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simulate.py
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simulate.py
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import numpy as np
from gpkit.small_scripts import mag
from gpkit.exceptions import InvalidGPConstraint
from gpkit.small_scripts import mag
from gpkit import Model, Variable, Monomial
from robust.robust import RobustModel
from robust.robust_gp_tools import RobustGPTools
from robust.simulations.read_simulation_data import objective_proboffailure_vs_gamma
import matplotlib.pyplot as plt
import multiprocessing as mp
import scipy.stats as stats
# For the following simulation functions, we define common inputs as the following:
# :model: GP or SP model of interest
# :model_name: string for printing
# :gamma: array of floats to specify set size
# :number_of_iterations: # of MC samples
# :numbers_of_linear_sections: array of integer sections
# :linearization_tolerance: max error of pwl approx
# :verbosity: 0-4 for printout
# :file_name: directory for printing
# :number_of_time_average_solves: # of solves for solution time analysis
# :methods: type of conservative approximation used, dict
# :uncertainty_sets: string defining type of set
# :nominal_solution: solution of model with zero uncertainty
# :nominal_solve_time: solve time of model with zero uncertainty
# :nominal_number_of_constraints:
# :directly_uncertain_vars_subs: dict of uncertain parameter MC samples
# :return:
def pickleable_robust_solve_time(robust_model, verbosity, min_num_of_linear_sections,
max_num_of_linear_sections, linearization_tolerance):
"""
Wrapper for robustsolve for parallelism.
"""
robust_model_solution = robust_model.robustsolve(verbosity=verbosity,
minNumOfLinearSections=min_num_of_linear_sections,
maxNumOfLinearSections=max_num_of_linear_sections,
linearizationTolerance=linearization_tolerance)
return robust_model_solution['soltime']
def get_avg_robust_solve_time(number_of_time_average_solves, robust_model, verbosity, min_num_of_linear_sections,
max_num_of_linear_sections, linearization_tolerance, parallel=False):
"""
Given a number of solves, gives the average solution time of a robust model. Parallel option.
"""
if parallel:
pool = mp.Pool(mp.cpu_count()-1)
processes = []
timesolutions = []
for i in range(number_of_time_average_solves):
p = pool.apply_async(pickleable_robust_solve_time, args=(robust_model, verbosity, min_num_of_linear_sections,
max_num_of_linear_sections,linearization_tolerance), callback=timesolutions.append)
processes.append(p)
pool.close()
pool.join()
else:
solutions = [robust_model.robustsolve(verbosity=verbosity)
for i in range(number_of_time_average_solves)]
timesolutions = [s['soltime'] for s in solutions]
return np.mean(timesolutions)
def simulate_robust_model(model, method, uncertainty_set, gamma, directly_uncertain_vars_subs,
number_of_iterations, linearization_tolerance, min_num_of_linear_sections,
max_num_of_linear_sections, verbosity, nominal_solution,
number_of_time_average_solves, parallel=False):
"""
Simulates a robust model given uncertain outcomes.
"""
print(
method[
'name'] + ' under ' + uncertainty_set + ' uncertainty set: \n' + '\t' + 'gamma = %s\n' % gamma
+ '\t' + 'minimum number of piecewise-linear sections = %s\n' % min_num_of_linear_sections
+ '\t' + 'maximum number of piecewise-linear sections = %s\n' % max_num_of_linear_sections)
robust_model = RobustModel(model, uncertainty_set, gamma=gamma, twoTerm=method['twoTerm'],
boyd=method['boyd'], simpleModel=method['simpleModel'],
nominalsolve=nominal_solution)
robust_model_solution = robust_model.robustsolve(verbosity=verbosity,
minNumOfLinearSections=min_num_of_linear_sections,
maxNumOfLinearSections=max_num_of_linear_sections,
linearizationTolerance=linearization_tolerance)
robust_model_solve_time = get_avg_robust_solve_time(number_of_time_average_solves,
robust_model, verbosity, min_num_of_linear_sections,
max_num_of_linear_sections,
linearization_tolerance, parallel)
simulation_results = RobustGPTools.probability_of_failure(model, robust_model_solution,
directly_uncertain_vars_subs,
number_of_iterations,
verbosity=0, parallel=parallel)
return robust_model, robust_model_solution, robust_model_solve_time, simulation_results
def print_simulation_results(robust_model, robust_model_solution, robust_model_solve_time,
