def maximize_points(self, players=None):
model = pyomo.ConcreteModel()
model.starting_roster = constants.starting_roster
model.positions = [
position for position in model.starting_roster.keys()
]
model.players = self.players if players is None else players
# Decision variable: who is being used?
model.used = pyomo.Var(model.players, within=pyomo.Binary)
model.used_by_pos = pyomo.Var(model.players,
model.positions,
within=pyomo.Binary)
# Decision variable: who is playing what position?
model.games_played = pyomo.Var(model.players,
model.positions,
within=pyomo.NonNegativeIntegers)
# Limit number of players used
model.cap_players_used = pyomo.Constraint(rule=self.cap_players_used)
# Limit starting roster
model.limit_roster_rule = pyomo.Constraint(model.positions,
rule=self.limit_roster)
# Limit positions players can play
model.limit_positions_rule = pyomo.Constraint(
model.players, model.positions, rule=self.limit_positions)
# Limit to 1 position per player
model.limit_playtime_rule = pyomo.Constraint(model.players,
rule=self.limit_playtime)
model.limit_playtime_bypos_rule1 = \
pyomo.Constraint(model.players, model.positions, rule=self.limit_playtime_bypos1)
model.limit_playtime_bypos_rule2 = \
pyomo.Constraint(model.players, model.positions, rule=self.limit_playtime_bypos2)
# Only true RP play RP - due to starts limit
model.only_true_rp_rule1 = pyomo.Constraint(model.players,
rule=self.only_true_rp1)
model.only_true_rp_rule2 = pyomo.Constraint(model.players,
rule=self.only_true_rp2)
# Constrain which players can be modeled as 'replaceable' to fill out remaining playing time at position
model.limit_replaceability = pyomo.Constraint(
model.players, model.positions, rule=self.limit_replaceability)
# Objective function
model.objective = pyomo.Objective(rule=self.objective,
sense=pyomo.maximize)
return model
model.m = pyomo.Param(within=pyomo.NonNegativeIntegers)
model.n = pyomo.Param(within=pyomo.NonNegativeIntegers)
# although not required, it is convenient to define index sets
model.I = pyomo.RangeSet(1, model.m)
model.J = pyomo.RangeSet(1, model.n)
# now we define the coefficients (which are themselves defined over index sets!)
model.a = pyomo.Param(model.I, model.J)
model.b = pyomo.Param(model.I)
model.c = pyomo.Param(model.J)
# the next line declares a variable indexed by the set J
model.x = pyomo.Var(model.J, domain=pyomo.NonNegativeReals)
def objective(model):
"""Abstract representation of our model objective."""
obj = pyomo.summation(model.c, model.x)
return obj
# add the objective function to the model object as an attribute (OBJ can be arbitrary!)
model.OBJ = pyomo.Objective(rule=objective)
def constraints(model, i):
"""Abstract representation of model constraints."""
# return the expression for the constraint for i
return sum(model.a[i,j] * model.x[j] for j in model.J) >= model.b[i]
# the next line creates one constraint for each member of the set model.I (CONS can be arbitrary!)
model.CONS = pyomo.Constraint(model.I, rule=constraints)
"""Agent faces a sequence of flow budget constraints"""
# extract variables
k = model.capital
c = model.consumption
i = model.investment
# extract parameters
r = model.r
w = model.w
l_bar = model.l_bar
return c[t] + i[t] == w[t] * l_bar + r * k[t]
model.budget_constraints = pyomo.Constraint(
model.periods,
rule=flow_budget_constraints,
doc='Agent faces a sequence of flow budget constraints.')
def capital_evolution_rule(model, t):
"""Agent's capital stock evolves depending on current capital stock and investment rate."""
