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problem_formulation_2.py
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# -*- coding: utf-8 -*-
"""
Created on Thu Mar 22 09:13:13 2018
@author: ciullo
"""
from dike_model_function import DikeNetwork # @UnresolvedImport
from ema_workbench import (Model, TimeSeriesOutcome, ScalarOutcome,
RealParameter, IntegerParameter, CategoricalParameter)
from ema_workbench.em_framework.outcomes import Constraint
from functools import partial
import numpy as np
def sum_over(*args):
return sum(args)
def relative_risk(init_risk, *args):
# only show relative risk change of each location
EADa0 = init_risk
EADa1 = args[0]
ratio = (EADa0 - EADa1) / EADa0
return ratio
def absolute_risk(init_risk, *args):
# only show relative risk change of each location
EADa0 = init_risk
EADa1 = args[0]
ratio = (EADa0 - EADa1)
return ratio
def risk_shift_distance(init_risk, *args):
EADa1 = args[0]
EADb1 = np.sum(args[1:])
EADa0, EADb0 = init_risk
r1 = (EADa0 - EADa1) / EADa0
r2 = (EADb0 - EADb1) / EADb0
# distance from the r1 = r2 line
distance = abs(r1 - r2) / np.sqrt(2)
return distance
def absolute_risk_shift_distance(init_risk, *args):
EADa1 = args[0]
EADb1 = np.sum(args[1:])
EADa0, EADb0 = init_risk
r1 = (EADa0 - EADa1) / (EADa0 + EADb0)
r2 = (EADb0 - EADb1) / (EADa0 + EADb0)
# distance from the r1 = r2 line
distance = abs(r1 - r2) / np.sqrt(2)
return distance
# Note on upperlim (maxs) of the risk tranfers criteria:
# no risk increase is allowed => 0<r<1 (i.e. when no risk reduction, r=0; when
# total risk reduction, r=1), thus 0<distance<1/sqrt(2) (=0.708)
def get_model_for_problem_formulation(problem_formulation_id):
function = DikeNetwork()
dike_model = Model('dikesnet', function=function)
# specify uncertainties, levers
# uncertainties
uncert = {'Bmax': [5, 350], 'pfail': [0, 1]}
cat_uncert = {'Brate': (1., 1.5, 10.)}
# dike levers
dike_lev = {'DikeIncrease': [0, 10]}
# Rfr project code, diversion policies,
rfr_lev = ['{}_rfr'.format(project_id) for project_id in list(range(0, 156))]
div_lev = {'Diversion_201.0': [-3, 3],
'Diversion_401.0': [-3, 3]}
uncertainties = []
levers = []
for dike in function.dikenodes:
for lev_name in dike_lev.keys():
name = "{}_{}".format(dike, lev_name)
levers.append(IntegerParameter(name, dike_lev[lev_name][0],
dike_lev[lev_name][1]))
for uncert_name in uncert.keys():
name = "{}_{}".format(dike, uncert_name)
lower, upper = uncert[uncert_name]
uncertainties.append(RealParameter(name, lower, upper))
for uncert_name in cat_uncert.keys():
name = "{}_{}".format(dike, uncert_name)
categories = cat_uncert[uncert_name]
uncertainties.append(CategoricalParameter(name, categories))
for lev_name in rfr_lev:
# choose or not a RfR project:
levers.append(IntegerParameter(lev_name, 0, 1))
for lev_name in div_lev.keys():
levers.append(IntegerParameter(lev_name, div_lev[lev_name][0],
div_lev[lev_name][1]))
dike_model.uncertainties = uncertainties
dike_model.levers = levers
direction = ScalarOutcome.MINIMIZE
# extra outcome of interest
output_list = ['Qpol', 'Qout', 'Qin', 'wl', 'status', 'critWL']
eooi = []
nl_areas = list(range(4))
de_areas = [4, 5]
nl_max_costs = 2 * 1e8
# general
if problem_formulation_id == 0:
mins, maxs = 0, 0
constraints = []
epsilons = []
areas = nl_areas + de_areas
