def to_quadratic_problem(self):
mdl = Model()
x = {
i: mdl.binary_var(name='x_{0}'.format(i))
for i in range(self.g.number_of_nodes())
}
for u, v in self.g.edges:
self.g.edges[u, v].setdefault('weight', 1)
objective = mdl.sum(self.g.edges[i, j]['weight'] * x[i] * (1 - x[j])
for i, j in self.g.edges)
mdl.maximize(objective)
# print(mdl.export_as_lp_string())
qp = QuadraticProgram()
qp.from_docplex(mdl)
#print(qp.export_as_lp_string())
self.qp = qp
return self.qp
def to_quadratic_program(self):
num_assets = len(self._mu)
mdl = AdvModel(name='portfolio')
x = [mdl.binary_var(name='x_{0}'.format(i)) for i in range(num_assets)]
quad = mdl.quad_matrix_sum(self._sigma, x)
linear = np.dot(self._mu, x)
mdl.minimize(quad + linear)
mdl.add_constraint(mdl.sum(x[i] for i in range(num_assets)) == self._budget)
qp = QuadraticProgram()
qp.from_docplex(mdl)
return qp
def to_quadratic_program(self) -> QuadraticProgram:
"""Convert a vehicle routing problem instance into a
:class:`~qiskit_optimization.problems.QuadraticProgram`
Returns:
The :class:`~qiskit_optimization.problems.QuadraticProgram` created
from the vehicle routing problem instance.
"""
mdl = Model(name='Vehicle routing')
n = self._graph.number_of_nodes()
x = {}
for i in range(n):
for j in range(n):
if i != j:
x[(i, j)] = mdl.binary_var(name='x_{0}_{1}'.format(i, j))
mdl.minimize(
mdl.sum(self._graph.edges[i, j]['weight'] * x[(i, j)]
for i in range(n) for j in range(n) if i != j))
# Only 1 edge goes out from each node
for i in range(n):
if i != self.depot:
mdl.add_constraint(
mdl.sum(x[i, j] for j in range(n) if i != j) == 1)
# Only 1 edge comes into each node
for j in range(n):
if j != self.depot:
mdl.add_constraint(
mdl.sum(x[i, j] for i in range(n) if i != j) == 1)
# For the depot node
mdl.add_constraint(
mdl.sum(x[i, self.depot] for i in range(n)
if i != self.depot) == self.num_vehicles)
mdl.add_constraint(
mdl.sum(x[self.depot, j] for j in range(n)
if j != self.depot) == self.num_vehicles)
# To eliminate sub-routes
node_list = [i for i in range(n) if i != self.depot]
clique_set = []
for i in range(2, len(node_list) + 1):
for comb in itertools.combinations(node_list, i):
clique_set.append(list(comb))
for clique in clique_set:
mdl.add_constraint(
mdl.sum(x[(i, j)] for i in clique
for j in clique if i != j) <= len(clique) - 1)
op = QuadraticProgram()
op.from_docplex(mdl)
return op
def __init__(self, model: Model):
"""
Args:
model: Docplex model
"""
self._model: Model = model
self._quadratic_program: QuadraticProgram = QuadraticProgram()
self._var_names: Dict[Var, str] = {}
self._var_bounds: Dict[str, Tuple[float, float]] = {}
def to_quadratic_program(self) -> QuadraticProgram:
"""Convert a vertex cover instance into a
:class:`~qiskit_optimization.problems.QuadraticProgram`
Returns:
The :class:`~qiskit_optimization.problems.QuadraticProgram` created
from the vertex cover instance.
"""
mdl = Model(name='Vertex cover')
n = self._graph.number_of_nodes()
x = {i: mdl.binary_var(name='x_{0}'.format(i)) for i in range(n)}
objective = mdl.sum(x[i] for i in x)
for w, v in self._graph.edges:
mdl.add_constraint(x[w] + x[v] >= 1)
mdl.minimize(objective)
op = QuadraticProgram()
op.from_docplex(mdl)
return op
def to_quadratic_program(self) -> QuadraticProgram:
"""Convert a number partitioning problem instance into a
:class:`~qiskit_optimization.problems.QuadraticProgram`
Returns:
The :class:`~qiskit_optimization.problems.QuadraticProgram` created
from the number partitioning problem instance.
"""
mdl = Model(name='Number partitioning')
x = {
i: mdl.binary_var(name='x_{0}'.format(i))
for i in range(len(self._number_set))
}
mdl.add_constraint(
mdl.sum(num * (-2 * x[i] + 1)
for i, num in enumerate(self._number_set)) == 0)
op = QuadraticProgram()
op.from_docplex(mdl)
return op
def to_quadratic_program(self) -> QuadraticProgram:
"""Convert a knapsack problem instance into a
:class:`~qiskit_optimization.problems.QuadraticProgram`
Returns:
The :class:`~qiskit_optimization.problems.QuadraticProgram` created
from the knapsack problem instance.
