def MeetShortage_rule(model):
lt_q = pyo.sum_product(model.LT_QF, model.LT_ACTION)
mt_q = pyo.quicksum(model.LT_QF[i] * model.LT_ACTION[i] * model.MT_EXP[i]
for i in model.LT)
st_q = pyo.quicksum(model.ST_Q[k] for k in model.ST)
tot_q = lt_q + mt_q + st_q
return tot_q >= model.SHORTAGE_Q['SH']
def test_quicksum(self):
m = ConcreteModel()
m.y = Var(domain=Binary)
m.c = Constraint(expr=quicksum([m.y, m.y], linear=True) == 1)
lbl = NumericLabeler('x')
smap = SymbolMap(lbl)
tc = StorageTreeChecker(m)
self.assertEqual(("x1 + x1", False),
expression_to_string(m.c.body, tc, smap=smap))
m.x = Var()
m.c2 = Constraint(expr=quicksum([m.x, m.y], linear=True) == 1)
self.assertEqual(("x2 + x1", False),
expression_to_string(m.c2.body, tc, smap=smap))
m.y.fix(1)
lbl = NumericLabeler('x')
smap = SymbolMap(lbl)
tc = StorageTreeChecker(m)
self.assertEqual(("1 + 1", False),
expression_to_string(m.c.body, tc, smap=smap))
m.x = Var()
m.c2 = Constraint(expr=quicksum([m.x, m.y], linear=True) == 1)
self.assertEqual(("x1 + 1", False),
expression_to_string(m.c2.body, tc, smap=smap))
def minimumDownTime2(pyM, loc, compName, p, t):
downTimeMin = getattr(compDict[compName], 'downTimeMin')
if t >= downTimeMin:
return opVarBin[loc, compName, p, t] <= 1 -pyomo.quicksum(opVarStopBin[loc, compName, p, t_down] for t_down in range(t-downTimeMin+1, t))
else:
return opVarBin[loc, compName, p, t] <= 1 -pyomo.quicksum(opVarStopBin[loc, compName, p, t_down] for t_down in range(0, t)) \
- pyomo.quicksum(opVarStopBin[loc, compName, p, t_down] for t_down in range(numberOfTimeSteps-(downTimeMin-t), numberOfTimeSteps))
def test_convex_relaxation_with_quadratic_only():
m = pe.ConcreteModel()
m.I = range(10)
m.x = pe.Var(m.I)
m.obj = pe.Objective(expr=pe.quicksum(m.x[i]*m.x[i] for i in m.I))
m.c0 = pe.Constraint(expr=pe.quicksum(2 * m.x[i] * m.x[i] for i in m.I) >= 0)
dag = problem_from_pyomo_model(m)
relaxation = _convex_relaxation(dag)
relaxed = relaxation.relax(dag)
assert relaxed.objective
# original constraint + 10 for disaggregated squares
assert len(relaxed.constraints) == 1 + 10
objective = relaxed.objective
constraint = relaxed.constraints[0]
assert isinstance(objective.root_expr, LinearExpression)
assert len(objective.root_expr.children) == 10
for constraint in relaxed.constraints[:-1]:
assert isinstance(constraint.root_expr, SumExpression)
children = constraint.root_expr.children
assert len(children) == 2
assert isinstance(children[0], LinearExpression)
assert isinstance(children[1], QuadraticExpression)
constraint = relaxed.constraints[-1]
assert len(constraint.root_expr.children) == 10
assert isinstance(constraint.root_expr, LinearExpression)
def test_linear_relaxation_with_quadratic_and_linear():
m = pe.ConcreteModel()
m.I = range(10)
m.x = pe.Var(m.I, bounds=(0, 1))
m.obj = pe.Objective(
expr=pe.quicksum(m.x[i]*m.x[i] for i in m.I) + pe.quicksum(m.x[i] for i in m.I)
)
m.c0 = pe.Constraint(
expr=pe.quicksum(2 * m.x[i] * m.x[i] for i in m.I) + pe.quicksum(m.x[i] for i in m.I) >= 0
)
dag = problem_from_pyomo_model(m)
relaxation = _linear_relaxation(dag)
relaxed = relaxation.relax(dag)
print_problem(relaxed)
assert relaxed.objective
# 1 objective, 1 c0, 4 * 10 x^2 (3 mccormick, 1 midpoint)
assert len(relaxed.constraints) == 1 + 1 + 4*10
objective = relaxed.objective
constraint = relaxed.constraint('c0')
assert isinstance(objective.root_expr, LinearExpression)
assert isinstance(constraint.root_expr, SumExpression)
# Root is only objvar
assert len(objective.root_expr.children) == 1
c0, c1 = constraint.root_expr.children
assert isinstance(c0, LinearExpression)