outcomes = []
[outcomes.append(ScalarOutcome('{}_EAD'.format(a))) for a in areas]
variable_name = []
[variable_name.append('{}_Dike Inv Cost'.format(a)) for a in nl_areas]
variable_name.append('RfR Total Costs')
outcomes.append(ScalarOutcome('Investment Costs_nl',
variable_name=variable_name,
function=sum_over))
variable_name = []
[variable_name.append('{}_Dike Inv Cost'.format(a)) for a in de_areas]
outcomes.append(ScalarOutcome('Investment Costs_de',
variable_name=variable_name,
function=sum_over))
for i in eooi:
[outcomes.append(TimeSeriesOutcome('{}_{}'.format(output_list[i], n))
) for n in function.dikenodes]
dike_model.outcomes = outcomes
# utilitarian
elif problem_formulation_id == 1:
constraints = []
epsilons = []
outcomes = []
variable_name = []
[variable_name.append('{}_Dike Inv Cost'.format(a)) for a in nl_areas]
variable_name.append('RfR Total Costs')
outcomes.append(ScalarOutcome('Investment Costs_nl',
variable_name=variable_name,
function=sum_over))
constraints.append(Constraint('Investment Costs_nl',
outcome_names='Investment Costs_nl',
function=lambda x: max(0, x - nl_max_costs)))
variable_name = []
for e in ['EAD', 'Dike Inv Cost']:
variable_name.extend('{}_{}'.format(a, e) for a in nl_areas)
variable_name.append('RfR Total Costs')
outcomes.append(ScalarOutcome('Total Costs_nl',
variable_name=variable_name,
function=sum_over, kind=direction))
epsilons.append(1e7)
variable_name = []
for e in ['EAD', 'Dike Inv Cost']:
variable_name.extend('{}_{}'.format(a, e) for a in de_areas)
outcomes.append(ScalarOutcome('Total Costs_de',
variable_name=variable_name,
function=sum_over, kind=direction))
epsilons.append(1e7)
mins = [0.0] * 2
maxs = [1.88 * 1e10, 1.71 * 1e9]
dike_model.outcomes = outcomes
# constrained utilitarian
elif problem_formulation_id == '1c':
constraints = []
epsilons = []
outcomes = []
variable_name = []
[variable_name.append('{}_Dike Inv Cost'.format(a)) for a in nl_areas]
variable_name.append('RfR Total Costs')
outcomes.append(ScalarOutcome('Investment Costs_nl',
variable_name=variable_name,
function=sum_over))
constraints.append(Constraint('Investment Costs_nl',
outcome_names='Investment Costs_nl',
function=lambda x: max(0, x - nl_max_costs)))
variable_name = []
for e in ['EAD', 'Dike Inv Cost']:
variable_name.extend('{}_{}'.format(a, e) for a in nl_areas)
variable_name.append('RfR Total Costs')
outcomes.append(ScalarOutcome('Total Costs_nl',
variable_name=variable_name,
function=sum_over, kind=direction))
epsilons.append(1e7)
variable_name = []
for e in ['EAD', 'Dike Inv Cost']:
variable_name.extend('{}_{}'.format(a, e) for a in de_areas)
outcomes.append(ScalarOutcome('Total Costs_de',
variable_name=variable_name,
function=sum_over, kind=direction))
epsilons.append(1e7)
for a in nl_areas:
init_risk = [function.R0['{}_EAD'.format(a)].values[0],
np.sum([function.R0['{}_EAD'.format(i)].values[0]
for i in nl_areas if i != a])]
variable_name = ['{}_EAD'.format(a)] + ['{}_EAD'.format(i
) for i in nl_areas if i != a]
outcomes.append(ScalarOutcome('{}_u'.format(a),
function=partial(
relative_risk, init_risk[0]),
variable_name=[variable_name[0]]))
# when x is positive, the function gives 0, the constraint is met
constraints.append(Constraint('{}_u'.format(a),
outcome_names='{}_u'.format(a),
function=lambda x: max(0, -x)))