nominal_model_solve_time, nominal_no_of_constraints, nominal_cost,
simulation_results, file_id):
file_id.write('\t\t\t' + 'Probability of failure: %s\n' % simulation_results[0])
file_id.write('\t\t\t' + 'Average performance: %s\n' % mag(simulation_results[1]))
file_id.write('\t\t\t' + 'Relative average performance: %s\n' %
(mag(simulation_results[1]) / float(mag(nominal_cost))))
file_id.write('\t\t\t' + 'Worst-case performance: %s\n' % mag(robust_model_solution['cost']))
file_id.write('\t\t\t' + 'Relative worst-case performance: %s\n' %
(mag(robust_model_solution['cost']) / float(mag(nominal_cost))))
try:
number_of_constraints = \
len([cnstrnt for cnstrnt in robust_model.get_robust_model().flat(constraintsets=False)])
except AttributeError:
number_of_constraints = \
len([cnstrnt for cnstrnt in robust_model.get_robust_model()[-1].flat(constraintsets=False)])
file_id.write('\t\t\t' + 'Number of constraints: %s\n' % number_of_constraints)
file_id.write('\t\t\t' + 'Relative number of constraints: %s\n' %
(number_of_constraints / float(nominal_no_of_constraints)))
file_id.write('\t\t\t' + 'Setup time: %s\n' % robust_model_solution['setuptime'])
file_id.write('\t\t\t' + 'Relative setup time: %s\n' %
(robust_model_solution['setuptime'] / float(nominal_model_solve_time)))
file_id.write('\t\t\t' + 'Solve time: %s\n' % robust_model_solve_time)
file_id.write('\t\t\t' + 'Relative solve time: %s\n' %
(robust_model_solve_time / float(nominal_model_solve_time)))
file_id.write('\t\t\t' + 'Number of linear sections: %s\n' % robust_model_solution['numoflinearsections'])
file_id.write(
'\t\t\t' + 'Upper lower relative error: %s\n' % mag(robust_model_solution['upperLowerRelError']))
def print_variable_gamma_results(model, model_name, gammas, number_of_iterations,
min_num_of_linear_sections, max_num_of_linear_sections, verbosity,
linearization_tolerance, file_name, number_of_time_average_solves,
methods, uncertainty_sets, nominal_solution, nominal_solve_time,
nominal_number_of_constraints, directly_uncertain_vars_subs):
f = open(file_name, 'w')
f.write(model_name + ' Results: variable gamma\n')
f.write('----------------------------------------------------------\n')
cost_label = model.cost.str_without()
split_label = cost_label.split(' ')
capitalized_cost_label = ''
for word in split_label:
capitalized_cost_label += word.capitalize() + ' '
f.write('Objective: %s\n' % capitalized_cost_label)
f.write('Units: %s\n' % model.cost.units)
f.write('----------------------------------------------------------\n')
f.write('Number of iterations: %s\n' % number_of_iterations)
f.write('Minimum number of piecewise-linear sections: %s\n' % min_num_of_linear_sections)
f.write('Maximum number of piecewise-linear sections: %s\n' % max_num_of_linear_sections)
f.write('Linearization tolerance: %s\n' % linearization_tolerance)
f.write('----------------------------------------------------------\n')
f.write('Nominal cost: %s\n' % nominal_solution['cost'])
f.write('Average nominal solve time: %s\n' % nominal_solve_time)
f.write('Nominal number of constraints: %s\n' % nominal_number_of_constraints)
f.write('----------------------------------------------------------\n')
for gamma in gammas:
f.write('Gamma = %s:\n' % gamma)
for method in methods:
f.write('\t' + method['name'] + ':\n')
for uncertainty_set in uncertainty_sets:
f.write('\t\t' + uncertainty_set + ':\n')
robust_model, robust_model_solution, robust_model_solve_time, simulation_results = \
simulate_robust_model(model, method, uncertainty_set, gamma, directly_uncertain_vars_subs,
number_of_iterations, linearization_tolerance,
min_num_of_linear_sections,
max_num_of_linear_sections, verbosity, nominal_solution,
number_of_time_average_solves)
print_simulation_results(robust_model, robust_model_solution, robust_model_solve_time,
nominal_solve_time, nominal_number_of_constraints, nominal_solution['cost'],
simulation_results, f)
f.close()
def variable_gamma_results(model, methods, gammas, number_of_iterations,
min_num_of_linear_sections, max_num_of_linear_sections, verbosity,
linearization_tolerance, number_of_time_average_solves,
uncertainty_sets, nominal_solution, directly_uncertain_vars_subs, parallel=False):
"""
Simulates a GP or SP model for a range of gammas, i.e. uncertainty set size.