"""
mdl = Model(name="Knapsack")
x = {
i: mdl.binary_var(name="x_{0}".format(i))
for i in range(len(self._values))
}
mdl.maximize(mdl.sum(self._values[i] * x[i] for i in x))
mdl.add_constraint(
mdl.sum(self._weights[i] * x[i] for i in x) <= self._max_weight)
op = QuadraticProgram()
op.from_docplex(mdl)
return op
def to_quadratic_program(self) -> QuadraticProgram:
"""Convert a stable set instance into a
:class:`~qiskit_optimization.problems.QuadraticProgram`
Returns:
The :class:`~qiskit_optimization.problems.QuadraticProgram` created
from the stable set instance.
"""
mdl = Model(name='Stable set')
n = self._graph.number_of_nodes()
x = {i: mdl.binary_var(name='x_{0}'.format(i)) for i in range(n)}
for w, v in self._graph.edges:
self._graph.edges[w, v].setdefault('weight', 1)
objective = mdl.sum(x[i] for i in x)
for w, v in self._graph.edges:
mdl.add_constraint(x[w] + x[v] <= 1)
mdl.maximize(objective)
op = QuadraticProgram()
op.from_docplex(mdl)
return op
def to_quadratic_program(self) -> QuadraticProgram:
"""Convert a Max-cut problem instance into a
:class:`~qiskit_optimization.problems.QuadraticProgram`
Returns:
The :class:`~qiskit_optimization.problems.QuadraticProgram` created
from the Max-cut problem instance.
"""
mdl = Model(name='Max-cut')
x = {i: mdl.binary_var(name='x_{0}'.format(i))
for i in range(self._graph.number_of_nodes())}
for w, v in self._graph.edges:
self._graph.edges[w, v].setdefault('weight', 1)
objective = mdl.sum(self._graph.edges[i, j]['weight'] * x[i]
* (1 - x[j]) + self._graph.edges[i, j]['weight'] * x[j]
* (1 - x[i]) for i, j in self._graph.edges)
mdl.maximize(objective)
op = QuadraticProgram()
op.from_docplex(mdl)
return op
def to_quadratic_program(self) -> QuadraticProgram:
"""Convert a graph partition instance into a
:class:`~qiskit_optimization.problems.QuadraticProgram`
Returns:
The :class:`~qiskit_optimization.problems.QuadraticProgram` created
from the graph partition instance.
"""
mdl = Model(name='Graph partition')
n = self._graph.number_of_nodes()
x = {i: mdl.binary_var(name='x_{0}'.format(i)) for i in range(n)}
for w, v in self._graph.edges:
self._graph.edges[w, v].setdefault('weight', 1)
objective = mdl.sum(self._graph.edges[i, j]['weight'] *
(x[i] + x[j] - 2*x[i]*x[j]) for i, j in self._graph.edges)
mdl.minimize(objective)
mdl.add_constraint(mdl.sum([x[i] for i in x]) == n//2)
op = QuadraticProgram()
op.from_docplex(mdl)
return op
def to_quadratic_program(self) -> QuadraticProgram:
"""Convert a set packing instance into a
:class:`~qiskit_optimization.problems.QuadraticProgram`
Returns:
The :class:`~qiskit_optimization.problems.QuadraticProgram` created
from the set packing instance.
"""
mdl = Model(name='Set packing')
x = {
i: mdl.binary_var(name='x_{0}'.format(i))
for i in range(len(self._subsets))
}
mdl.maximize(mdl.sum(x[i] for i in x))
for element in self._set:
mdl.add_constraint(
mdl.sum(x[i] for i, sub in enumerate(self._subsets)
if element in sub) <= 1)
op = QuadraticProgram()
op.from_docplex(mdl)
return op
def to_quadratic_program(self) -> QuadraticProgram:
"""Convert a clique problem instance into a
:class:`~qiskit_optimization.problems.QuadraticProgram`.
When "size" is None, this makes an optimization model for a maximal clique
instead of the specified size of a clique.
Returns:
The :class:`~qiskit_optimization.problems.QuadraticProgram` created
from the clique problem instance.
