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from __future__ import print_function 

from __future__ import absolute_import 

from __future__ import division 

from builtins import range 

from builtins import object 

from gpkit import Model, Variable, SignomialsEnabled 

from gpkit.nomials import SignomialInequality, MonomialEquality 

from gpkit.exceptions import InvalidGPConstraint 

from gpkit.nomials import SingleSignomialEquality 

import numpy as np 

from time import time 

import warnings 

from scipy.stats import norm 

 

from .robust_gp_tools import RobustGPTools 

from .equivalent_posynomials import EquivalentPosynomials 

from .equivalent_models import TwoTermBoydModel 

from .twoterm_approximation import TwoTermApproximation 

from .robustify_large_posynomial import RobustifyLargePosynomial 

from .linearize_twoterm_posynomials import LinearizeTwoTermPosynomials 

 

 

class RobustnessSetting(object): 

def __init__(self, **options): 

self._options = { 

'gamma': 1, 

'simpleModel': False, 

'numberOfRegressionPoints': 2, 

'numberOfRegressionPointsElliptical': 25, 

'linearizeTwoTerm': True, 

'enableSP': True, 

'boyd': False, 

'twoTerm': True, 

'simpleTwoTerm': False, 

'smartTwoTermChoose': False, 

'allowedNumOfPerms': 30, 

'linearizationTolerance': 0.001, 

'minNumOfLinearSections': 12, 

'maxNumOfLinearSections': 20, 

'iterationsRelativeTolerance': 1e-4, 

'iterationLimit': 10, 

'probabilityOfSuccess': 0.9, 

'lognormal': True 

} 

for key, value in options.items(): 

self._options[key] = value 

 

if self._options['twoTerm']: 

self._options['linearizeTwoTerm'] = True 

self._options['enableSP'] = False 

 

if self._options['simpleModel']: 

self._options['allowedNumOfPerms'] = 1 

 

def get(self, option_name): 

return self._options[option_name] 

 

def set(self, option_name, value): 

self._options[option_name] = value 

 

 

class RobustModel(object): 

""" 

RobustModel extends gpkit.Model through the robust counterpart. 

It uses the nominal solution of the GP or SP to 

""" 

def __init__(self, model, type_of_uncertainty_set, **options): 

self.nominal_model = model 

self.substitutions = model.substitutions 

self.type_of_uncertainty_set = type_of_uncertainty_set 

 

self.setting = RobustnessSetting(**options) 

slopes_intercepts = LinearizeTwoTermPosynomials. \ 

two_term_posynomial_linearization_coeff(self.setting.get('minNumOfLinearSections')) 

self.robust_solve_properties = {'setuptime': 0, 

'numoflinearsections': self.setting.get('minNumOfLinearSections'), 

'slopes': slopes_intercepts[0], 

'intercepts': slopes_intercepts[1] 

} 

 

self.number_of_stds = norm.ppf(self.setting.get("probabilityOfSuccess") / 2.0 + 0.5) 

 

if 'nominalsolve' in options: 

self.nominal_solve = options['nominalsolve'] 

else: 

self.nominal_solve = RobustModel.internalsolve(model, verbosity=0) 

self.nominal_solution = self.nominal_solve.get('variables') 

self.nominal_cost = self.nominal_solve['cost'] 

 

self._sequence_of_rgps = [] 

self._robust_model = None 

 

self.lower_approximation_is_feasible = False 

 

if self.type_of_uncertainty_set == 'box': 

self.dependent_uncertainty_set = False 

else: 

self.dependent_uncertainty_set = True 

if self.type_of_uncertainty_set == 'elliptical': 

self.setting.set('numberOfRegressionPoints', self.setting.get('numberOfRegressionPointsElliptical')) 

 

self.ready_gp_constraints = [] 

self.to_linearize_gp_posynomials = [] 

self.large_gp_posynomials = [] 

self.sp_constraints = [] 

self.sp_equality_constraints = [] 