# only take one criteria in germany, cause there are only two locations.
# A to B or B to A is the same
for a in de_areas:
init_risk = [function.R0['{}_EAD'.format(a)].values[0],
np.sum([function.R0['{}_EAD'.format(i)].values[0]
for i in de_areas if i != a])]
variable_name = ['{}_EAD'.format(a)] + ['{}_EAD'.format(i
) for i in de_areas if i != a]
outcomes.append(ScalarOutcome('{}_u'.format(a),
function=partial(
relative_risk, init_risk[0]),
variable_name=[variable_name[0]]))
# when x is positive, the function gives 0, the constraint is met
constraints.append(Constraint('{}_u'.format(a),
outcome_names='{}_u'.format(a),
function=lambda x: max(0, -x)))
mins = [0.0] * 2
maxs = [1.88 * 1e10, 1.71 * 1e9]
dike_model.outcomes = outcomes
# utilitarian + relative risk trnafers
elif problem_formulation_id == 2:
constraints = []
epsilons = []
outcomes = []
variable_name = []
[variable_name.append('{}_Dike Inv Cost'.format(a)) for a in nl_areas]
variable_name.append('RfR Total Costs')
outcomes.append(ScalarOutcome('Investment Costs_nl',
variable_name=variable_name,
function=sum_over))
constraints.append(Constraint('Investment Costs_nl',
outcome_names='Investment Costs_nl',
function=lambda x: max(0, x - nl_max_costs)))
variable_name = []
for e in ['EAD', 'Dike Inv Cost']:
variable_name.extend('{}_{}'.format(a, e) for a in nl_areas)
variable_name.append('RfR Total Costs')
outcomes.append(ScalarOutcome('Total Costs_nl',
variable_name=variable_name,
function=sum_over, kind=direction))
epsilons.append(1e8)
variable_name = []
for e in ['EAD', 'Dike Inv Cost']:
variable_name.extend('{}_{}'.format(a, e) for a in de_areas)
outcomes.append(ScalarOutcome('Total Costs_de',
variable_name=variable_name,
function=sum_over, kind=direction))
epsilons.append(1e8)
for a in nl_areas:
init_risk = [function.R0['{}_EAD'.format(a)].values[0],
np.sum([function.R0['{}_EAD'.format(i)].values[0]
for i in nl_areas if i != a])]
variable_name = ['{}_EAD'.format(a)] + ['{}_EAD'.format(i
) for i in nl_areas if i != a]
outcomes.append(ScalarOutcome('{}_d'.format(a),
function=partial(risk_shift_distance,
init_risk),
variable_name=variable_name, kind=direction))
outcomes.append(ScalarOutcome('{}_u'.format(a),
function=partial(
relative_risk, init_risk[0]),
variable_name=[variable_name[0]]))
# when x is positive, the function gives 0, the constraint is met
constraints.append(Constraint('{}_u'.format(a),
outcome_names='{}_u'.format(a),
function=lambda x: max(0, -x)))