"""
complement_g = nx.complement(self._graph)
mdl = Model(name='Clique')
n = self._graph.number_of_nodes()
x = {i: mdl.binary_var(name='x_{0}'.format(i)) for i in range(n)}
for w, v in complement_g.edges:
mdl.add_constraint(x[w] + x[v] <= 1)
if self.size is None:
mdl.maximize(mdl.sum(x[i] for i in x))
else:
mdl.add_constraint(mdl.sum(x[i] for i in x) == self.size)
op = QuadraticProgram()
op.from_docplex(mdl)
return op
def to_ising(quad_prog: QuadraticProgram) -> Tuple[OperatorBase, float]:
"""Return the Ising Hamiltonian of this problem.
Variables are mapped to qubits in the same order, i.e.,
i-th variable is mapped to i-th qubit.
See https://github.com/Qiskit/qiskit-terra/issues/1148 for details.
Returns:
qubit_op: The qubit operator for the problem
offset: The constant value in the Ising Hamiltonian.
Raises:
QiskitOptimizationError: If an integer variable or a continuous variable exists
in the problem.
QiskitOptimizationError: If constraints exist in the problem.
"""
# if problem has variables that are not binary, raise an error
if quad_prog.get_num_vars() > quad_prog.get_num_binary_vars():
raise QiskitOptimizationError(
"The type of all variables must be binary. "
"You can use `QuadraticProgramToQubo` converter "
"to convert integer variables to binary variables. "
"If the problem contains continuous variables, `to_ising` cannot handle it. "
"You might be able to solve it with `ADMMOptimizer`.")
# if constraints exist, raise an error
if quad_prog.linear_constraints or quad_prog.quadratic_constraints:
raise QiskitOptimizationError(
"There must be no constraint in the problem. "
"You can use `QuadraticProgramToQubo` converter "
"to convert constraints to penalty terms of the objective function."
)
# initialize Hamiltonian.
num_nodes = quad_prog.get_num_vars()
pauli_list = []
offset = 0.0
zero = np.zeros(num_nodes, dtype=bool)
# set a sign corresponding to a maximized or minimized problem.
# sign == 1 is for minimized problem. sign == -1 is for maximized problem.
sense = quad_prog.objective.sense.value
# convert a constant part of the object function into Hamiltonian.
offset += quad_prog.objective.constant * sense
# convert linear parts of the object function into Hamiltonian.
for idx, coef in quad_prog.objective.linear.to_dict().items():
z_p = zero.copy()
weight = coef * sense / 2
z_p[idx] = True
pauli_list.append(PauliOp(Pauli((z_p, zero)), -weight))
offset += weight
# create Pauli terms
for (i, j), coeff in quad_prog.objective.quadratic.to_dict().items():
weight = coeff * sense / 4
if i == j:
offset += weight
else:
z_p = zero.copy()
z_p[i] = True
z_p[j] = True
pauli_list.append(PauliOp(Pauli((z_p, zero)), weight))
z_p = zero.copy()
z_p[i] = True
pauli_list.append(PauliOp(Pauli((z_p, zero)), -weight))
z_p = zero.copy()
z_p[j] = True
pauli_list.append(PauliOp(Pauli((z_p, zero)), -weight))
offset += weight
# Remove paulis whose coefficients are zeros.
qubit_op = sum(pauli_list)
# qubit_op could be the integer 0, in this case return an identity operator of
# appropriate size
if isinstance(qubit_op, OperatorBase):
qubit_op = qubit_op.reduce()
else:
qubit_op = I ^ num_nodes
return qubit_op, offset
class _FromDocplexMp:
_sense_dict = {
ComparisonType.EQ: "==",
ComparisonType.LE: "<=",
ComparisonType.GE: ">="
}
def __init__(self, model: Model):
"""
Args:
model: Docplex model
"""
self._model: Model = model
self._quadratic_program: QuadraticProgram = QuadraticProgram()
self._var_names: Dict[Var, str] = {}
self._var_bounds: Dict[str, Tuple[float, float]] = {}
def _variables(self):
# keep track of names separately, since docplex allows to have None names.
for x in self._model.iter_variables():
if isinstance(x.vartype, ContinuousVarType):
x_new = self._quadratic_program.continuous_var(
x.lb, x.ub, x.name)
elif isinstance(x.vartype, BinaryVarType):
x_new = self._quadratic_program.binary_var(x.name)
elif isinstance(x.vartype, IntegerVarType):
x_new = self._quadratic_program.integer_var(x.lb, x.ub, x.name)
else:
raise QiskitOptimizationError(
f"Unsupported variable type: {x.name} {x.vartype}")
self._var_names[x] = x_new.name
self._var_bounds[x.name] = (x_new.lowerbound, x_new.upperbound)
def _linear_expr(self, expr: AbstractLinearExpr) -> Dict[str, float]:
# AbstractLinearExpr is a parent of LinearExpr, ConstantExpr, and ZeroExpr
linear = {}
for x, coeff in expr.iter_terms():
linear[self._var_names[x]] = coeff
return linear
def _quadratic_expr(
self, expr: QuadExpr
) -> Tuple[Dict[str, float], Dict[Tuple[str, str], float]]:
linear = self._linear_expr(expr.get_linear_part())
quad = {}
for x, y, coeff in expr.iter_quad_triplets():
i = self._var_names[x]
j = self._var_names[y]
quad[i, j] = coeff
return linear, quad
def quadratic_program(
self, indicator_big_m: Optional[float]) -> QuadraticProgram:
"""Generate a quadratic program corresponding to the input Docplex model.
