# x_2_c = 1
# x_2_d = 1
#
# Image 3:
# x_3_b = 1
# x_3_c = 1
# x_3_d = 1
r = {'A': 5.0, 'B': 10.0, 'C': 7.0, 'D': 12.0}
m = Model()
binary = (Domain.inRange(0.0, 1.0), Domain.isInteger())
# Provide a variable for each image and command. This is 1 if the command
# is not run as part of a clique for the image.
x_1_a = m.variable('x_1_a', *binary)
x_1_b = m.variable('x_1_b', *binary)
x_2_a = m.variable('x_2_a', *binary)
x_2_b = m.variable('x_2_b', *binary)
x_2_c = m.variable('x_2_c', *binary)
x_2_d = m.variable('x_2_d', *binary)
x_3_b = m.variable('x_3_b', *binary)
x_3_c = m.variable('x_3_c', *binary)
x_3_d = m.variable('x_3_d', *binary)
# Each command must be run once for each image.
m.constraint('c_1_a', Expr.add([x_1_a]), Domain.equalsTo(1.0))
m.constraint('c_1_b', Expr.add([x_1_b]), Domain.equalsTo(1.0))
m.constraint('c_2_a', Expr.add([x_2_a]), Domain.equalsTo(1.0))
# x_3_c = 0
# x_3_d = 0
#
# Cliques:
# x_23_bcd = 0
# x_123_b = 1
# x_123_b_23_cd = 1
r = {'A': 5.0, 'B': 10.0, 'C': 7.0, 'D': 12.0}
m = Model()
binary = (Domain.inRange(0.0, 1.0), Domain.isInteger())
# Provide a variable for each image and command. This is 1 if the command
# is not run as part of a clique for the image.
x_1_a = m.variable('x_1_a', *binary)
x_1_b = m.variable('x_1_b', *binary)
x_2_a = m.variable('x_2_a', *binary)
x_2_b = m.variable('x_2_b', *binary)
x_2_c = m.variable('x_2_c', *binary)
x_2_d = m.variable('x_2_d', *binary)
x_3_b = m.variable('x_3_b', *binary)
x_3_c = m.variable('x_3_c', *binary)
x_3_d = m.variable('x_3_d', *binary)
# Provide a variable for each maximal clique and maximal sub-clique.
x_23_bcd = m.variable('x_23_bcd', *binary)
x_123_b = m.variable('x_123_b', *binary)
# w_2 = 1
# w_3 = 1
#
# Commands:
# y_a = 0
# y_b = 1
# y_c = 1
# y_d = 1
r = {'A': 5.0, 'B': 10.0, 'C': 7.0, 'D': 12.0}
m = Model()
binary = (Domain.inRange(0.0, 1.0), Domain.isInteger())
# Variables to determine if we include commands in the clique.
y_a = m.variable('y_a', *binary)
y_b = m.variable('y_b', *binary)
y_c = m.variable('y_c', *binary)
y_d = m.variable('y_d', *binary)
# Variables to determine if we include images in the clique.
w_1 = m.variable('w_1', *binary)
w_2 = m.variable('w_2', *binary)
w_3 = m.variable('w_3', *binary)
# Variables to enforce relationships between y and w decisions.
z_1_a = m.variable('z_1_a', *binary)
z_1_b = m.variable('z_1_b', *binary)
z_2_a = m.variable('z_2_a', *binary)
z_2_b = m.variable('z_2_b', *binary)
# y_d = 0
#
# Interactions:
# m_2 = 0
# m_3 = 0
# n_b = 1
# n_c = 0
# n_d = 0
r = {'A': 5.0, 'B': 10.0, 'C': 7.0, 'D': 12.0}
m = Model()
binary = (Domain.inRange(0.0, 1.0), Domain.isInteger())
# Variables to determine if we include commands in the clique.
y_a = m.variable('y_a', *binary)
y_b = m.variable('y_b', *binary)
y_c = m.variable('y_c', *binary)
y_d = m.variable('y_d', *binary)