assert isinstance(c1, LinearExpression)
assert len(c0.children) == 10
assert len(c1.children) == 10
def minimumUpTime2(pyM, loc, compName, p, t):
upTimeMin = getattr(compDict[compName], 'upTimeMin')
if t >= upTimeMin:
return opVarBin[loc, compName, p, t] >= pyomo.quicksum(opVarStartBin[loc, compName, p, t_up] for t_up in range(t-upTimeMin+1, t))
else:
return opVarBin[loc, compName, p, t] >= pyomo.quicksum(opVarStartBin[loc, compName, p, t_up] for t_up in range(0, t)) \
+ pyomo.quicksum(opVarStartBin[loc, compName, p, t_up] for t_up in range(numberOfTimeSteps-(upTimeMin-t), numberOfTimeSteps))
def rule(x, compute_values=False):
if compute_values:
return (quicksum(value(index_coef_dict[i]) * x[i]
for i in x) + value(constant))
else:
return quicksum(index_coef_dict[i] * x[i]
for i in x) + constant
def MeetShortage_rule(model):
lt_q = model.LT_ACTION['RETRO']
exp_vop_q = pyo.quicksum(model.EXP_VOP_ACTION[i] *
model.LT_EXP_PERMIT_ACTION[i]
for i in model.LT_EXP)
st_q = pyo.quicksum(model.ST_ACTION[i] for i in model.ST)
short_q = pyo.quicksum(model.SHORT_ACTION[i] for i in model.SHORT_ACTION)
return lt_q + st_q + exp_vop_q + short_q >= model.SHORTAGE_Q['SH']
def ComputeSecondStageCost_rule(model):
expansion_cost = pyo.quicksum(model.EXP_ACTION[i] * model.LT_EXP_COST[i]
for i in model.LT_EXP)
baseline_op_cost = pyo.quicksum(model.EXP_BOP_ACTION[i] *
data['LT_EXP'][i]['baseline_op_cost']
for i in model.LT_EXP)
return expansion_cost + baseline_op_cost
def ComputeThirdStageCost_rule(model):
st_actions = pyo.sum_product(model.C_ST, model.ST_ACTION)
short_cost = pyo.quicksum(model.SHORT_ACTION[i] * model.SHORT_COST[i]
for i in model.SHORT_ACTION)
exp_op_cost = pyo.quicksum(model.EXP_VOP_ACTION[i] *
data['LT_EXP'][i]['variable_op_cost']
for i in model.LT_EXP)
return st_actions + short_cost + exp_op_cost
def test_fixed_linear_expr(self):
# Note that this checks both that a fixed variable is fixed, and
# that the resulting model type is correctly classified (in this
# case, fixing a binary makes this an LP)
m = ConcreteModel()
m.y = Var(within=Binary)
m.y.fix(0)
m.x = Var(bounds=(0,None))
m.c1 = Constraint(expr=quicksum([m.y, m.y], linear=True) >= 0)
m.c2 = Constraint(expr=quicksum([m.x, m.y], linear=True) == 1)
m.obj = Objective(expr=m.x)
self._check_baseline(m)
def Objective_mls(mod):
'''
multivariate response least squares objective
'''
M = mod.M
P = mod.P
T = mod.T
return (pyo.quicksum(mod.Q[m][p1, p2] * mod.beta[m, p1] * mod.beta[m, p2]
for m in range(M) for p1 in range(P)
for p2 in range(P)) +
pyo.quicksum(mod.R[m][p] * mod.beta[m, p] for m in range(M)
for p in range(P)) + pyo.quicksum(mod.C))
def Objective_mls_shrinkl1(mod):
M = mod.M
P = mod.P
T = mod.T
return (pyo.quicksum(mod.Q[m][p1, p2] * mod.beta[m, p1] * mod.beta[m, p2]
for m in range(M) for p1 in range(P)
for p2 in range(P)) +
pyo.quicksum(mod.R[m][p] * mod.beta[m, p] for m in range(M)
for p in range(P)) + pyo.quicksum(mod.C) +
pyo.quicksum(mod.param_gamma *
(mod.beta_tilde[m, p, 0] + mod.beta_tilde[m, p, 1])
for p in range(P) for m in range(M)))
def test_sum2(self):
model = ConcreteModel()
model.A = Set(initialize=[1,2,3], doc='set A')
model.x = Var(model.A)
expr = quicksum(model.x[i] for i in model.x)
baseline = "x[1] + x[2] + x[3]"
self.assertEqual( str(expr), baseline )
def conv_rule(model, scenario_name, var_name):
return model.x[var_name] \
+ model.slack_plus[scenario_name, var_name] \
- model.slack_minus[scenario_name, var_name] \
== pyo.quicksum(model.conv[scenario_name, ix] *
points[scenario_name][ix][var_name]
for ix in range(len(points[scenario_name])))
def Portfolio():
m = pe.ConcreteModel()