Args:
indicator_big_m: The big-M value used for the big-M formulation to convert
indicator constraints into linear constraints.
If ``None``, it is automatically derived from the model.
Returns:
a quadratic program corresponding to the input Docplex model.
"""
self._quadratic_program = QuadraticProgram(self._model.name)
# prepare variables
self._variables()
# objective sense
minimize = self._model.objective_sense.is_minimize()
# make sure objective expression is linear or quadratic and not a variable
if isinstance(self._model.objective_expr, Var):
self._model.objective_expr = self._model.objective_expr + 0 # Var + 0 -> LinearExpr
constant = self._model.objective_expr.constant
if isinstance(self._model.objective_expr, QuadExpr):
linear, quadratic = self._quadratic_expr(
self._model.objective_expr)
else:
linear = self._linear_expr(
self._model.objective_expr.get_linear_part())
quadratic = {}
# set objective
if minimize:
self._quadratic_program.minimize(constant, linear, quadratic)
else:
self._quadratic_program.maximize(constant, linear, quadratic)
# set linear constraints
for constraint in self._model.iter_linear_constraints():
linear, sense, rhs = self._linear_constraint(constraint)
if not linear: # lhs == 0
warn(f"Trivial constraint: {constraint}", stacklevel=3)
self._quadratic_program.linear_constraint(linear, sense, rhs,
constraint.name)
# set quadratic constraints
for constraint in self._model.iter_quadratic_constraints():
linear, quadratic, sense, rhs = self._quadratic_constraint(
constraint)
if not linear and not quadratic: # lhs == 0
warn(f"Trivial constraint: {constraint}", stacklevel=3)
self._quadratic_program.quadratic_constraint(
linear, quadratic, sense, rhs, constraint.name)
# set indicator constraints
for index, constraint in enumerate(
self._model.iter_indicator_constraints()):
linear, _, _ = self._linear_constraint(
constraint.linear_constraint)
if not linear: # lhs == 0
warn(f"Trivial constraint: {constraint}", stacklevel=3)
prefix = constraint.name or f"ind{index}"
linear_constraints = self._indicator_constraints(
constraint, prefix, indicator_big_m)
for linear, sense, rhs, name in linear_constraints:
self._quadratic_program.linear_constraint(
linear, sense, rhs, name)
return self._quadratic_program
@staticmethod
def _subtract(dict1: Dict[Any, float],
dict2: Dict[Any, float]) -> Dict[Any, float]:
"""Calculate dict1 - dict2"""
ret = dict1.copy()
for key, val2 in dict2.items():
if key in dict1:
val1 = ret[key]
if isclose(val1, val2):
del ret[key]
else:
ret[key] -= val2
else:
ret[key] = -val2
return ret
def _linear_constraint(
self, constraint: LinearConstraint
) -> Tuple[Dict[str, float], str, float]:
left_expr = constraint.get_left_expr()
right_expr = constraint.get_right_expr()
# for linear constraints we may get an instance of Var instead of expression,
# e.g. x + y = z
if not isinstance(left_expr, (Expr, Var)):
raise QiskitOptimizationError(
f"Unsupported expression: {left_expr} {type(left_expr)}")
if not isinstance(right_expr, (Expr, Var)):
raise QiskitOptimizationError(
f"Unsupported expression: {right_expr} {type(right_expr)}")
if constraint.sense not in self._sense_dict:
raise QiskitOptimizationError(
f"Unsupported constraint sense: {constraint}")
if isinstance(left_expr, Var):
left_expr = left_expr + 0 # Var + 0 -> LinearExpr
left_linear = self._linear_expr(left_expr)
if isinstance(right_expr, Var):
right_expr = right_expr + 0
right_linear = self._linear_expr(right_expr)
linear = self._subtract(left_linear, right_linear)
rhs = right_expr.constant - left_expr.constant
return linear, self._sense_dict[constraint.sense], rhs
def _quadratic_constraint(