 

equality_constraints = False 

 

if self.setting.get('boyd'): 

self.setting.set('iterationLimit', 1) 

try: 

safe_model = TwoTermBoydModel(model) 

except InvalidGPConstraint: 

raise Exception("boyd's formulation is not supported for sp models") 

safe_model_constraints = safe_model.flat(constraintsets=False) 

del safe_model 

for cs in safe_model_constraints: 

if isinstance(cs, MonomialEquality): 

self.ready_gp_constraints += [cs] 

equality_constraints = True 

else: 

p = cs.as_posyslt1()[0] 

if len(p.exps) == 1: 

robust_monomial = self.robustify_monomial(p) 

self.ready_gp_constraints += [robust_monomial <= 1] 

else: 

self.to_linearize_gp_posynomials += [p] 

del safe_model_constraints 

 

if equality_constraints: 

warnings.warn('equality constraints will not be robustified') 

self.number_of_gp_posynomials = 0 

return 

 

all_constraints = model.flat(constraintsets=False) 

 

gp_posynomials = [] 

 

for cs in all_constraints: 

if isinstance(cs, SingleSignomialEquality): 

self.sp_equality_constraints.append(cs) 

elif isinstance(cs, SignomialInequality): 

self.sp_constraints.append(cs) 

elif isinstance(cs, MonomialEquality): 

self.ready_gp_constraints += [cs] 

equality_constraints = True 

 

else: 

gp_posynomials += cs.as_posyslt1() 

 

self.number_of_gp_posynomials = len(gp_posynomials) 

 

constraints_posynomials_tuple = self.classify_gp_constraints(gp_posynomials) 

 

self.ready_gp_constraints += constraints_posynomials_tuple[0] 

self.to_linearize_gp_posynomials = constraints_posynomials_tuple[1] 

self.large_gp_posynomials = constraints_posynomials_tuple[2] 

 

if equality_constraints: 

warnings.warn('equality constraints will not be robustified') 

 

def setup(self, verbosity=0, **options): 

for option, key in options.items(): 

self.setting.set(option, key) 

 

start_time = time() 

 

old_solution = self.nominal_solve 

reached_feasibility = 0 

 

for count in range(self.setting.get('iterationLimit')): 

if verbosity > 0: 

print("iteration %s" % (count + 1)) 

ready_sp_constraints, to_linearize_sp_posynomials, large_sp_posynomials = self. \ 

approximate_and_classify_sp_constraints(old_solution, self.number_of_gp_posynomials) 

 

ready_constraints = self.ready_gp_constraints + ready_sp_constraints 

to_linearize_posynomials = self.to_linearize_gp_posynomials + to_linearize_sp_posynomials 

large_posynomials = self.large_gp_posynomials + large_sp_posynomials 

 

permutation_indices = self.new_permutation_indices(old_solution, large_posynomials) 

 

two_term_data_posynomials = [] 

 

for i, two_term_approximation in enumerate(large_posynomials): 

permutation = two_term_approximation.list_of_permutations[permutation_indices[i]] 

no_data, data = TwoTermApproximation. \ 

two_term_equivalent_posynomial(two_term_approximation.p, i, permutation, False) 

ready_constraints += no_data 

two_term_data_posynomials += [constraint.as_posyslt1()[0] for constraint in data] 

two_term_data_posynomials += to_linearize_posynomials 

if reached_feasibility: 

self._robust_model, _ = self. \ 

linearize_and_return_upper_lower_models(two_term_data_posynomials, 

self.robust_solve_properties['numoflinearsections'], 

ready_constraints) 

new_solution = RobustModel.internalsolve(self._robust_model, verbosity=0) 

else: 

try: 

self.robust_solve_properties['numoflinearsections'], new_solution, self._robust_model = self. \ 

find_number_of_piece_wise_linearization(two_term_data_posynomials, ready_constraints) 

reached_feasibility += 1 

except Exception: 

self.robust_solve_properties['numoflinearsections'], new_solution, self._robust_model = self. \ 

find_number_of_piece_wise_linearization(two_term_data_posynomials, ready_constraints, 

feasible=True) 

rel_tol = np.abs((new_solution['cost'] - old_solution['cost']) / old_solution['cost']) 

if verbosity > 0: 

if not reached_feasibility: 

print("feasibility is not reached yet") 

elif reached_feasibility == 1: 

print("feasibility is reached") 

print("relative tolerance = %s" % rel_tol) 

if reached_feasibility <= 1 and two_term_data_posynomials: 

self.robust_solve_properties['slopes'], self.robust_solve_properties['intercepts'], _, _, _ = \ 

