def test_empty_problem(self):
""" Test empty problem """
op = QuadraticProgram()
conv = InequalityToEquality()
op = conv.convert(op)
conv = IntegerToBinary()
op = conv.convert(op)
conv = LinearEqualityToPenalty()
op = conv.convert(op)
_, shift = op.to_ising()
self.assertEqual(shift, 0.0)
def test_inequality_mode_auto(self):
""" Test auto mode of InequalityToEqualityConverter() """
op = QuadraticProgram()
for i in range(3):
op.binary_var(name='x{}'.format(i))
# Linear constraints
linear_constraint = {'x0': 1, 'x1': 1}
op.linear_constraint(linear_constraint, Constraint.Sense.EQ, 1, 'x0x1')
linear_constraint = {'x1': 1, 'x2': -1}
op.linear_constraint(linear_constraint, Constraint.Sense.LE, 2, 'x1x2')
linear_constraint = {'x0': 1.1, 'x2': 2.2}
op.linear_constraint(linear_constraint, Constraint.Sense.GE, 3.3, 'x0x2')
conv = InequalityToEquality(mode='auto')
op2 = conv.convert(op)
lst = [op2.variables[3].vartype, op2.variables[4].vartype]
self.assertListEqual(lst, [Variable.Type.INTEGER, Variable.Type.CONTINUOUS])
def test_inequality_mode_continuous(self):
""" Test continuous mode of InequalityToEqualityConverter() """
op = QuadraticProgram()
for i in range(3):
op.binary_var(name='x{}'.format(i))
# Linear constraints
linear_constraint = {}
linear_constraint['x0'] = 1
linear_constraint['x1'] = 1
op.linear_constraint(linear_constraint, Constraint.Sense.EQ, 1, 'x0x1')
linear_constraint = {}
linear_constraint['x1'] = 1
linear_constraint['x2'] = -1
op.linear_constraint(linear_constraint, Constraint.Sense.LE, 2, 'x1x2')
linear_constraint = {}
linear_constraint['x0'] = 1
linear_constraint['x2'] = 3
op.linear_constraint(linear_constraint, Constraint.Sense.GE, 2, 'x0x2')
conv = InequalityToEquality(mode='continuous')
op2 = conv.convert(op)
lst = [op2.variables[3].vartype, op2.variables[4].vartype]
self.assertListEqual(lst, [Variable.Type.CONTINUOUS, Variable.Type.CONTINUOUS])
def test_0var_range_inequality(self):
""" Test InequalityToEquality converter when the var_rang of the slack variable is 0"""
op = QuadraticProgram()
op.binary_var('x')
op.binary_var('y')
op.linear_constraint(linear={
'x': 1,
'y': 1
},
sense='LE',
rhs=0,
name='xy_leq1')
op.linear_constraint(linear={
'x': 1,
'y': 1
},
sense='GE',
rhs=2,
name='xy_geq1')
op.quadratic_constraint(quadratic={('x', 'x'): 1},
sense='LE',
rhs=0,
name='xy_leq2')
op.quadratic_constraint(quadratic={('x', 'y'): 1},
sense='GE',
rhs=1,
name='xy_geq2')
ineq2eq = InequalityToEquality()
new_op = ineq2eq.convert(op)
self.assertEqual(new_op.get_num_vars(), 2)
self.assertTrue(
all(l_const.sense == Constraint.Sense.EQ
for l_const in new_op.linear_constraints))
self.assertTrue(
all(q_const.sense == Constraint.Sense.EQ
for q_const in new_op.quadratic_constraints))
def test_inequality_binary(self):
""" Test InequalityToEqualityConverter with binary variables """
op = QuadraticProgram()
for i in range(3):
op.binary_var(name='x{}'.format(i))
# Linear constraints
linear_constraint = {'x0': 1, 'x1': 1}
op.linear_constraint(linear_constraint, Constraint.Sense.EQ, 1, 'x0x1')
linear_constraint = {'x1': 1, 'x2': -1}
op.linear_constraint(linear_constraint, Constraint.Sense.LE, 2, 'x1x2')
linear_constraint = {'x0': 1, 'x2': 3}
op.linear_constraint(linear_constraint, Constraint.Sense.GE, 2, 'x0x2')
# Quadratic constraints
quadratic = {('x0', 'x1'): 1, ('x1', 'x2'): 2}
op.quadratic_constraint({}, quadratic, Constraint.Sense.LE, 3,
'x0x1_x1x2LE')
quadratic = {('x0', 'x1'): 3, ('x1', 'x2'): 4}
op.quadratic_constraint({}, quadratic, Constraint.Sense.GE, 3,