# Variables to determine if we include images in the clique.
w_1 = m.variable('w_1', *binary)
w_2 = m.variable('w_2', *binary)
w_3 = m.variable('w_3', *binary)
# Variables to enforce relationships between y and w decisions.
z_1_a = m.variable('z_1_a', *binary)
z_1_b = m.variable('z_1_b', *binary)
z_2_a = m.variable('z_2_a', *binary)
z_2_b = m.variable('z_2_b', *binary)
# w_3 = 1
#
# Commands:
# y_a = 0
# y_b = 1
# y_c = 1
# y_d = 1
r = {'A': 5.0, 'B': 10.0, 'C': 7.0, 'D': 12.0}
m = Model()
binary = (Domain.inRange(0.0, 1.0), Domain.isInteger())
# Variables to determine if we include commands in the clique.
y_a = m.variable('y_a', *binary)
y_b = m.variable('y_b', *binary)
y_c = m.variable('y_c', *binary)
y_d = m.variable('y_d', *binary)
# Variables to determine if we include images in the clique.
w_1 = m.variable('w_1', *binary)
w_2 = m.variable('w_2', *binary)
w_3 = m.variable('w_3', *binary)
# Variables to enforce relationships between y and w decisions.
z_1_a = m.variable('z_1_a', *binary)
z_1_b = m.variable('z_1_b', *binary)
z_2_a = m.variable('z_2_a', *binary)
z_2_b = m.variable('z_2_b', *binary)
# x_3_d = 0
#
# Cliques:
# x_23_bcd = 0
# x_123_b = 1
# x_123_b_23_cd = 1
# x_12_a = 0
r = {'A': 5.0, 'B': 10.0, 'C': 7.0, 'D': 12.0}
m = Model()
binary = (Domain.inRange(0.0, 1.0), Domain.isInteger())
# Provide a variable for each image and command. This is 1 if the command
# is not run as part of a clique for the image.
x_1_a = m.variable('x_1_a', *binary)
x_1_b = m.variable('x_1_b', *binary)
x_2_a = m.variable('x_2_a', *binary)
x_2_b = m.variable('x_2_b', *binary)
x_2_c = m.variable('x_2_c', *binary)
x_2_d = m.variable('x_2_d', *binary)
x_3_b = m.variable('x_3_b', *binary)
x_3_c = m.variable('x_3_c', *binary)
x_3_d = m.variable('x_3_d', *binary)
# Provide a variable for each maximal clique and maximal sub-clique.
x_23_bcd = m.variable('x_23_bcd', *binary)
x_123_b = m.variable('x_123_b', *binary)
# y_d = 0
#
# Interactions:
# m_2 = 0
# m_3 = 0
# n_b = 1
# n_c = 0
# n_d = 0
r = {'A': 5.0, 'B': 10.0, 'C': 7.0, 'D': 12.0}
m = Model()
binary = (Domain.inRange(0.0, 1.0), Domain.isInteger())
# Variables to determine if we include commands in the clique.
y_a = m.variable('y_a', *binary)
y_b = m.variable('y_b', *binary)
y_c = m.variable('y_c', *binary)
y_d = m.variable('y_d', *binary)
# Variables to determine if we include images in the clique.
w_1 = m.variable('w_1', *binary)
w_2 = m.variable('w_2', *binary)
w_3 = m.variable('w_3', *binary)