Outputs are dicts that have the key format: [deltaValue (float), methodName (string), uncertaintySet (string)]
"""
solutions = {}
solve_times = {}
simulations = {}
number_of_constraints = {}
for gamma in gammas:
for method in methods:
for uncertainty_set in uncertainty_sets:
ind = (gamma, method['name'], uncertainty_set)
robust_model, robust_model_solution, robust_model_solve_time, simulation_results = \
simulate_robust_model(model, method, uncertainty_set, gamma, directly_uncertain_vars_subs,
number_of_iterations, linearization_tolerance,
min_num_of_linear_sections,
max_num_of_linear_sections, verbosity, nominal_solution,
number_of_time_average_solves, parallel)
try:
nconstraints = \
len([cnstrnt for cnstrnt in robust_model.get_robust_model().flat(constraintsets=False)])
except AttributeError:
nconstraints = \
len([cnstrnt for cnstrnt in robust_model.get_robust_model()[-1].flat(constraintsets=False)])
solutions[ind] = robust_model_solution
solve_times[ind] = robust_model_solve_time
simulations[ind] = simulation_results
number_of_constraints[ind] = nconstraints
return solutions, solve_times, simulations, number_of_constraints
def variable_goal_results(model, methods, deltas, number_of_iterations,
min_num_of_linear_sections, max_num_of_linear_sections, verbosity,
linearization_tolerance, number_of_time_average_solves,
uncertainty_sets, nominal_solution, directly_uncertain_vars_subs, parallel=False):
"""
Simulates a GP or SP model for a range of deltas in the goal programming form.
i.e. maximizes uncertainty set size given an acceptable penalty delta on the objective.
Outputs are dicts that have the key format: [deltaValue (float), methodName (string), uncertaintySet (string)]
"""
solutions = {}
solve_times = {}
simulations = {}
number_of_constraints = {}
Gamma = Variable('\\Gamma', '-', 'Uncertainty bound')
solBound = Variable('1+\\delta', '-', 'Acceptable optimal solution bound', fix = True)
origcost = model.cost
mGoal = Model(1 / Gamma, [model, origcost <= Monomial(nominal_solution(origcost)) * solBound, Gamma <= 1e30, solBound <= 1e30],
model.substitutions)
for delta in deltas:
mGoal.substitutions.update({'1+\\delta': 1 + delta})
for method in methods:
for uncertainty_set in uncertainty_sets:
robust_goal_model = RobustModel(mGoal, uncertainty_set, gamma=Gamma, twoTerm=method['twoTerm'],
boyd=method['boyd'], simpleModel=method['simpleModel'])
robust_model_solution = robust_goal_model.robustsolve(verbosity=verbosity,
minNumOfLinearSections=min_num_of_linear_sections,
maxNumOfLinearSections=max_num_of_linear_sections,
linearizationTolerance=linearization_tolerance)
robust_model_solve_time = get_avg_robust_solve_time(number_of_time_average_solves,
robust_goal_model, verbosity, min_num_of_linear_sections,
max_num_of_linear_sections,
linearization_tolerance, parallel)
simulation_results = RobustGPTools.probability_of_failure(model, robust_model_solution,
directly_uncertain_vars_subs,
number_of_iterations,
verbosity=0, parallel=parallel)
try:
nconstraints = \
len([cnstrnt for cnstrnt in robust_goal_model.get_robust_model().flat(constraintsets=False)])
except AttributeError:
nconstraints = \
len([cnstrnt for cnstrnt in robust_goal_model.get_robust_model()[-1].flat(constraintsets=False)])
ind = (delta, method['name'], uncertainty_set)
solutions[ind] = robust_model_solution
solve_times[ind] = robust_model_solve_time
simulations[ind] = simulation_results
number_of_constraints[ind] = nconstraints
return solutions, solve_times, simulations, number_of_constraints
def filter_gamma_result_dict(dict, tupInd1, tupVal1, tupInd2, tupVal2):
"""
Filters the items in outputs of variable_gamma_results or variable_goal_results
with 2 out of 3 keys.
"""
filteredResult = {}
for i in sorted(dict.iterkeys()):
if i[tupInd1] == tupVal1 and i[tupInd2] == tupVal2:
filteredResult[i] = dict[i]
return filteredResult
def plot_gamma_result_PoFandCost(title, objective_name, objective_units, filteredResult, filteredSimulations, stddev = True):
gammas = []
objective_costs = []
pofs = []
objective_stddev = []
for i in sorted(filteredResult.keys()):
gammas.append(i[0])
objective_stddev.append(filteredSimulations[i][2])
objective_costs.append(filteredSimulations[i][1])
pofs.append(filteredSimulations[i][0])
if not stddev:
objective_stddev = None
objective_proboffailure_vs_gamma(gammas, objective_costs, objective_name, objective_units,
np.min(objective_costs), np.max(objective_costs), pofs, title, objective_stddev)
def plot_goal_result_PoFandCost(title, objective_name, objective_varkey, objective_units, filteredResult, filteredSimulations):
gammas = []
objective_costs = []
pofs = []
objective_stddev = []
for i in sorted(filteredResult.keys()):
gammas.append(filteredResult[i]("\\Gamma").magnitude)
objective_stddev.append(filteredSimulations[i][2])
objective_costs.append(mag(filteredResult[i](objective_varkey)))
pofs.append(filteredSimulations[i][0])
objective_proboffailure_vs_gamma(gammas, objective_costs, objective_name, objective_units,
np.min(objective_costs), np.max(objective_costs), pofs, title, None)
def print_variable_pwlsections_results(model, model_name, gamma, number_of_iterations,
numbers_of_linear_sections, linearization_tolerance,
verbosity, file_name, number_of_time_average_solves,
methods, uncertainty_sets, nominal_solution, nominal_solve_time,
nominal_number_of_constraints, directly_uncertain_vars_subs):
"""
Simulates a model for different numbers of PWL sections for each posy.
