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problem_formulation_4b.py
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# -*- coding: utf-8 -*-
"""
Created on Fri Jun 14 15:26:31 2019
@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 itertools import combinations
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 risk_diff(init_risk, *args):
EADa0 = init_risk
EADa1 = args[0]
ratio = (EADa0 - EADa1)
return ratio
def risk_shift_distance(init_risks, *args):
r1 = (init_risks[0] - args[0]) / (init_risks[0]+0.00001)
r2 = (init_risks[1] - args[1]) / (init_risks[1]+0.00001)
distance = abs(r1 - r2) / np.sqrt(2)
return distance
def max_risk_shift_distance(init_risks, *args):
distance = []
for comb in combinations(range(len(init_risks)),2):
a1, a2 = comb
# if both areas have initinial risk higher than zero
if not (init_risks[a1]*init_risks[a2] == 0):
r1 = (init_risks[a1] - args[a1]) / (init_risks[a1])
r2 = (init_risks[a2] - args[a2]) / (init_risks[a2])
# distance from the r1 = r2 line
distance.append(abs(r1 - r2) / np.sqrt(2))
else:
distance.append(0)
return np.max(distance)
#def max_risk_shift_distance(init_risks, *args):
#
# distance = []
# count = 0
# for arg in args:
# for i in range(len(init_risks)):
# if not i == count:
# r1 = (init_risks[count] - arg) / init_risks[count]
# r2 = (init_risks[i] - args[i]) / init_risks[i]
#
# # distance from the r1 = r2 line
# distance.append(abs(r1 - r2) / np.sqrt(2))
# count += 1
# return np.max(distance)
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]
dikerings = np.unique(DikeNetwork().tree.dikering.T)
# nl_max_costs = 2 * 1e8
risk_keys = {0: 'minR', 1: 'EAD', 2: 'maxR'}
ri = risk_keys[1] # risk indicator
# general
if problem_formulation_id == 0:
constraints = []
mins, maxs = 0, 0
epsilons = []
outcomes = []
variable_name = []
[outcomes.append(ScalarOutcome('{}_{}'.format(r, ri))) for r in dikerings]
for i in eooi:
[outcomes.append(TimeSeriesOutcome('{}_{}'.format(output_list[i], n))
) for n in function.dikenodes]
dike_model.outcomes = outcomes
# non-cooperative
elif problem_formulation_id == 1:
constraints = []
epsilons = []
outcomes = []
# adapt this constraint
# 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 ['{}'.format(ri), '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 ['{}'.format(ri), '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 = [1.9 * 1e10, 2.16 * 1e9]
dike_model.outcomes = outcomes
# intra-country cooperation:
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 ['{}'.format(ri), '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 ['{}'.format(ri), '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)
init_risks = []
variable_name = []
for a in nl_areas:
init_risks.append(function.R0['{}_{}'.format(a, ri)].values[0])
variable_name.append('{}_{}'.format(a, ri))
outcomes.append(ScalarOutcome('{}_EAD'.format(a),
variable_name=['{}_EAD'.format(a)]))
# when x is positive, the function gives 0, the constraint is met
constraints.append(Constraint('{}_EAD'.format(a),
outcome_names='{}_EAD'.format(a),
function=lambda x: max(0, -x)))
outcomes.append(ScalarOutcome('max_distance_nl',
function=partial(max_risk_shift_distance, init_risks),
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)))
init_risks = []
variable_name = []
for a in de_areas:
init_risks.append(function.R0['{}_{}'.format(a, ri)].values[0])
variable_name.append('{}_{}'.format(a, ri))
outcomes.append(ScalarOutcome('{}_EAD'.format(a),
variable_name=['{}_EAD'.format(a)]))
# when x is positive, the function gives 0, the constraint is met
constraints.append(Constraint('{}_EAD'.format(a),
outcome_names='{}_EAD'.format(a),
function=lambda x: max(0, -x)))
outcomes.append(ScalarOutcome('max_distance_de',
function=partial(max_risk_shift_distance, init_risks),
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 = [1.9 * 1e10, 2.16 * 1e9] + 2 * [0.708] # 1/np.sqrt(2)
dike_model.outcomes = outcomes
# intra-country cooperation:
elif problem_formulation_id == '2b':
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 ['{}'.format(ri), '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 ['{}'.format(ri), '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)