'x0x1_x1x2GE')
# Convert inequality constraints into equality constraints
conv = InequalityToEquality()
op2 = conv.convert(op)
self.assertListEqual([v.name for v in op2.variables], [
'x0', 'x1', 'x2', 'x1x2@int_slack', 'x0x2@int_slack',
'x0x1_x1x2LE@int_slack', 'x0x1_x1x2GE@int_slack'
])
# Check names and objective senses
self.assertEqual(op.name, op2.name)
self.assertEqual(op.objective.sense, op2.objective.sense)
# For linear constraints
lst = [
op2.linear_constraints[0].linear.to_dict()[0],
op2.linear_constraints[0].linear.to_dict()[1],
]
self.assertListEqual(lst, [1, 1])
self.assertEqual(op2.linear_constraints[0].sense, Constraint.Sense.EQ)
lst = [
op2.linear_constraints[1].linear.to_dict()[1],
op2.linear_constraints[1].linear.to_dict()[2],
op2.linear_constraints[1].linear.to_dict()[3],
]
self.assertListEqual(lst, [1, -1, 1])
lst = [op2.variables[3].lowerbound, op2.variables[3].upperbound]
self.assertListEqual(lst, [0, 3])
self.assertEqual(op2.linear_constraints[1].sense, Constraint.Sense.EQ)
lst = [
op2.linear_constraints[2].linear.to_dict()[0],
op2.linear_constraints[2].linear.to_dict()[2],
op2.linear_constraints[2].linear.to_dict()[4],
]
self.assertListEqual(lst, [1, 3, -1])
lst = [op2.variables[4].lowerbound, op2.variables[4].upperbound]
self.assertListEqual(lst, [0, 2])
self.assertEqual(op2.linear_constraints[2].sense, Constraint.Sense.EQ)
# For quadratic constraints
lst = [
op2.quadratic_constraints[0].quadratic.to_dict()[(0, 1)],
op2.quadratic_constraints[0].quadratic.to_dict()[(1, 2)],
op2.quadratic_constraints[0].linear.to_dict()[5],
]
self.assertListEqual(lst, [1, 2, 1])
lst = [op2.variables[5].lowerbound, op2.variables[5].upperbound]
self.assertListEqual(lst, [0, 3])
lst = [
op2.quadratic_constraints[1].quadratic.to_dict()[(0, 1)],
op2.quadratic_constraints[1].quadratic.to_dict()[(1, 2)],
op2.quadratic_constraints[1].linear.to_dict()[6],
]
self.assertListEqual(lst, [3, 4, -1])
lst = [op2.variables[6].lowerbound, op2.variables[6].upperbound]
self.assertListEqual(lst, [0, 4])
new_x = conv.interpret(np.arange(7))
np.testing.assert_array_almost_equal(new_x, np.arange(3))
def test_inequality_integer(self):
""" Test InequalityToEqualityConverter with integer variables """
op = QuadraticProgram()
for i in range(3):
op.integer_var(name='x{}'.format(i), lowerbound=-3, upperbound=3)
# Linear constraints
linear_constraint = {'x0': 1, 'x1': 1}
op.linear_constraint(linear_constraint, Constraint.Sense.EQ, 1, 'x0x1')
linear_constraint = {'x1': 1, 'x2': -1}
op.linear_constraint(linear_constraint, Constraint.Sense.LE, 2, 'x1x2')
linear_constraint = {'x0': 1, 'x2': 3}
op.linear_constraint(linear_constraint, Constraint.Sense.GE, 2, 'x0x2')
# Quadratic constraints
quadratic = {('x0', 'x1'): 1, ('x1', 'x2'): 2}
op.quadratic_constraint({}, quadratic, Constraint.Sense.LE, 3,
'x0x1_x1x2LE')
quadratic = {('x0', 'x1'): 3, ('x1', 'x2'): 4}
op.quadratic_constraint({}, quadratic, Constraint.Sense.GE, 3,
'x0x1_x1x2GE')
conv = InequalityToEquality()
op2 = conv.convert(op)
self.assertListEqual([v.name for v in op2.variables], [
'x0', 'x1', 'x2', 'x1x2@int_slack', 'x0x2@int_slack',
'x0x1_x1x2LE@int_slack', 'x0x1_x1x2GE@int_slack'
])
# For linear constraints
lst = [
op2.linear_constraints[0].linear.to_dict()[0],
op2.linear_constraints[0].linear.to_dict()[1],
]
self.assertListEqual(lst, [1, 1])
self.assertEqual(op2.linear_constraints[0].sense, Constraint.Sense.EQ)
lst = [
op2.linear_constraints[1].linear.to_dict()[1],
op2.linear_constraints[1].linear.to_dict()[2],
op2.linear_constraints[1].linear.to_dict()[3],