# extract variables
k = model.capital
i = model.investment
# extract parameters
delta = model.delta
return k[t + 1] == (1 - delta) * k[t] + i[t]
def create_optimal_model(self, team_players, available_players,
prob_avail_after):
model = pyomo.ConcreteModel()
# Set bounds of problem
model.weeks = constants.week_weights.keys()
model.positions = constants.roster.keys()
model.roster_size = sum(constants.roster.values())
mcfadden = PlayerClass.Player('D. McFadden Dal - RB')
points = {
1: 4.74,
2: 11.89,
3: 12.09,
4: 11.99,
5: 12.2,
6: 0,
7: 11.61,
8: 13.25,
9: 3.43,
10: 3.21,
11: 3.44,
12: 3.52,
13: 3.44,
14: 3.27,
15: 3.24,
16: 3.33
}
mcfadden.add_points(points)
# Determine current and available players
model.team_players = team_players + [mcfadden]
model.avail_players = available_players
model.players = model.team_players + model.avail_players
model.prob_avail_after = {
key: prob_avail_after[key]
for key in prob_avail_after.keys()
}
for player in model.team_players:
model.prob_avail_after[player] = 1.0
########### Decision Variables ###########
model.starting = pyomo.Var(model.players,
model.positions,
model.weeks,
within=pyomo.Binary)
model.starts = pyomo.Var(model.players,
within=pyomo.NonNegativeIntegers)
model.used = pyomo.Var(model.players, within=pyomo.Binary)
########### Constraints ###########
model.position_eligibility = pyomo.Constraint(
model.players,
model.positions,
model.weeks,
rule=self.position_eligibility)
model.weekly_roster_size = pyomo.Constraint(
model.positions, model.weeks, rule=self.weekly_roster_size)
model.only_one_position = pyomo.Constraint(model.players,
model.weeks,
rule=self.only_one_position)
model.set_starts = pyomo.Constraint(model.players,
rule=self.set_starts)
model.set_used = pyomo.Constraint(model.players, rule=self.set_used)
model.set_used2 = pyomo.Constraint(model.players, rule=self.set_used2)
model.cap_used = pyomo.Constraint(model.players, rule=self.cap_used)
########### Objective function ###########
model.objective = pyomo.Objective(rule=self.objective,
sense=pyomo.maximize)
return model
def flow_budget_constraints(model, t):
"""Agent faces a sequence of flow budget constraints"""
# extract variables
c = model.consumption
l = model.labor_supply
A = model.assets
# extract parameters
r = model.r
w = model.w
return c[t] + A[t + 1] == w[t] * l[t] + (1 + r) * A[t]
model.budget_constraints = pyomo.Constraint(
model.periods,
rule=flow_budget_constraints,
doc='Agent faces a sequence of flow budget constraints.')
def borrowing_constraint(model, t):
"""Agent's assets cannot fall below some minimum amount."""
return model.assets[t] >= model.minimum_assets
model.borrowing_constraint = pyomo.Constraint(
model.periods,
rule=borrowing_constraint,
doc='There is a lower bound on agent assets.')
def endowment(model):
def add_constraint(self, name, expression, time=None):
cname = self._t_id(name, time) if time is not None else name
self._model.add_component(cname,
pyomo.Constraint(name=name, rule=expression))
def add_constraint_set(self, name, index, expression):
cname = self._id(name)
self._parent_problem().add_component_to_problem(
pyomo.Constraint(index, name=cname, rule=expression))
def add_constraint(self, name, time, expression):
'''Create a new constraint and add it to the object's constraints and the model's constraints.'''
cname = self._t_id(name, time)
self._parent_problem().add_component_to_problem(
pyomo.Constraint(name=cname, rule=expression))
k = model.capital
c = model.consumption
b = model.debt
# extract parameters
r = model.r
w = model.w
q = model.q
l_bar = model.l_bar
return c[t] + q[t] * k[t + 1] + (1 + r) * b[t] == w[t] * l_bar + (
r + q[t]) * k[t] + b[t + 1]
model.budget_constraints = pyomo.Constraint(
model.periods,
rule=flow_budget_constraints,
doc='Agent faces a sequence of flow budget constraints.')
def borrowing_constraint(model, t):
"""Agent's borrowing capacity depends on collateral."""
# extract variables
k = model.capital
b = model.debt
# extract parameters
theta = model.theta
r = model.r
q = model.q
return (1 + r) * b[t] <= theta * q[t + 1] * k[t]
def create_model(data, timesteps):
""" Create a VICUS model object from input data.