init_risks = function.R0
variable_name = []
for r in dikerings:
variable_name.append('{}_{}'.format(r, ri))
outcomes.append(ScalarOutcome('{}_EADred'.format(r),
variable_name=['{}_EAD'.format(r)],
function=partial(risk_diff,
init_risks['{}_EAD'.format(r)].values[0])))
# outcomes.append(ScalarOutcome('{}_EAD'.format(r),
# variable_name=['{}_EAD'.format(r)]))
# when x is positive, the function gives 0, the constraint is met
constraints.append(Constraint('{}_EADred'.format(r),
outcome_names='{}_EADred'.format(r),
function=lambda x: max(0, -x)))
outcomes.append(ScalarOutcome('max_distance',
function=partial(max_risk_shift_distance,
init_risks.values[0]),
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 = [1.9 * 1e10, 2.16 * 1e9] + 5 * [0.708] # 1/np.sqrt(2)
dike_model.outcomes = outcomes
# inter-country cooperation
elif problem_formulation_id == 3:
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+de_areas)
variable_name.append('RfR Total Costs')
outcomes.append(ScalarOutcome('Total Costs',
variable_name=variable_name,
function=sum_over, kind=direction))
epsilons.append(1e7)
init_risks = function.R0
variable_name = []
for r in dikerings:
variable_name.append('{}_{}'.format(r, ri))
outcomes.append(ScalarOutcome('{}_EADred'.format(r),
variable_name=['{}_EAD'.format(r)],
function=partial(risk_diff,
init_risks['{}_EAD'.format(r)].values[0])))
# outcomes.append(ScalarOutcome('{}_EAD'.format(r),
# variable_name=['{}_EAD'.format(r)]))
# when x is positive, the function gives 0, the constraint is met
constraints.append(Constraint('{}_EADred'.format(r),
outcome_names='{}_EADred'.format(r),
function=lambda x: max(0, -x)))
outcomes.append(ScalarOutcome('max_distance',
function=partial(max_risk_shift_distance,
init_risks.values[0]),
variable_name=variable_name, kind=direction))
epsilons.extend([0.05] * 5)
mins = [0.0] * 7
maxs = [1.9 * 1e10, 2.16 * 1e9] + 5 * [0.708] # 1/np.sqrt(2)
dike_model.outcomes = outcomes
# most-disaggregated version
elif problem_formulation_id == 'disaggregated':
constraints = []
epsilons = []
outcomes = []
variable_name = []
for e in [ri, 'Dike Inv Cost']:
if e not in ['Dike Inv Cost']:
for r in dikerings:
outcomes.append(ScalarOutcome('{}_{}'.format(r, e)))
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))
variable_name = []
for e in ['{}'.format(ri), '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))
# for e in ['EAD', 'Dike Inv Cost']:
# for r in dikerings:
# outcomes.append(ScalarOutcome('{}_{}'.format(r, e)))
# variable_name.extend(['{}_{}'.format(r, e)])
# variable_name.append('RfR Total Costs')
#
# outcomes.append(ScalarOutcome('Total Costs',
# variable_name=variable_name,
# function=sum_over, kind=direction))
# outcomes.append(ScalarOutcome('RfR Total Costs'))
# for r in dikerings:
# outcomes.append(ScalarOutcome('{}_Dike Inv Cost'.format(r)))
# outcomes.append(ScalarOutcome('{}_EAD'.format(r)))
init_risks = function.R0.values[0]
for comb in combinations(range(len(init_risks)),2):
a1, a2 = comb
n1, n2 = dikerings[a1], dikerings[a2]
outcomes.append(ScalarOutcome('{}_{}_distance'.format(n1,n2),
function=partial(risk_shift_distance,
init_risks[[a1,a2]]),
variable_name=['{}_EAD'.format(n1), '{}_EAD'.format(n2)],
kind=direction))
# variable_name = []
# [variable_name.append('{}_Dike Inv Cost'.format(a)) for a in nl_areas+de-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+de_areas)
# variable_name.append('RfR Total Costs')
#
# outcomes.append(ScalarOutcome('Total Costs',
# variable_name=variable_name,
# function=sum_over, kind=direction))
#
#
# init_risks = function.R0.values[0]
# variable_name = []
#
# for a in nl_areas+de_areas:
# variable_name.append('{}_{}'.format(a, ri))
#
# outcomes.append(ScalarOutcome('{}_EAD'.format(a),
# variable_name=['{}_EAD'.format(a)]))
#
# outcomes.append(ScalarOutcome('max_distance',
# function=partial(max_risk_shift_distance, init_risks),
# 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)))
dike_model.outcomes = outcomes
mins, maxs = [0,0]
else:
raise TypeError('unknonw problem formulation')
return dike_model, epsilons, (mins, maxs), constraints