LinearizeTwoTermPosynomials.two_term_posynomial_linearization_coeff( 

self.robust_solve_properties['numoflinearsections']) 

 

self._sequence_of_rgps.append(self._robust_model) 

 

if rel_tol <= self.setting.get('iterationsRelativeTolerance'): 

break 

else: 

old_solution = new_solution 

 

if reached_feasibility < 1: 

raise Exception("feasibility is not reached. If the solution seems to converge, try " 

"increasing iterationLimit = %s. Increasing the allowed number of permutations might also " 

"help" % self.setting.get('iterationLimit')) 

self.robust_solve_properties['setuptime'] = time() - start_time 

 

def robustsolve(self, verbosity=1, **options): 

if self._robust_model is None: 

self.setup(verbosity, **options) 

try: 

sol = self._robust_model.solve(verbosity=verbosity) 

except InvalidGPConstraint: 

sol = self._robust_model.localsolve(verbosity=verbosity) 

if verbosity > 0: 

print ("solving needed %s iterations." % len(self._sequence_of_rgps)) 

print ("setting up took %s seconds." % self.robust_solve_properties['setuptime']) 

sol.update(self.robust_solve_properties) 

return sol 

 

def approximate_and_classify_sp_constraints(self, solution, number_of_gp_posynomials): 

sp_gp_approximation = [] 

with SignomialsEnabled(): 

for cs in self.sp_constraints: 

css = SignomialInequality(cs.left.sub(solution["constants"]), cs.oper, cs.right.sub(solution["constants"])) 

sp_gp_approximation.append(css.as_gpconstr(x0=solution["freevariables"]).as_posyslt1()[0]) 

ready_sp_constraints, to_linearize_sp_posynomials, large_sp_posynomial = self.\ 

classify_gp_constraints(sp_gp_approximation, number_of_gp_posynomials) 

for cs in self.sp_equality_constraints: 

css = SingleSignomialEquality(cs.left.sub(solution["constants"]), cs.right.sub(solution["constants"])) 

ready_sp_constraints.append(css.as_gpconstr(x0=solution["freevariables"])) 

return ready_sp_constraints, to_linearize_sp_posynomials, large_sp_posynomial 

 

def classify_gp_constraints(self, gp_posynomials, offset=0): 

data_gp_posynomials = [] 

ready_gp_constraints = [] 

for i, p in enumerate(gp_posynomials): 

equivalent_p = EquivalentPosynomials(p, i + offset, self.setting.get('simpleModel'), 

self.dependent_uncertainty_set) 

no_data, data = equivalent_p.no_data_constraints, equivalent_p.data_constraints 

data_gp_posynomials += [posy.as_posyslt1()[0] for posy in data] 

ready_gp_constraints += no_data 

 

to_linearize_gp_posynomials = [] 

large_gp_posynomials = [] 

for i, p in enumerate(data_gp_posynomials): 

if len(p.exps) == 1: 

robust_monomial = self.robustify_monomial(p) 

ready_gp_constraints += [robust_monomial <= 1] 

elif len(p.exps) == 2 and self.setting.get('linearizeTwoTerm'): 

to_linearize_gp_posynomials += [p] 

else: 

if self.setting.get('twoTerm'): 

two_term_approximation = TwoTermApproximation(p, self.setting) 

large_gp_posynomials.append(two_term_approximation) 

else: 

robust_large_p = RobustifyLargePosynomial(p, self.type_of_uncertainty_set, 

self.number_of_stds, self.setting) 

ready_gp_constraints += robust_large_p. \ 

robustify_large_posynomial(self.type_of_uncertainty_set, i + offset, self.setting) 