self, constraint: QuadraticConstraint
) -> Tuple[Dict[str, float], Dict[Tuple[str, str], float], str, float]:
left_expr = constraint.get_left_expr()
right_expr = constraint.get_right_expr()
if not isinstance(left_expr, (Expr, Var)):
raise QiskitOptimizationError(
f"Unsupported expression: {left_expr} {type(left_expr)}")
if not isinstance(right_expr, (Expr, Var)):
raise QiskitOptimizationError(
f"Unsupported expression: {right_expr} {type(right_expr)}")
if constraint.sense not in self._sense_dict:
raise QiskitOptimizationError(
f"Unsupported constraint sense: {constraint}")
if isinstance(left_expr, Var):
left_expr = left_expr + 0 # Var + 0 -> LinearExpr
if left_expr.is_quad_expr():
left_lin, left_quad = self._quadratic_expr(left_expr)
else:
left_lin = self._linear_expr(left_expr)
left_quad = {}
if isinstance(right_expr, Var):
right_expr = right_expr + 0
if right_expr.is_quad_expr():
right_lin, right_quad = self._quadratic_expr(right_expr)
else:
right_lin = self._linear_expr(right_expr)
right_quad = {}
linear = self._subtract(left_lin, right_lin)
quadratic = self._subtract(left_quad, right_quad)
rhs = right_expr.constant - left_expr.constant
return linear, quadratic, self._sense_dict[constraint.sense], rhs
def _linear_bounds(self, linear: Dict[str, float]):
linear_lb = 0.0
linear_ub = 0.0
for var_name, val in linear.items():
x_lb, x_ub = self._var_bounds[var_name]
x_lb *= val
x_ub *= val
linear_lb += min(x_lb, x_ub)
linear_ub += max(x_lb, x_ub)
return linear_lb, linear_ub
def _indicator_constraints(
self,
constraint: IndicatorConstraint,
name: str,
indicator_big_m: Optional[float] = None,
):
binary_var = constraint.binary_var
active_value = constraint.active_value
linear_constraint = constraint.linear_constraint
linear, sense, rhs = self._linear_constraint(linear_constraint)
linear_lb, linear_ub = self._linear_bounds(linear)
ret = []
if sense in ["<=", "=="]:
big_m = max(0.0, linear_ub -
rhs) if indicator_big_m is None else indicator_big_m
if active_value:
# rhs += big_m * (1 - binary_var)
linear2 = self._subtract(linear, {binary_var.name: -big_m})
rhs2 = rhs + big_m
else:
# rhs += big_m * binary_var
linear2 = self._subtract(linear, {binary_var.name: big_m})
rhs2 = rhs
name2 = name + "_LE" if sense == "==" else name
ret.append((linear2, "<=", rhs2, name2))
if sense in [">=", "=="]:
big_m = max(
0.0, rhs -
linear_lb) if indicator_big_m is None else indicator_big_m
if active_value:
# rhs += -big_m * (1 - binary_var)
linear2 = self._subtract(linear, {binary_var.name: big_m})
rhs2 = rhs - big_m
else:
# rhs += -big_m * binary_var
linear2 = self._subtract(linear, {binary_var.name: -big_m})
rhs2 = rhs
name2 = name + "_GE" if sense == "==" else name
ret.append((linear2, ">=", rhs2, name2))
if sense not in ["<=", ">=", "=="]:
raise QiskitOptimizationError(
f"Internal error: invalid sense of indicator constraint: {sense}"
)
return ret
def from_gurobipy(model: Model) -> QuadraticProgram:
"""Translate a gurobipy model into a quadratic program.
Note that this supports only basic functions of gurobipy as follows:
- quadratic objective function
- linear / quadratic constraints
- binary / integer / continuous variables
Args:
model: The gurobipy model to be loaded.
Returns:
The quadratic program corresponding to the model.
Raises:
QiskitOptimizationError: if the model contains unsupported elements.
MissingOptionalLibraryError: if gurobipy is not installed.
"""
_check_gurobipy_is_installed("from_gurobipy")
if not isinstance(model, Model):
raise QiskitOptimizationError(f"The model is not compatible: {model}")
quadratic_program = QuadraticProgram()
# Update the model to make sure everything works as expected
model.update()