# Variables to enforce relationships between y and w decisions.
z_1_a = m.variable('z_1_a', *binary)
z_1_b = m.variable('z_1_b', *binary)
z_2_a = m.variable('z_2_a', *binary)
z_2_b = m.variable('z_2_b', *binary)
def Build_Co_Model(self):
r = len(self.roads)
mu, sigma = self.mu, self.sigma
m, n, r = self.m, self.n, len(self.roads)
f, h = self.f, self.h
M, N = m + n + r, 2 * m + 2 * n + r
A = self.__Construct_A_Matrix()
A_Mat = Matrix.dense(A)
b = self.__Construct_b_vector()
# ---- build Mosek Model
COModel = Model()
# -- Decision Variable
Z = COModel.variable('Z', m, Domain.inRange(0.0, 1.0))
I = COModel.variable('I', m, Domain.greaterThan(0.0))
Alpha = COModel.variable('Alpha', M,
Domain.unbounded()) # M by 1 vector
Beta = COModel.variable('Beta', M, Domain.unbounded()) # M by 1 vector
Theta = COModel.variable('Theta', N,
Domain.unbounded()) # N by 1 vector
# M1_matrix related decision variables
'''
[tau, xi^T, phi^T
M1 = xi, eta, psi^t
phi, psi, w ]
'''
# no-need speedup variables
Psi = COModel.variable('Psi', [N, n], Domain.unbounded())
Xi = COModel.variable('Xi', n, Domain.unbounded()) # n by 1 vector
Phi = COModel.variable('Phi', N, Domain.unbounded()) # N by 1 vector
# has the potential to speedup
Tau, Eta, W = self.__Declare_SpeedUp_Vars(COModel)
# M2 matrix decision variables
'''
[a, b^T, c^T
M2 = b, e, d^t
c, d, f ]
'''
a_M2 = COModel.variable('a_M2', 1, Domain.greaterThan(0.0))
b_M2 = COModel.variable('b_M2', n, Domain.greaterThan(0.0))
c_M2 = COModel.variable('c_M2', N, Domain.greaterThan(0.0))
e_M2 = COModel.variable('e_M2', [n, n], Domain.greaterThan(0.0))
d_M2 = COModel.variable('d_M2', [N, n], Domain.greaterThan(0.0))
f_M2 = COModel.variable('f_M2', [N, N], Domain.greaterThan(0.0))
# -- Objective Function
obj_1 = Expr.dot(f, Z)
obj_2 = Expr.dot(h, I)
obj_3 = Expr.dot(b, Alpha)
obj_4 = Expr.dot(b, Beta)
obj_5 = Expr.dot([1], Expr.add(Tau, a_M2))
obj_6 = Expr.dot([2 * mean for mean in mu], Expr.add(Xi, b_M2))
obj_7 = Expr.dot(sigma, Expr.add(Eta, e_M2))
COModel.objective(
ObjectiveSense.Minimize,
Expr.add([obj_1, obj_2, obj_3, obj_4, obj_5, obj_6, obj_7]))
# Constraint 1
_expr = Expr.sub(Expr.mul(A_Mat.transpose(), Alpha), Theta)
_expr = Expr.sub(_expr, Expr.mul(2, Expr.add(Phi, c_M2)))
_expr_rhs = Expr.vstack(Expr.constTerm([0.0] * n), Expr.mul(-1, I),
Expr.constTerm([0.0] * M))
COModel.constraint('constr1', Expr.sub(_expr, _expr_rhs),
Domain.equalsTo(0.0))
del _expr, _expr_rhs
# Constraint 2
_first_term = Expr.add([
Expr.mul(Beta.index(row),
np.outer(A[row], A[row]).tolist()) for row in range(M)
])
_second_term = Expr.add([
Expr.mul(Theta.index(k), Matrix.sparse(N, N, [k], [k], [1]))
for k in range(N)
])
_third_term = Expr.add(W, f_M2)
_expr = Expr.sub(Expr.add(_first_term, _second_term), _third_term)
COModel.constraint('constr2', _expr, Domain.equalsTo(0.0))
del _expr, _first_term, _second_term, _third_term
# Constraint 3
_expr = Expr.mul(-2, Expr.add(Psi, d_M2))
_expr_rhs = Matrix.sparse([[Matrix.eye(n)], [Matrix.sparse(N - n, n)]])
COModel.constraint('constr3', Expr.sub(_expr, _expr_rhs),
Domain.equalsTo(0))
del _expr, _expr_rhs
# Constraint 4: I <= M*Z
COModel.constraint('constr4', Expr.sub(Expr.mul(20000.0, Z), I),
Domain.greaterThan(0.0))
# Constraint 5: M1 is SDP
COModel.constraint(
'constr5',
Expr.vstack(Expr.hstack(Tau, Xi.transpose(), Phi.transpose()),
Expr.hstack(Xi, Eta, Psi.transpose()),
Expr.hstack(Phi, Psi, W)), Domain.inPSDCone(1 + n + N))
return COModel