"""
f = open(file_name, 'w')
f.write(model_name + ' Results: variable piecewise-linear sections\n')
f.write('----------------------------------------------------------\n')
cost_label = model.cost.str_without()
split_label = cost_label.split(' ')
capitalized_cost_label = ''
for word in split_label:
capitalized_cost_label += word.capitalize() + ' '
f.write('Objective: %s\n' % capitalized_cost_label)
f.write('Units: %s\n' % model.cost.units)
f.write('----------------------------------------------------------\n')
f.write('Number of iterations: %s\n' % number_of_iterations)
f.write('gamma: %s\n' % gamma)
f.write('Linearization tolerance: %s\n' % linearization_tolerance)
f.write('----------------------------------------------------------\n')
f.write('Nominal cost: %s\n' % nominal_solution['cost'])
f.write('Average nominal solve time: %s\n' % nominal_solve_time)
f.write('Nominal number of constraints: %s\n' % nominal_number_of_constraints)
f.write('----------------------------------------------------------\n')
for number_of_linear_sections in numbers_of_linear_sections:
f.write('number of piecewise-linear sections = %s:\n' % number_of_linear_sections)
for method in methods:
f.write('\t' + method['name'] + ':\n')
for uncertainty_set in uncertainty_sets:
f.write('\t\t' + uncertainty_set + ':\n')
robust_model, robust_model_solution, robust_model_solve_time, simulation_results = \
simulate_robust_model(model, method, uncertainty_set, gamma, directly_uncertain_vars_subs,
number_of_iterations, linearization_tolerance,
number_of_linear_sections,
number_of_linear_sections, verbosity, nominal_solution,
number_of_time_average_solves)
print_simulation_results(robust_model, robust_model_solution, robust_model_solve_time,
nominal_solve_time, nominal_number_of_constraints, nominal_solution['cost'],
simulation_results, f)
f.close()
def generate_model_properties(model, number_of_time_average_solves, number_of_iterations, distribution = None):
"""
Solves the nominal model, and generates MC samples
:param model: GP or SP model of interest, with uncertainties
:param number_of_time_average_solves: # of solves for solution time analysis
:param number_of_iterations: # of MC samples for simulation
:param distribution: distribution for MC samples, 'normal' or 'uniform otherwise
:return: nominal solution, nominal solve time, nominal number of constraints, and MC samples of uncertain inputs
"""
try:
nominal_solution = model.solve(verbosity=0)
nominal_solve_time = nominal_solution['soltime']
for i in xrange(number_of_time_average_solves-1):
nominal_solve_time += model.solve(verbosity=0)['soltime']
except InvalidGPConstraint:
nominal_solution = model.localsolve(verbosity=0)
nominal_solve_time = nominal_solution['soltime']
for i in xrange(number_of_time_average_solves-1):
nominal_solve_time += model.localsolve(verbosity=0)['soltime']
nominal_solve_time = nominal_solve_time / number_of_time_average_solves
if distribution == 'normal' or 'Gaussian':
directly_uncertain_vars_subs = [{k: stats.truncnorm.rvs(-3. , 3. , loc=v, scale=(v*k.key.pr/300.))
for k, v in model.substitutions.items()
if k in model.varkeys and RobustGPTools.is_directly_uncertain(k)}
for _ in xrange(number_of_iterations)]
else:
directly_uncertain_vars_subs = [{k: np.random.uniform(v - k.key.pr * v / 100.0, v + k.key.pr * v / 100.0)
for k, v in model.substitutions.items()
if k in model.varkeys and RobustGPTools.is_directly_uncertain(k)}
for _ in xrange(number_of_iterations)]
nominal_number_of_constraints = len([cs for cs in model.flat(constraintsets=False)])
return nominal_solution, nominal_solve_time, nominal_number_of_constraints, directly_uncertain_vars_subs
if __name__ == '__main__':
pass