# get name
quadratic_program.name = model.ModelName
# get variables
# keep track of names separately, since gurobipy allows to have None names.
var_names = {}
for x in model.getVars():
if x.vtype == gp.GRB.CONTINUOUS:
x_new = quadratic_program.continuous_var(x.lb, x.ub, x.VarName)
elif x.vtype == gp.GRB.BINARY:
x_new = quadratic_program.binary_var(x.VarName)
elif x.vtype == gp.GRB.INTEGER:
x_new = quadratic_program.integer_var(x.lb, x.ub, x.VarName)
else:
raise QiskitOptimizationError(
f"Unsupported variable type: {x.VarName} {x.vtype}")
var_names[x] = x_new.name
# objective sense
minimize = model.ModelSense == gp.GRB.MINIMIZE
# Retrieve the objective
objective = model.getObjective()
has_quadratic_objective = False
# Retrieve the linear part in case it is a quadratic objective
if isinstance(objective, gp.QuadExpr):
linear_part = objective.getLinExpr()
has_quadratic_objective = True
else:
linear_part = objective
# Get the constant
constant = linear_part.getConstant()
# get linear part of objective
linear = {}
for i in range(linear_part.size()):
linear[var_names[linear_part.getVar(i)]] = linear_part.getCoeff(i)
# get quadratic part of objective
quadratic = {}
if has_quadratic_objective:
for i in range(objective.size()):
x = var_names[objective.getVar1(i)]
y = var_names[objective.getVar2(i)]
v = objective.getCoeff(i)
quadratic[x, y] = v
# set objective
if minimize:
quadratic_program.minimize(constant, linear, quadratic)
else:
quadratic_program.maximize(constant, linear, quadratic)
# check whether there are any general constraints
if model.NumSOS > 0 or model.NumGenConstrs > 0:
raise QiskitOptimizationError(
"Unsupported constraint: SOS or General Constraint")
# get linear constraints
for constraint in model.getConstrs():
name = constraint.ConstrName
sense = constraint.Sense
left_expr = model.getRow(constraint)
rhs = constraint.RHS
lhs = {}
for i in range(left_expr.size()):
lhs[var_names[left_expr.getVar(i)]] = left_expr.getCoeff(i)
if sense == gp.GRB.EQUAL:
quadratic_program.linear_constraint(lhs, "==", rhs, name)
elif sense == gp.GRB.GREATER_EQUAL:
quadratic_program.linear_constraint(lhs, ">=", rhs, name)
elif sense == gp.GRB.LESS_EQUAL:
quadratic_program.linear_constraint(lhs, "<=", rhs, name)
else:
raise QiskitOptimizationError(
f"Unsupported constraint sense: {constraint}")
# get quadratic constraints
for constraint in model.getQConstrs():
name = constraint.QCName
sense = constraint.QCSense
left_expr = model.getQCRow(constraint)
rhs = constraint.QCRHS
linear = {}
quadratic = {}
linear_part = left_expr.getLinExpr()
for i in range(linear_part.size()):
linear[var_names[linear_part.getVar(i)]] = linear_part.getCoeff(i)
for i in range(left_expr.size()):
x = var_names[left_expr.getVar1(i)]
y = var_names[left_expr.getVar2(i)]
v = left_expr.getCoeff(i)
quadratic[x, y] = v
if sense == gp.GRB.EQUAL:
quadratic_program.quadratic_constraint(linear, quadratic, "==",
rhs, name)
elif sense == gp.GRB.GREATER_EQUAL:
quadratic_program.quadratic_constraint(linear, quadratic, ">=",
rhs, name)
elif sense == gp.GRB.LESS_EQUAL:
quadratic_program.quadratic_constraint(linear, quadratic, "<=",
rhs, name)
else:
raise QiskitOptimizationError(
f"Unsupported constraint sense: {constraint}")
return quadratic_program
def quadratic_program(
self, indicator_big_m: Optional[float]) -> QuadraticProgram:
"""Generate a quadratic program corresponding to the input Docplex model.
Args:
indicator_big_m: The big-M value used for the big-M formulation to convert
indicator constraints into linear constraints.
If ``None``, it is automatically derived from the model.
Returns:
a quadratic program corresponding to the input Docplex model.
