warn_deprecation("'ScipyOptimizer' provides backwards compatibility " "with OpenMDAO <= 2.2 ; use 'ScipyOptimizeDriver' instead.")