m.cons = pe.ConstraintList()
N = 5
index = list(range(N))
mean = [0.1, 0.3, 0.5, 0.7, 0.4]
m.x = pe.Var(index, bounds=(0, 1))
m.z = pe.Var(within=pe.PositiveReals)
m.U = ro.UncSet()
m.r = ro.UncParam(index, uncset=m.U, nominal=mean)
r = m.r
expr = 0
for i in index:
expr += (m.r[i] - mean[i])**2
m.U.cons = pe.Constraint(expr=expr <= 0.0005)
m.Elib = ro.uncset.EllipsoidalSet(mean,
[[0.0005, 0, 0, 0, 0],
[0, 0.0005, 0, 0, 0],
[0, 0, 0.0005, 0, 0],
[0, 0, 0, 0.0005, 0],
[0, 0, 0, 0, 0.0005]])
P = [[1, 1, 0, 0, 0],
[-1, 1, 0, 0, 0],
[1, -1, 0, 0, 0],
[-1, -1, 0, 0, 0],
[0, 0, 1, 0, 0],
[0, 0, -1, 0, 0],
[0, 0, 0, 1, 0],
[0, 0, 0, -1, 0],
[0, 0, 0, 0, 1],
[0, 0, 0, 0, -1]]
rhs = [0.001 + mean[0] + mean[1],
0.001 - mean[0] + mean[1],
0.001 + mean[0] - mean[1],
0.001 - mean[0] - mean[1],
0.001 + mean[2],
0.001 - mean[2],
0.001 + mean[3],
0.001 - mean[3],
0.001 + mean[4],
0.001 - mean[4]]
m.Plib = ro.uncset.PolyhedralSet(P, rhs)
m.P = ro.UncSet()
m.P.cons = pe.ConstraintList()
for i, row in enumerate(P):
m.P.cons.add(expr=pe.quicksum(row[j]*m.r[j] for j in m.r) <= rhs[i])
m.Obj = pe.Objective(expr=m.z, sense=pe.maximize)
# x0 = m.x[0]
# expr = x0*3
expr = sum([m.x[i] for i in index]) == 1
m.cons.add(expr)
m.cons.add(sum([r[i]*m.x[i] for i in index]) >= m.z)
return m
def _extract_objective(self, mip):
''' Extract the original part of the provided MIP's objective function
(no dual or prox terms), and create a copy containing the QP
variables in place of the MIP variables.
Args:
mip (Pyomo ConcreteModel): MIP model for a scenario or bundle.
Returns:
obj (Pyomo Objective): objective function extracted
from the MIP
new (Pyomo Expression): expression from the MIP model
objective with the MIP variables replaced by QP variables.
Does not inculde dual or prox terms.
Notes:
Acts on either a single-scenario model or a bundle
'''
mip_to_qp = mip._mpisppy_data.mip_to_qp
obj = find_active_objective(mip)
repn = generate_standard_repn(obj.expr, quadratic=True)
if len(repn.nonlinear_vars) > 0:
raise ValueError("FWPH does not support models with nonlinear objective functions")
linear_vars = [mip_to_qp[id(var)] for var in repn.linear_vars]
new = LinearExpression(
constant=repn.constant, linear_coefs=repn.linear_coefs, linear_vars=linear_vars
)
if repn.quadratic_vars:
quadratic_vars = (
(mip_to_qp[id(x)], mip_to_qp[id(y)]) for x,y in repn.quadratic_vars
)
new += pyo.quicksum(
(coef*x*y for coef,(x,y) in zip(repn.quadratic_coefs, quadratic_vars))
)
return obj, new
def distribution_system_pumping_power_rule(
problem,
time_step
):
# Distributed Secondary Pumping
if distributed_secondary_pumping:
rule = (
problem.distribution_system_total_power[time_step]
== py.quicksum(
(1 / self.parameters.distribution_system["pump efficiency secondary pump [-]"])
* self.parameters.physics["water density [kg/m^3]"]
* self.parameters.physics["gravitational acceleration [m^2/s]"]
* ds_head_differences_time_array[str(time_step)][building_id]
* problem.ets_flows_var[time_step, building_id]
for building_id in problem.building_ids
)
)
return rule
# Central Secondary Pumping
else:
rule = (
problem.distribution_system_total_power[time_step]
== (
(1 / self.parameters.distribution_system["pump efficiency secondary pump [-]"])
* self.parameters.physics["water density [kg/m^3]"]
* self.parameters.physics["gravitational acceleration [m^2/s]"]
* ds_head_differences_time_array[str(time_step)].max()
* problem.total_flow_demand[time_step]
)
)
return rule
def __prevent_excessive_township_supply_constraint(self):
"""
Prevent excessive supply from warehouses to townships, especially during profit maximisation.