Creates and returns a Pyomo ConcreteModel object, given a model
input file (supported formats: Excel spreadsheet [planned: SQLite DB])
Args:
data: input dict with fields for Commodities, Processes,
Storage and timeseries for Demand and SupIm
timesteps: numpy array of timestep labels, matching the ones
used in the Demand and SupIm timeseries
Returns:
A coopr.pyomo ConcreteModel object, ready to be instantiated and
solved.
"""
m = pyomo.ConcreteModel()
m.name = 'VICUS'
m.created = datetime.now().strftime('%Y%m%dT%H%M%S', )
# Preparations
# ============
# Data import. Syntax to access a value within equation definitions looks
# like this:
#
# m.process.loc[sit, pro, coin, cout][attribute]
#
get_inputs = itemgetter("commodity", "process", "storage", "demand",
"supim")
(m.commodity, m.process, m.storage, m.demand, m.supim) = get_inputs(data)
# Sets
# ====
# Syntax: m.{name} = Set({domain}, initialize={values})
# where name: set name
# domain: set domain for tuple sets, a cartesian set product
# values: set values, a list or array of element tuples
m.t = pyomo.Set(ordered=True, initialize=timesteps)
m.tm = pyomo.Set(within=m.t, initialize=timesteps[1:])
m.co = pyomo.Set(initialize=m.commodity.index.levels[0])
m.coin = pyomo.Set(within=m.co, initialize=m.process.index.levels[1])
m.cout = pyomo.Set(within=m.co, initialize=m.process.index.levels[2])
m.co_type = pyomo.Set(initialize=m.commodity.index.levels[1])
m.pro = pyomo.Set(initialize=m.process.index.levels[0])
m.sto = pyomo.Set(initialize=m.storage.index.levels[0])
m.cost_type = pyomo.Set(initialize=['Inv', 'Fix', 'Var', 'Fuel'])
# sets of existing tuples:
# co_tuples = [('Coal', 'Stock'), ('Wind', 'SupIm'), ('ElecAC', 'Demand')...]
# pro_tuples = [('pp', 'Coal', 'ElecAC'), ('wt', 'Wind', 'ElecAC')...]
# sto_tuples = [('bat', 'ElecDC'), ('pst', 'ElecAC')...]
m.co_tuples = pyomo.Set(within=m.co * m.co_type,
initialize=m.commodity.index)
m.pro_tuples = pyomo.Set(within=m.pro * m.coin * m.cout,
initialize=m.process.index)
m.sto_tuples = pyomo.Set(within=m.sto * m.co, initialize=m.storage.index)
# subsets of commodities by type
# for shorter equations that apply to only one commodity type
m.co_supim = pyomo.Set(within=m.co,
initialize=(c[0] for c in m.co_tuples
if c[1] == 'SupIm'))
m.co_stock = pyomo.Set(within=m.co,
initialize=(c[0] for c in m.co_tuples
if c[1] == 'Stock'))
m.co_demand = pyomo.Set(within=m.co,
initialize=(c[0] for c in m.co_tuples
if c[1] == 'Demand'))