 

return ready_gp_constraints, to_linearize_gp_posynomials, large_gp_posynomials 

 

def robustify_monomial(self, monomial): 

new_monomial_exps = RobustGPTools. \ 

only_uncertain_vars_monomial(monomial.exps[0]) 

m_direct_uncertain_vars = [var for var in list(new_monomial_exps.keys()) if RobustGPTools.is_uncertain(var)] 

 

l_norm = 0 

for var in m_direct_uncertain_vars: 

eta_min, eta_max = RobustGPTools.generate_etas(var) 

scale = eta_max 

exponent = -new_monomial_exps.get(var.key) 

pert = exponent * scale 

 

if self.type_of_uncertainty_set == 'box': 

l_norm += np.abs(pert) 

elif self.type_of_uncertainty_set == 'elliptical': 

l_norm += pert ** 2 

elif self.type_of_uncertainty_set == 'one norm': 

l_norm = max(l_norm, np.abs(pert)) 

else: 

raise Exception('This type of set is not supported') 

if self.type_of_uncertainty_set == 'elliptical': 

l_norm = np.sqrt(l_norm) 

g = self.setting.get('gamma') 

# Fifth order Taylor approx of the e**gamma, so that gamma can be a variable 

robust_monomial = monomial * (1.+g+1./2.*g**2+1./6.*g**3+1./24.*g**4+1./120.*g**5)**l_norm 

return robust_monomial 

 

def robustify_set_of_monomials(self, set_of_monomials, feasible=False): 

robust_set_of_monomial_constraints = [] 

slackvar = Variable() 

for monomial in set_of_monomials: 

robust_monomial = self.robustify_monomial(monomial) 

robust_set_of_monomial_constraints += [robust_monomial <= slackvar ** feasible] 

robust_set_of_monomial_constraints += [slackvar >= 1, slackvar <= 1000] 

return robust_set_of_monomial_constraints, slackvar 

 

def calculate_value_of_two_term_approximated_posynomial(self, two_term_approximation, index_of_permutation, 

solution): 

permutation = two_term_approximation.list_of_permutations[index_of_permutation] 

 

number_of_two_terms = int(len(permutation) / 2) 

num_of_linear_sections = self.robust_solve_properties['numoflinearsections'] 

slopes = self.robust_solve_properties['slopes'] 

intercepts = self.robust_solve_properties['intercepts'] 

values = [] 

 

mons = two_term_approximation.chop() 

 

for i in range(number_of_two_terms): 

monomials = [] 

first_monomial = mons[2*i] 

second_monomial = mons[2*i+1] 

 

monomials += [first_monomial] 

for j in range(num_of_linear_sections - 2): 

monomials += [first_monomial ** slopes[num_of_linear_sections - 3 - j] * 

second_monomial ** slopes[j] * np.exp(intercepts[j])] 

monomials += [second_monomial] 

subs_monomials = [] 

for j in range(len(monomials)): 

# st3 = time() 

robust_monomial = self.robustify_monomial(monomials[j]) 

monomials[j] = robust_monomial.sub(solution['variables']) 

# print "subs for a monomial is taking too much time", time()-st3 

subs_monomials.append(monomials[j].cs[0]) 

values.append(max(subs_monomials)) 

if number_of_two_terms % 2 != 0: 

monomial = mons[len(permutation) - 1] 

robust_monomial = self.robustify_monomial(monomial) 

monomial = robust_monomial.sub(solution['variables']) 

values.append(monomial.cs[0]) 

return sum(values) 

 

def find_permutation_with_minimum_value(self, two_term_approximation, solution): 

minimum_value = np.inf 

minimum_index = len(two_term_approximation.list_of_permutations) 

for i in range(len(two_term_approximation.list_of_permutations)): 

temp_value = self. \ 

calculate_value_of_two_term_approximated_posynomial(two_term_approximation, i, solution) 

if temp_value < minimum_value: 

minimum_value = temp_value 

minimum_index = i 

return minimum_index 

 

def linearize_and_return_upper_lower_models(self, two_term_data_posynomials, r, ready_constraints, feasible=False): 

no_data_upper_constraints = [] 

no_data_lower_constraints = [] 

data_posynomials = [] 