"""
for t in self.model.T:
self.model.prevent_excessive_township_supply_constraint.add(
pyo.quicksum(self.model.x_assign[w, t]
for w in self.model.W) <= self.model.t_demand[t])
def __township_demand_fulfillment_constraint(self):
"""
All township demands must be fulfilled.
"""
for t in self.model.T:
self.model.township_demand_fulfillment_constraint.add(
pyo.quicksum(self.model.x_assign[w, t]
for w in self.model.W) >= self.model.t_demand[t])
def __warehouse_supply_constraint(self):
"""
Warehouse supply to townships must not exceed warehouse's capacity (volume).
"""
for w in self.model.W:
self.model.warehouse_supply_constraint.add(
pyo.quicksum(self.model.x_assign[w, t]
for t in self.model.T) <= self.model.w_volume[w])
def scenario_creator_callback(self, scenario_name, **kwargs):
## fist, get the model out
model = self._scenario_tree_instance_factory.construct_scenario_instance(
scenario_name, self._pysp_scenario_tree)
tree_scenario = self._pysp_scenario_tree.get_scenario(scenario_name)
non_leaf_nodes = tree_scenario.node_list[:-1]
for node in non_leaf_nodes:
if node.is_leaf_node():
raise Exception("Unexpected leaf node")
node._mpisppy_cost_expression = _get_cost_expression(
model, node._cost_variable)
node._mpisppy_nonant_list = _get_nonant_list(model, node)
node._mpisppy_nonant_ef_suppl_list = _get_derived_nonant_list(
model, node)
## add the things mpisppy expects to the model
model._mpisppy_probability = tree_scenario.probability
model._mpisppy_node_list = [
mpisppyScenarioNode(
name=node._mpisppy_name,
cond_prob=node.conditional_probability,
stage=node._mpisppy_stage,
cost_expression=node._mpisppy_cost_expression,
scen_name_list=None,
nonant_list=node._mpisppy_nonant_list,
scen_model=None,
nonant_ef_suppl_list=node._mpisppy_nonant_ef_suppl_list,
parent_name=node._mpisppy_parent_name,
) for node in non_leaf_nodes
]
for _ in model.component_data_objects(pyo.Objective,
active=True,
descend_into=True):
break
else: # no break
print(
"Provided model has no objective; using PySP auto-generated objective"
)
# attach PySP objective
leaf_node = tree_scenario.node_list[-1]
leaf_node._mpisppy_cost_expression = _get_cost_expression(
model, leaf_node._cost_variable)
if hasattr(model, "_PySPModel_objective"):
raise RuntimeError(
"provided model has attribute _PySPModel_objective")
model._PySPModel_objective = pyo.Objective(expr=\
pyo.quicksum(node._mpisppy_cost_expression for node in tree_scenario.node_list))
return model
def test_uncparam_has_no_uncset(self):
m = pe.ConcreteModel()
m.w = ro.UncParam(range(3), nominal=(1, 2, 3))
m.x = pe.Var(range(3))
expr = pe.quicksum(m.w[i] * m.x[i] for i in range(3))
m.cons = pe.Constraint(expr=expr <= 5)
m.obj = pe.Objective(expr=m.x[0], sense=pe.maximize)
solver = pe.SolverFactory('romodel.reformulation')
self.assertRaises(AssertionError, lambda: solver.solve(m))
def __warehouse_selection_constraint(self):
"""
Warehouse selection constraint to apply fixed monthly cost if any supply is provided from a warehouse.