"""
self._quadratic_program = QuadraticProgram(self._model.name)
# prepare variables
self._variables()
# objective sense
minimize = self._model.objective_sense.is_minimize()
# make sure objective expression is linear or quadratic and not a variable
if isinstance(self._model.objective_expr, Var):
self._model.objective_expr = self._model.objective_expr + 0 # Var + 0 -> LinearExpr
constant = self._model.objective_expr.constant
if isinstance(self._model.objective_expr, QuadExpr):
linear, quadratic = self._quadratic_expr(
self._model.objective_expr)
else:
linear = self._linear_expr(
self._model.objective_expr.get_linear_part())
quadratic = {}
# set objective
if minimize:
self._quadratic_program.minimize(constant, linear, quadratic)
else:
self._quadratic_program.maximize(constant, linear, quadratic)
# set linear constraints
for constraint in self._model.iter_linear_constraints():
linear, sense, rhs = self._linear_constraint(constraint)
if not linear: # lhs == 0
warn(f"Trivial constraint: {constraint}", stacklevel=3)
self._quadratic_program.linear_constraint(linear, sense, rhs,
constraint.name)
# set quadratic constraints
for constraint in self._model.iter_quadratic_constraints():
linear, quadratic, sense, rhs = self._quadratic_constraint(
constraint)
if not linear and not quadratic: # lhs == 0
warn(f"Trivial constraint: {constraint}", stacklevel=3)
self._quadratic_program.quadratic_constraint(
linear, quadratic, sense, rhs, constraint.name)
# set indicator constraints
for index, constraint in enumerate(
self._model.iter_indicator_constraints()):
linear, _, _ = self._linear_constraint(
constraint.linear_constraint)
if not linear: # lhs == 0
warn(f"Trivial constraint: {constraint}", stacklevel=3)
prefix = constraint.name or f"ind{index}"
linear_constraints = self._indicator_constraints(
constraint, prefix, indicator_big_m)
for linear, sense, rhs, name in linear_constraints:
self._quadratic_program.linear_constraint(
linear, sense, rhs, name)
return self._quadratic_program
def from_docplex_mp(
model: Model,
indicator_big_m: Optional[float] = None) -> QuadraticProgram:
"""Translate a docplex.mp model into a quadratic program.
Note that this supports only basic functions of docplex as follows:
- quadratic objective function
- linear / quadratic / indicator constraints
- binary / integer / continuous variables
Args:
model: The docplex.mp model to be loaded.
indicator_big_m: The big-M value used for the big-M formulation to convert
indicator constraints into linear constraints.
If ``None``, it is automatically derived from the model.
Returns:
The quadratic program corresponding to the model.
Raises:
QiskitOptimizationError: if the model contains unsupported elements.
"""
if not isinstance(model, Model):
raise QiskitOptimizationError(f"The model is not compatible: {model}")
if model.number_of_user_cut_constraints > 0:
raise QiskitOptimizationError("User cut constraints are not supported")
if model.number_of_lazy_constraints > 0:
raise QiskitOptimizationError("Lazy constraints are not supported")
if model.number_of_sos > 0:
raise QiskitOptimizationError("SOS sets are not supported")
# get name
quadratic_program = QuadraticProgram(model.name)
# get variables
# keep track of names separately, since docplex allows to have None names.
var_names = {}
var_bounds = {}
for x in model.iter_variables():
if isinstance(x.vartype, ContinuousVarType):
x_new = quadratic_program.continuous_var(x.lb, x.ub, x.name)
elif isinstance(x.vartype, BinaryVarType):
x_new = quadratic_program.binary_var(x.name)
elif isinstance(x.vartype, IntegerVarType):
x_new = quadratic_program.integer_var(x.lb, x.ub, x.name)
else:
raise QiskitOptimizationError(
f"Unsupported variable type: {x.name} {x.vartype}")
var_names[x] = x_new.name
var_bounds[x.name] = (x_new.lowerbound, x_new.upperbound)
# objective sense
minimize = model.objective_sense.is_minimize()
# make sure objective expression is linear or quadratic and not a variable
if isinstance(model.objective_expr, Var):
model.objective_expr = model.objective_expr + 0
# get objective offset
constant = model.objective_expr.constant
# get linear part of objective
linear = {}
linear_part = model.objective_expr.get_linear_part()
for x in linear_part.iter_variables():
linear[var_names[x]] = linear_part.get_coef(x)
# get quadratic part of objective
quadratic = {}
if isinstance(model.objective_expr, QuadExpr):
for quad_triplet in model.objective_expr.iter_quad_triplets():
i = var_names[quad_triplet[0]]
j = var_names[quad_triplet[1]]
v = quad_triplet[2]
quadratic[i, j] = v
# set objective
if minimize:
quadratic_program.minimize(constant, linear, quadratic)
else:
quadratic_program.maximize(constant, linear, quadratic)
# check constraint type
for constraint in model.iter_constraints():
# If any constraint is not linear/quadratic/indicator constraints, it raises an error.
if isinstance(constraint, LinearConstraint):
if isinstance(constraint, NotEqualConstraint):