# only take one criteria in germany, cause there are only two locations.
# A to B or B to A is the same
for a in de_areas:
init_risk = [function.R0['{}_EAD'.format(a)].values[0],
np.sum([function.R0['{}_EAD'.format(i)].values[0]
for i in de_areas if i != a])]
variable_name = ['{}_EAD'.format(a)] + ['{}_EAD'.format(i
) for i in de_areas if i != a]
if a == 5:
outcomes.append(ScalarOutcome('{}_d'.format(a),
function=partial(
risk_shift_distance, init_risk),
variable_name=variable_name, kind=direction))
outcomes.append(ScalarOutcome('{}_u'.format(a),
function=partial(
relative_risk, init_risk[0]),
variable_name=[variable_name[0]]))
# when x is positive, the function gives 0, the constraint is met
constraints.append(Constraint('{}_u'.format(a),
outcome_names='{}_u'.format(a),
function=lambda x: max(0, -x)))
epsilons.extend([0.05] * 5)
mins = [0.0] * 7
maxs = [1.88 * 1e10, 1.71 * 1e9] + 5 * [0.708] # 1/np.sqrt(2)
dike_model.outcomes = outcomes
# utilitarian + absolute risk trnafers
elif problem_formulation_id == '2a':
constraints = []
epsilons = []
outcomes = []
variable_name = []
[variable_name.append('{}_Dike Inv Cost'.format(a)) for a in nl_areas]
variable_name.append('RfR Total Costs')
outcomes.append(ScalarOutcome('Investment Costs_nl',
variable_name=variable_name,
function=sum_over))
constraints.append(Constraint('Investment Costs_nl',
outcome_names='Investment Costs_nl',
function=lambda x: max(0, x - nl_max_costs)))
variable_name = []
for e in ['EAD', 'Dike Inv Cost']:
variable_name.extend('{}_{}'.format(a, e) for a in nl_areas)
variable_name.append('RfR Total Costs')
outcomes.append(ScalarOutcome('Total Costs_nl',
variable_name=variable_name,
function=sum_over, kind=direction))
epsilons.append(1e8)
variable_name = []
for e in ['EAD', 'Dike Inv Cost']:
variable_name.extend('{}_{}'.format(a, e) for a in de_areas)
outcomes.append(ScalarOutcome('Total Costs_de',
variable_name=variable_name,
function=sum_over, kind=direction))
epsilons.append(1e8)
for a in nl_areas:
init_risk = [function.R0['{}_EAD'.format(a)].values[0],
np.sum([function.R0['{}_EAD'.format(i)].values[0]
for i in nl_areas if i != a])]
variable_name = ['{}_EAD'.format(a)] + ['{}_EAD'.format(i
) for i in nl_areas if i != a]
outcomes.append(ScalarOutcome('{}_d'.format(a),
function=partial(absolute_risk_shift_distance,
init_risk),
variable_name=variable_name, kind=direction))
outcomes.append(ScalarOutcome('{}_u'.format(a),
function=partial(
absolute_risk, init_risk[0]),
variable_name=[variable_name[0]]))
# when x is positive, the function gives 0, the constraint is met
constraints.append(Constraint('{}_u'.format(a),
outcome_names='{}_u'.format(a),
function=lambda x: max(0, -x)))
# only take one criteria in germany, cause there are only two locations.
# A to B or B to A is the same
for a in de_areas:
init_risk = [function.R0['{}_EAD'.format(a)].values[0],
np.sum([function.R0['{}_EAD'.format(i)].values[0]
for i in de_areas if i != a])]
variable_name = ['{}_EAD'.format(a)] + ['{}_EAD'.format(i
) for i in de_areas if i != a]
if a == 5:
outcomes.append(ScalarOutcome('{}_d'.format(a),
function=partial(
absolute_risk_shift_distance, init_risk),
variable_name=variable_name, kind=direction))
outcomes.append(ScalarOutcome('{}_u'.format(a),
function=partial(
absolute_risk, init_risk[0]),
variable_name=[variable_name[0]]))
# when x is positive, the function gives 0, the constraint is met
constraints.append(Constraint('{}_u'.format(a),
outcome_names='{}_u'.format(a),
function=lambda x: max(0, -x)))
epsilons.extend([0.05] * 5)
mins = [0.0] * 7
maxs = [1.88 * 1e10, 1.71 * 1e9] + 5 * [0.708]
dike_model.outcomes = outcomes
else:
raise TypeError('unknonw identifier')
return dike_model, epsilons, (mins, maxs), constraints