"""
for w in self.model.W:
self.model.warehouse_selection_constraint.add(
pyo.quicksum(
self.model.x_assign[w, t]
for t in self.model.T) <= 9_999_999 * self.model.x[w])
def test_quicksum_integer_var_fixed(self):
m = ConcreteModel()
m.x = Var()
m.y = Var(domain=Binary)
m.c = Constraint(expr=quicksum([m.y, m.y], linear=True) == 1)
m.o = Objective(expr=m.x ** 2)
m.y.fix(1)
outs = StringIO()
m.write(outs, format='gams')
self.assertIn("USING nlp", outs.getvalue())
def e_negentropy(model):
"""
Calculation of the negative Shannon entropy for minimization problem
Parameters
----------
model : InvPBaseModel
"""
return quicksum(model.PEST[n] * log(model.PEST[n]) for n in model.NZPSET)
def objective_cost_minimum(
problem
):
rule = (
py.quicksum(
(
problem.costs[time_step]
) for time_step in problem.time_set
)
)
return rule
def ComputeFirstStageCost_rule(model):
lt_actions = pyo.sum_product(model.C_LT, model.LT_ACTION)
lt_exp_actions = pyo.sum_product(model.LT_EXP_ACTION, model.LT_EXP_COST)
lt_exp_permit_action = pyo.quicksum(model.LT_EXP_PERMIT_ACTION[i] *
model.LT_EXP_PERMIT_COST[i]
for i in model.LT_EXP)
return lt_actions + lt_exp_actions + lt_exp_permit_action
def solve_pyomo_kernel(self, solver='cplex'):
"""
Solve the problem using the kernel library of the Pyomo package.
Parameters
----------
solver (str, default:'cplex'): defines the solver used to solve the optimization problem
Returns
-------
obj_fun (real): objective function
sol (list): optimal solution of variables
"""
# Model
m = pk.block()
# Sets
m.i = range(self.nvar)
m.j = range(self.ncon)
# Variables
m.x = pk.variable_list()
for _ in m.i:
m.x.append(pk.variable(domain=pk.Reals, lb=0))
# Objective function
m.obj = pk.objective(pe.quicksum(self.c[i] * m.x[i] for i in m.i),
sense=pk.minimize)
# Constraints
m.con = pk.constraint_list()
for j in m.j:
m.con.append(
pk.constraint(body=pe.quicksum(self.A[j][i] * m.x[i]
for i in m.i),
lb=None,
ub=self.b[j]))
# Solve problem
res = pe.SolverFactory(solver).solve(m,
symbolic_solver_labels=True,
tee=True)
print(res['Solver'][0])
# Output
return round(m.obj(), 2), [round(m.x[i].value, 2) for i in m.i]
def build_scenario_model(fname, scenario_ix):
''' Multiple threads could be parsing the same file at the same
time but they're all read-only, should this should not present any
problems (famous last words)
'''
data = parse(fname, scenario_ix=scenario_ix)
num_nodes = data['N']
adj = data['A'] # Adjacency matrix
edges = data['el'] # Edge list
c = data['c'] # First-stage cost matrix (per edge)
d = data['d'] # Second-stage cost matrix (per edge)
u = data['u'] # Capacity of each arc
b = data['b'] # Demand of each node
p = data['p'] # Probability of scenario
model = pyo.ConcreteModel()
model.x = pyo.Var(edges, domain=pyo.Binary) # First stage vars
model.y = pyo.Var(edges, domain=pyo.NonNegativeReals) # Second stage vars
model.edges = edges
model.PySP_prob = p
''' Objective '''
model.FirstStageCost = pyo.quicksum(c[e] * model.x[e] for e in edges)
model.SecondStageCost = pyo.quicksum(d[e] * model.y[e] for e in edges)
obj_expr = model.FirstStageCost + model.SecondStageCost
model.MinCost = pyo.Objective(expr=obj_expr, sense=pyo.minimize)
''' Variable upper bound constraints on each edge '''
model.vubs = pyo.ConstraintList()
for e in edges:
expr = model.y[e] - u[e] * model.x[e]
model.vubs.add(expr <= 0)
''' Flow balance constraints for each node '''
model.bals = pyo.ConstraintList()
for i in range(num_nodes):
in_nbs = np.where(adj[:, i] > 0)[0]
out_nbs = np.where(adj[i, :] > 0)[0]
lhs = pyo.quicksum(model.y[i,j] for j in out_nbs) - \
pyo.quicksum(model.y[j,i] for j in in_nbs)
model.bals.add(lhs == b[i])
return model