 

for i, two_term_p in enumerate(two_term_data_posynomials): 

linearize_p = LinearizeTwoTermPosynomials(two_term_p) 

no_data_upper, no_data_lower, data = linearize_p. \ 

linearize_two_term_posynomial(i, r) 

no_data_upper_constraints += no_data_upper 

no_data_lower_constraints += no_data_lower 

data_posynomials += [constraint.as_posyslt1()[0] for constraint in data] 

del linearize_p, no_data_lower, no_data_upper 

data_constraints, slackvar = self.robustify_set_of_monomials(data_posynomials, feasible) 

 

upper_cons, lower_cons = [no_data_upper_constraints, ready_constraints, data_constraints], \ 

[no_data_lower_constraints, ready_constraints, data_constraints] 

 

model_upper = Model(self.nominal_model.cost * slackvar ** (100 * feasible), upper_cons) 

model_lower = Model(self.nominal_model.cost * slackvar ** (100 * feasible), lower_cons) 

model_upper.substitutions.update(self.substitutions) 

model_lower.substitutions.update(self.substitutions) 

model_upper.unique_varkeys, model_lower.unique_varkeys = [self.nominal_model.varkeys] * 2 

model_upper.reset_varkeys() 

model_lower.reset_varkeys() 

del upper_cons, lower_cons, no_data_lower_constraints, no_data_upper_constraints, data_posynomials 

return model_upper, model_lower 

 

def find_number_of_piece_wise_linearization(self, two_term_data_posynomials, ready_constraints, feasible=False): 

 

the_min_r = self.setting.get('minNumOfLinearSections') 

the_max_r = self.setting.get('maxNumOfLinearSections') 

r = None 

error = None 

sol_upper = None 

 

model_upper = None 

 

while the_min_r <= the_max_r: 

r = int((the_min_r + the_max_r) / 2.0) 

model_upper, model_lower = self. \ 

linearize_and_return_upper_lower_models(two_term_data_posynomials, r, ready_constraints, feasible) 

upper_model_infeasible = 0 

try: 

sol_upper = RobustModel.internalsolve(model_upper, verbosity=0) 

except RuntimeWarning: 

upper_model_infeasible = 1 

try: 

sol_lower = RobustModel.internalsolve(model_lower, verbosity=0) 

except RuntimeWarning: 

raise Exception("The model is infeasible") 

if not two_term_data_posynomials: 

self.robust_solve_properties['upperLowerRelError'] = 0 

return 0, sol_upper, model_upper 

if upper_model_infeasible != 1: 

error = (sol_upper.get('cost') - sol_lower.get('cost')) / sol_lower.get('cost') 

if error <= self.setting.get('linearizationTolerance'): 

the_max_r = r 

else: 

the_min_r = r + 1 

elif r == self.setting.get('maxNumOfLinearSections'): 

self.lower_approximation_is_feasible = True 

raise Exception("The model is infeasible. The lower approximation of the model is feasible, try " 

"increasing the maximum number of linear sections") 

else: 

the_min_r = r + 1 

del model_lower, sol_lower 

if the_max_r == the_min_r and r == the_max_r: 

break 

self.robust_solve_properties['upperLowerRelError'] = error 

return r, sol_upper, model_upper 

 

def new_permutation_indices(self, solution, large_posynomials): 

permutation_indices = [] 

for two_term_approximation in large_posynomials: 

permutation_indices.append(self.find_permutation_with_minimum_value(two_term_approximation, solution)) 

return permutation_indices 

 

@staticmethod 

def internalsolve(model, verbosity=0): 

try: 

return model.solve(verbosity=verbosity) 

except InvalidGPConstraint: 

return model.localsolve(verbosity=verbosity) 

 

def get_robust_model(self): 

if self.sp_constraints: 

return self._sequence_of_rgps 

else: 

return self._robust_model 

 

def nominalsolve(self): 

return self.nominal_solve