# Parameters
# ==========
# for model entities (commodity, process, storage) no Pyomo params
# are needed, just use the DataFrames m.commodity, m.process and
# m.storage directly.
# Syntax: m.{name} = Param({domain}, initialize={values})
# where name: param name
# domain: one or multiple model sets; empty for scalar parameters
# values: dict of values, addressed by elements of domain sets
m.weight = pyomo.Param(initialize=float(8760) / len(m.t))
# Variables
# =========
# listed alphabetically
# Syntax: m.{name} = Var({domain}, within={range})
# where name: variable name
# domain: variable domain, consisting of one or multiple sets
# range: variable values, like Binary, Integer, NonNegativeReals
m.cap_pro = pyomo.Var(m.pro_tuples,
within=pyomo.NonNegativeReals,
doc='Total process capacity (kW)')
m.cap_pro_new = pyomo.Var(m.pro_tuples,
within=pyomo.NonNegativeReals,
doc='New process capacity (kW)')
m.cap_sto_c = pyomo.Var(m.sto_tuples,
within=pyomo.NonNegativeReals,
doc='Total storage size (kWh)')
m.cap_sto_c_new = pyomo.Var(m.sto_tuples,
within=pyomo.NonNegativeReals,
doc='New storage capacity (kWh)')
m.cap_sto_p = pyomo.Var(m.sto_tuples,
within=pyomo.NonNegativeReals,
doc='Total storage power (kW)')
m.cap_sto_p_new = pyomo.Var(m.sto_tuples,
within=pyomo.NonNegativeReals,
doc='New storage power (kW)')
m.co2_pro_out = pyomo.Var(
m.tm,
m.pro_tuples,
within=pyomo.NonNegativeReals,
doc='CO2 emissions from processes (kg) per timestep')
m.costs = pyomo.Var(m.cost_type,
within=pyomo.NonNegativeReals,
doc='Costs by type (EUR/a)')
m.e_co_stock = pyomo.Var(
m.tm,
m.co_stock,
within=pyomo.NonNegativeReals,
doc='Source power flow from stock commodities (kW) per timestep')
m.e_pro_in = pyomo.Var(m.tm,
m.pro_tuples,
within=pyomo.NonNegativeReals,
doc='Power flow into process (kW) per timestep')
m.e_pro_out = pyomo.Var(m.tm,
m.pro_tuples,
within=pyomo.NonNegativeReals,
doc='Power flow out of process (kW) per timestep')
m.e_sto_in = pyomo.Var(m.tm,
m.sto_tuples,
within=pyomo.NonNegativeReals,
doc='Power flow into storage (kW) per timestep')
m.e_sto_out = pyomo.Var(m.tm,
m.sto_tuples,
within=pyomo.NonNegativeReals,
doc='Power flow out of storage (kW) per timestep')
m.e_sto_con = pyomo.Var(m.t,
m.sto_tuples,
within=pyomo.NonNegativeReals,
doc='Energy content of storage (kWh) in timestep')
# Equation definition
# ===================
# listed by topic. All equations except the Objective function are
# of type Constraint, although there are two semantics for those,
# indicated by the name prefix (def, res).
# - def: definition, usually equations, defining variable values
# - res: restriction, usually inequalities, limiting variable values
# topics
# - commodity
# - process
# - storage
# - emissions
# - costs
# commodity
def res_demand_rule(m, tm, co, co_type):
if co not in m.co_demand:
return pyomo.Constraint.Skip
else:
provided_energy = -commodity_balance(m, tm, co)
return provided_energy >= \
m.demand.loc[tm][co] * \
m.commodity.loc[co, co_type]['peak']
def def_e_co_stock_rule(m, tm, co, co_type):
if co not in m.co_stock:
return pyomo.Constraint.Skip
else:
return m.e_co_stock[tm, co] == commodity_balance(m, tm, co)
def res_stock_hour_rule(m, tm, co, co_type):
if co not in m.co_stock:
return pyomo.Constraint.Skip
else:
return m.e_co_stock[tm, co] <= \
m.commodity.loc[co, co_type]['maxperhour']
def res_stock_total_rule(m, co, co_type):
if co not in m.co_stock:
return pyomo.Constraint.Skip
else:
# calculate total consumption of commodity co
total_consumption = 0
for tm in m.tm:
total_consumption += m.e_co_stock[tm, co] * m.weight
return total_consumption <= m.commodity.loc[co, co_type]['max']
# process
def def_process_capacity_rule(m, tm, pro, coin, cout):
return m.cap_pro[pro,coin,cout] == \
m.cap_pro_new[pro,coin,cout] + \
m.process.loc[pro,coin,cout]['inst-cap']
def def_process_output_rule(m, tm, pro, coin, cout):
return m.e_pro_out[tm, pro, coin, cout] == \
m.e_pro_in[tm, pro, coin, cout] * \
m.process.loc[pro, coin, cout]['eff']
def def_intermittent_supply_rule(m, tm, pro, coin, cout):
if coin in m.co_supim:
return m.e_pro_in[tm, pro, coin, cout] == \
m.cap_pro[pro, coin, cout] * m.supim.loc[tm][coin]
else:
return pyomo.Constraint.Skip
def def_co2_emissions_rule(m, tm, pro, coin, cout):
return m.co2_pro_out[tm, pro, coin, cout] == \
m.e_pro_in[tm, pro, coin, cout] * \
m.process.loc[pro, coin, cout]['co2'] * \
m.weight
def res_process_output_by_capacity_rule(m, tm, pro, coin, cout):
return m.e_pro_out[tm, pro, coin, cout] <= m.cap_pro[pro, coin, cout]
def res_process_capacity_rule(m, pro, coin, cout):
return (m.process.loc[pro, coin, cout]['cap-lo'],
m.cap_pro[pro, coin, cout], m.process.loc[pro, coin,
cout]['cap-up'])
# storage
def def_storage_state_rule(m, t, sto, co):
return m.e_sto_con[t, sto, co] == \
m.e_sto_con[t-1, sto, co] + \
m.e_sto_in[t, sto, co] * m.storage.loc[sto, co]['eff-in'] - \
m.e_sto_out[t, sto, co] / m.storage.loc[sto, co]['eff-out']
def def_storage_power_rule(m, sto, co):
return m.cap_sto_p[sto, co] == \
m.cap_sto_p_new[sto, co] + \
m.storage.loc[sto, co]['inst-cap-p']
def def_storage_capacity_rule(m, sto, co):
return m.cap_sto_c[sto, co] == \
m.cap_sto_c_new[sto, co] + \
m.storage.loc[sto, co]['inst-cap-p']
def res_storage_input_by_power_rule(m, t, sto, co):
return m.e_sto_in[t, sto, co] <= m.cap_sto_p[sto, co]
def res_storage_output_by_power_rule(m, t, sto, co):
return m.e_sto_out[t, sto, co] <= m.cap_sto_p[sto, co]
def res_storage_state_by_capacity_rule(m, t, sto, co):
return m.e_sto_con[t, sto, co] <= m.cap_sto_c[sto, co]
def res_storage_power_rule(m, sto, co):
return (m.storage.loc[sto, co]['cap-lo-p'], m.cap_sto_p[sto, co],
m.storage.loc[sto, co]['cap-up-p'])
def res_storage_capacity_rule(m, sto, co):
return (m.storage.loc[sto, co]['cap-lo-c'], m.cap_sto_c[sto, co],
m.storage.loc[sto, co]['cap-up-c'])
def res_initial_and_final_storage_state_rule(m, t, sto, co):
if t == m.t[1]: # first timestep (Pyomo uses 1-based indexing)
return m.e_sto_con[t, sto, co] == \
m.cap_sto_c[sto, co] * \
m.storage.loc[sto, co]['init']
elif t == m.t[-1]: # last timestep
return m.e_sto_con[t, sto, co] >= \
m.cap_sto_c[sto, co] * \
m.storage.loc[sto, co]['init']
else:
return pyomo.Constraint.Skip
# emissions
def res_co2_emission_rule(m):
return pyomo.summation(m.co2_pro_out) <= \
m.commodity.loc['CO2','Env']['max']
# costs
def def_costs_rule(m, cost_type):
""" Calculate total costs by cost type.
Sums up process activity and capacity expansions
and sums them in the cost types that are specified in the set
m.cost_type. To change or add cost types, add/change entries
there and modify the if/elif cases in this function accordingly.
Cost types are
- Investment costs for process power, storage power and
storage capacity, annualized.
- Fixed costs for process & storage power, storage capacity.
- Variable costs for process and storage activity.
- Fuel costs for purchased stock commodities.
"""
if cost_type == 'Inv':
return m.costs['Inv'] == \
sum(m.cap_pro_new[p] *
m.process.loc[p]['inv-cost'] *
m.process.loc[p]['annuity_factor']
for p in m.pro_tuples) + \
sum(m.cap_sto_p_new[s] *
m.storage.loc[s]['inv-cost-p'] *
m.storage.loc[s]['annuity_factor'] +
m.cap_sto_c_new[s] *
m.storage.loc[s]['inv-cost-c'] *
m.storage.loc[s]['annuity_factor']
for s in m.sto_tuples)
elif cost_type == 'Fix':
return m.costs['Fix'] == \
sum(m.cap_pro[p] * m.process.loc[p]['fix-cost']
for p in m.pro_tuples) + \
sum(m.cap_sto_p[s] * m.storage.loc[s]['fix-cost-p'] +
m.cap_sto_c[s] * m.storage.loc[s]['fix-cost-c']
for s in m.sto_tuples)
elif cost_type == 'Var':
return m.costs['Var'] == \
sum(m.e_pro_out[(tm,) + p] *
m.process.loc[p]['var-cost'] *
m.weight
for tm in m.tm for p in m.pro_tuples) + \
sum(m.e_sto_con[(tm,) + s] *
m.storage.loc[s]['var-cost-c'] * m.weight +
(m.e_sto_in[(tm,) + s] + m.e_sto_out[(tm,) + s]) *
m.storage.loc[s]['var-cost-p'] * m.weight
for tm in m.tm for s in m.sto_tuples)
elif cost_type == 'Fuel':
return m.costs['Fuel'] == \
sum(m.e_co_stock[(tm,c[0])] *
m.commodity.loc[c]['price'] *
m.weight
for tm in m.tm for c in m.co_tuples
if c[0] in m.co_stock)
else:
raise NotImplementedError("Unknown cost type!")