]
self.assertListEqual(lst, [1, -1, 1])
lst = [op2.variables[3].lowerbound, op2.variables[3].upperbound]
self.assertListEqual(lst, [0, 8])
self.assertEqual(op2.linear_constraints[1].sense, Constraint.Sense.EQ)
lst = [
op2.linear_constraints[2].linear.to_dict()[0],
op2.linear_constraints[2].linear.to_dict()[2],
op2.linear_constraints[2].linear.to_dict()[4],
]
self.assertListEqual(lst, [1, 3, -1])
lst = [op2.variables[4].lowerbound, op2.variables[4].upperbound]
self.assertListEqual(lst, [0, 10])
self.assertEqual(op2.linear_constraints[2].sense, Constraint.Sense.EQ)
# For quadratic constraints
lst = [
op2.quadratic_constraints[0].quadratic.to_dict()[(0, 1)],
op2.quadratic_constraints[0].quadratic.to_dict()[(1, 2)],
op2.quadratic_constraints[0].linear.to_dict()[5],
]
self.assertListEqual(lst, [1, 2, 1])
lst = [op2.variables[5].lowerbound, op2.variables[5].upperbound]
self.assertListEqual(lst, [0, 30])
lst = [
op2.quadratic_constraints[1].quadratic.to_dict()[(0, 1)],
op2.quadratic_constraints[1].quadratic.to_dict()[(1, 2)],
op2.quadratic_constraints[1].linear.to_dict()[6],
]
self.assertListEqual(lst, [3, 4, -1])
lst = [op2.variables[6].lowerbound, op2.variables[6].upperbound]
self.assertListEqual(lst, [0, 60])
result = OptimizationResult(x=np.arange(7),
fval=0,
variables=op2.variables)
new_result = conv.interpret(result)
np.testing.assert_array_almost_equal(new_result.x, np.arange(3))
self.assertListEqual(new_result.variable_names, ['x0', 'x1', 'x2'])
self.assertDictEqual(new_result.variables_dict, {
'x0': 0,
'x1': 1,
'x2': 2
})
def test_inequality_binary(self):
""" Test InequalityToEqualityConverter with binary variables """
op = QuadraticProgram()
for i in range(3):
op.binary_var(name='x{}'.format(i))
# Linear constraints
linear_constraint = {}
linear_constraint['x0'] = 1
linear_constraint['x1'] = 1
op.linear_constraint(linear_constraint, Constraint.Sense.EQ, 1, 'x0x1')
linear_constraint = {}
linear_constraint['x1'] = 1
linear_constraint['x2'] = -1
op.linear_constraint(linear_constraint, Constraint.Sense.LE, 2, 'x1x2')
linear_constraint = {}
linear_constraint['x0'] = 1
linear_constraint['x2'] = 3
op.linear_constraint(linear_constraint, Constraint.Sense.GE, 2, 'x0x2')
# Quadratic constraints
quadratic = {}
quadratic[('x0', 'x1')] = 1
quadratic[('x1', 'x2')] = 2
op.quadratic_constraint({}, quadratic, Constraint.Sense.LE, 3, 'x0x1_x1x2LE')
quadratic = {}
quadratic[('x0', 'x1')] = 3
quadratic[('x1', 'x2')] = 4
op.quadratic_constraint({}, quadratic, Constraint.Sense.GE, 3, 'x0x1_x1x2GE')
# Convert inequality constraints into equality constraints
conv = InequalityToEquality()
op2 = conv.convert(op)
# Check names and objective senses
self.assertEqual(op.name, op2.name)
self.assertEqual(op.objective.sense, op2.objective.sense)
# For linear constraints
lst = [
op2.linear_constraints[0].linear.to_dict()[0],
op2.linear_constraints[0].linear.to_dict()[1],
]
self.assertListEqual(lst, [1, 1])
self.assertEqual(op2.linear_constraints[0].sense, Constraint.Sense.EQ)
lst = [
op2.linear_constraints[1].linear.to_dict()[1],
op2.linear_constraints[1].linear.to_dict()[2],
op2.linear_constraints[1].linear.to_dict()[3],
]
self.assertListEqual(lst, [1, -1, 1])
lst = [op2.variables[3].lowerbound, op2.variables[3].upperbound]
self.assertListEqual(lst, [0, 3])
self.assertEqual(op2.linear_constraints[1].sense, Constraint.Sense.EQ)
lst = [
op2.linear_constraints[2].linear.to_dict()[0],
op2.linear_constraints[2].linear.to_dict()[2],
op2.linear_constraints[2].linear.to_dict()[4],
]