# Notice that NotEqualConstraint is a subclass of Docplex's LinearConstraint,
# but it cannot be handled by optimization.
raise QiskitOptimizationError(
f"Unsupported constraint: {constraint}")
elif not isinstance(constraint,
(QuadraticConstraint, IndicatorConstraint)):
raise QiskitOptimizationError(
f"Unsupported constraint: {constraint}")
# get linear constraints
for constraint in model.iter_linear_constraints():
lhs, sense, rhs = _FromDocplexMp._linear_constraint(
var_names, constraint)
quadratic_program.linear_constraint(lhs, sense, rhs, constraint.name)
# get quadratic constraints
for constraint in model.iter_quadratic_constraints():
linear, quadratic, sense, rhs = _FromDocplexMp._quadratic_constraint(
var_names, constraint)
quadratic_program.quadratic_constraint(linear, quadratic, sense, rhs,
constraint.name)
# get indicator constraints
for constraint in model.iter_indicator_constraints():
linear_constraints = _FromDocplexMp._indicator_constraints(
var_names, var_bounds, constraint, indicator_big_m)
for linear, sense, rhs, name in linear_constraints:
quadratic_program.linear_constraint(linear, sense, rhs, name)
return quadratic_program
def from_ising(
qubit_op: OperatorBase,
offset: float = 0.0,
linear: bool = False,
) -> QuadraticProgram:
r"""Create a quadratic program from a qubit operator and a shift value.
Variables are mapped to qubits in the same order, i.e.,
i-th variable is mapped to i-th qubit.
See https://github.com/Qiskit/qiskit-terra/issues/1148 for details.
Args:
qubit_op: The qubit operator of the problem.
offset: The constant term in the Ising Hamiltonian.
linear: If linear is True, :math:`x^2` is treated as a linear term
since :math:`x^2 = x` for :math:`x \in \{0,1\}`.
Otherwise, :math:`x^2` is treat as a quadratic term.
The default value is False.
Returns:
The quadratic program corresponding to the qubit operator.
Raises:
QiskitOptimizationError: if there are Pauli Xs or Ys in any Pauli term
QiskitOptimizationError: if there are more than 2 Pauli Zs in any Pauli term
QiskitOptimizationError: if any Pauli term has an imaginary coefficient
NotImplementedError: If the input operator is a ListOp
"""
if isinstance(qubit_op, PauliSumOp):
qubit_op = qubit_op.to_pauli_op()
# No support for ListOp yet, this can be added in future
# pylint: disable=unidiomatic-typecheck
if type(qubit_op) == ListOp:
raise NotImplementedError(
"Conversion of a ListOp is not supported, convert each "
"operator in the ListOp separately.")
quad_prog = QuadraticProgram()
quad_prog.binary_var_list(qubit_op.num_qubits)
if not isinstance(qubit_op, SummedOp):
pauli_list = [qubit_op.to_pauli_op()]
else:
pauli_list = qubit_op.to_pauli_op()
# prepare a matrix of coefficients of Pauli terms
# `pauli_coeffs_diag` is the diagonal part
# `pauli_coeffs_triu` is the upper triangular part
pauli_coeffs_diag = [0.0] * qubit_op.num_qubits
pauli_coeffs_triu = {}
for pauli_op in pauli_list:
pauli_op = pauli_op.to_pauli_op()
pauli = pauli_op.primitive
coeff = pauli_op.coeff
if not math.isclose(coeff.imag, 0.0, abs_tol=1e-10):
raise QiskitOptimizationError(
f"Imaginary coefficient exists: {pauli_op}")
if np.any(pauli.x):
raise QiskitOptimizationError(
f"Pauli X or Y exists in the Pauli term: {pauli}")
# indices of Pauli Zs in the Pauli term
z_index = np.where(pauli.z)[0]
num_z = len(z_index)
if num_z == 1:
pauli_coeffs_diag[z_index[0]] = coeff.real
elif num_z == 2:
pauli_coeffs_triu[z_index[0], z_index[1]] = coeff.real
else:
raise QiskitOptimizationError(
f"There are more than 2 Pauli Zs in the Pauli term: {pauli}")
linear_terms = {}
quadratic_terms = {}
# For quadratic pauli terms of operator
# x_i * x_j = (1 - Z_i - Z_j + Z_i * Z_j)/4
for (i, j), weight in pauli_coeffs_triu.items():
# Add a quadratic term to the object function of `QuadraticProgram`
# The coefficient of the quadratic term in `QuadraticProgram` is
# 4 * weight of the pauli
quadratic_terms[i, j] = 4 * weight
pauli_coeffs_diag[i] += weight
pauli_coeffs_diag[j] += weight
offset -= weight
# After processing quadratic pauli terms, only linear paulis are left
# x_i = (1 - Z_i)/2
for i, weight in enumerate(pauli_coeffs_diag):
# Add a linear term to the object function of `QuadraticProgram`
# The coefficient of the linear term in `QuadraticProgram` is
# 2 * weight of the pauli
if linear:
linear_terms[i] = -2 * weight
else:
quadratic_terms[i, i] = -2 * weight
offset += weight
quad_prog.minimize(constant=offset,
linear=linear_terms,
quadratic=quadratic_terms)
return quad_prog