def obj_rule(m):
""" Return sum of total costs over all cost types.
Simply calculates the sum of m.costs over all m.cost_types.
"""
return pyomo.summation(m.costs)
# Equation declaration
# ====================
# declarations connect rule functions to the model, specifying
# the model sets for which the constraints are enforced.
# commodity
m.res_demand = pyomo.Constraint(m.tm,
m.co_tuples,
doc='storage + process balance >= demand')
m.def_e_co_stock = pyomo.Constraint(
m.tm,
m.co_tuples,
doc='commodity source term = hourly commodity consumption')
m.res_stock_hour = pyomo.Constraint(
m.tm,
m.co_tuples,
doc='hourly commodity source term <= commodity.maxperhour')
m.res_stock_total = pyomo.Constraint(
m.co_tuples, doc='total commodity source term <= commodity.max')
# process
m.def_process_capacity = pyomo.Constraint(
m.tm,
m.pro_tuples,
doc='total process capacity = inst-cap + new capacity')
m.def_process_output = pyomo.Constraint(
m.tm, m.pro_tuples, doc='process output = process input * efficiency')
m.def_intermittent_supply = pyomo.Constraint(
m.tm,
m.pro_tuples,
doc='process output = process capacity * supim timeseries')
m.def_co2_emissions = pyomo.Constraint(
m.tm,
m.pro_tuples,
doc='process co2 output = process input * process.co2 * weight')
m.res_process_output_by_capacity = pyomo.Constraint(
m.tm, m.pro_tuples, doc='process output <= process capacity')
m.res_process_capacity = pyomo.Constraint(
m.pro_tuples,
doc='process.cap-lo <= process capacity <= process.cap-up')
# storage
m.def_storage_state = pyomo.Constraint(
m.tm, m.sto_tuples, doc='storage[t] = storage[t-1] + input - output')
m.def_storage_power = pyomo.Constraint(
m.sto_tuples, doc='storage power = inst-cap + new power')
m.def_storage_capacity = pyomo.Constraint(
m.sto_tuples, doc='storage capacity = inst-cap + new capacity')
m.res_storage_input_by_power = pyomo.Constraint(
m.tm, m.sto_tuples, doc='storage input <= storage power')
m.res_storage_output_by_power = pyomo.Constraint(
m.tm, m.sto_tuples, doc='storage output <= storage power')
m.res_storage_state_by_capacity = pyomo.Constraint(
m.t, m.sto_tuples, doc='storage content <= storage capacity')
m.res_storage_power = pyomo.Constraint(
m.sto_tuples, doc='storage.cap-lo <= storage power <= storage.cap-up')
m.res_storage_capacity = pyomo.Constraint(
m.sto_tuples,
doc='storage.cap-lo <= storage capacity <= storage.cap-up')
m.res_initial_and_final_storage_state = pyomo.Constraint(
m.t,
m.sto_tuples,
doc='storage content initial == and final >= storage.init * capacity')
# emissions
m.res_co2_emission = pyomo.Constraint(
doc='total co2 emissions <= commodity.co2.max')
# costs
m.def_costs = pyomo.Constraint(m.cost_type,
doc='main cost function by cost type')
m.obj = pyomo.Objective(sense=pyomo.minimize,
doc='cost = sum of all cost types')
return m