self.assertListEqual(lst, [1, 3, -1])
lst = [op2.variables[4].lowerbound, op2.variables[4].upperbound]
self.assertListEqual(lst, [0, 2])
self.assertEqual(op2.linear_constraints[2].sense, Constraint.Sense.EQ)
# For quadratic constraints
lst = [
op2.quadratic_constraints[0].quadratic.to_dict()[(0, 1)],
op2.quadratic_constraints[0].quadratic.to_dict()[(1, 2)],
op2.quadratic_constraints[0].linear.to_dict()[5],
]
self.assertListEqual(lst, [1, 2, 1])
lst = [op2.variables[5].lowerbound, op2.variables[5].upperbound]
self.assertListEqual(lst, [0, 3])
lst = [
op2.quadratic_constraints[1].quadratic.to_dict()[(0, 1)],
op2.quadratic_constraints[1].quadratic.to_dict()[(1, 2)],
op2.quadratic_constraints[1].linear.to_dict()[6],
]
self.assertListEqual(lst, [3, 4, -1])
lst = [op2.variables[6].lowerbound, op2.variables[6].upperbound]
self.assertListEqual(lst, [0, 4])
def test_inequality_integer(self):
""" Test InequalityToEqualityConverter with integer variables """
op = QuadraticProgram()
for i in range(3):
op.integer_var(name='x{}'.format(i), lowerbound=-3, upperbound=3)
# Linear constraints
linear_constraint = {}
linear_constraint['x0'] = 1
linear_constraint['x1'] = 1
op.linear_constraint(linear_constraint, Constraint.Sense.EQ, 1, 'x0x1')
linear_constraint = {}
linear_constraint['x1'] = 1
linear_constraint['x2'] = -1
op.linear_constraint(linear_constraint, Constraint.Sense.LE, 2, 'x1x2')
linear_constraint = {}
linear_constraint['x0'] = 1
linear_constraint['x2'] = 3
op.linear_constraint(linear_constraint, Constraint.Sense.GE, 2, 'x0x2')
# Quadratic constraints
quadratic = {}
quadratic[('x0', 'x1')] = 1
quadratic[('x1', 'x2')] = 2
op.quadratic_constraint({}, quadratic, Constraint.Sense.LE, 3, 'x0x1_x1x2LE')
quadratic = {}
quadratic[('x0', 'x1')] = 3
quadratic[('x1', 'x2')] = 4
op.quadratic_constraint({}, quadratic, Constraint.Sense.GE, 3, 'x0x1_x1x2GE')
conv = InequalityToEquality()
op2 = conv.convert(op)
# For linear constraints
lst = [
op2.linear_constraints[0].linear.to_dict()[0],
op2.linear_constraints[0].linear.to_dict()[1],
]
self.assertListEqual(lst, [1, 1])
self.assertEqual(op2.linear_constraints[0].sense, Constraint.Sense.EQ)
lst = [
op2.linear_constraints[1].linear.to_dict()[1],
op2.linear_constraints[1].linear.to_dict()[2],
op2.linear_constraints[1].linear.to_dict()[3],
]
self.assertListEqual(lst, [1, -1, 1])
lst = [op2.variables[3].lowerbound, op2.variables[3].upperbound]
self.assertListEqual(lst, [0, 8])
self.assertEqual(op2.linear_constraints[1].sense, Constraint.Sense.EQ)
lst = [
op2.linear_constraints[2].linear.to_dict()[0],
op2.linear_constraints[2].linear.to_dict()[2],
op2.linear_constraints[2].linear.to_dict()[4],
]
self.assertListEqual(lst, [1, 3, -1])
lst = [op2.variables[4].lowerbound, op2.variables[4].upperbound]
self.assertListEqual(lst, [0, 10])
self.assertEqual(op2.linear_constraints[2].sense, Constraint.Sense.EQ)
# For quadratic constraints
lst = [
op2.quadratic_constraints[0].quadratic.to_dict()[(0, 1)],
op2.quadratic_constraints[0].quadratic.to_dict()[(1, 2)],
op2.quadratic_constraints[0].linear.to_dict()[5],
]
self.assertListEqual(lst, [1, 2, 1])
lst = [op2.variables[5].lowerbound, op2.variables[5].upperbound]
self.assertListEqual(lst, [0, 30])
lst = [
op2.quadratic_constraints[1].quadratic.to_dict()[(0, 1)],
op2.quadratic_constraints[1].quadratic.to_dict()[(1, 2)],
op2.quadratic_constraints[1].linear.to_dict()[6],
]
self.assertListEqual(lst, [3, 4, -1])
lst = [op2.variables[6].lowerbound, op2.variables[6].upperbound]
self.assertListEqual(lst, [0, 60])
