def __Update_Z_Constr(pure_model: Model, constr_z: Dict[int,
int]) -> Model:
Z = pure_model.getVariable('Z')
if len(constr_z) == 1:
for key, value in constr_z.items(): # only one iteration
pure_model.constraint('BB', Z.index(key),
Domain.equalsTo(value))
if len(constr_z) >= 2:
expression = Expr.vstack([Z.index(key) for key in constr_z.keys()])
values = [value for key, value in constr_z.items()]
pure_model.constraint('BB', expression, Domain.equalsTo(values))
return pure_model
# 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))
m.constraint('c_2_b', Expr.add([x_2_b]), Domain.equalsTo(1.0))
m.constraint('c_2_c', Expr.add([x_2_c]), Domain.equalsTo(1.0))
m.constraint('c_2_d', Expr.add([x_2_d]), Domain.equalsTo(1.0))
m.constraint('c_3_b', Expr.add([x_3_b]), Domain.equalsTo(1.0))
m.constraint('c_3_c', Expr.add([x_3_c]), Domain.equalsTo(1.0))
m.constraint('c_3_d', Expr.add([x_3_d]), Domain.equalsTo(1.0))
# Minimize resources required to construct all images.
obj = [Expr.mul(c, x) for c, x in [
# Individual image/command pairs
(r['A'], x_1_a), (r['B'], x_1_b),
(r['A'], x_2_a), (r['B'], x_2_b), (r['C'], x_2_c), (r['D'], x_2_d),
(r['B'], x_3_b), (r['C'], x_3_c), (r['D'], x_3_d),
z_2_a = m.variable('z_2_a', *binary)
z_2_b = m.variable('z_2_b', *binary)
z_2_c = m.variable('z_2_c', *binary)
z_2_d = m.variable('z_2_d', *binary)
z_3_b = m.variable('z_3_b', *binary)
z_3_c = m.variable('z_3_c', *binary)
z_3_d = m.variable('z_3_d', *binary)
# Inclusion of an image and a command means that image must
# use all command invocation from the clique.
# For instance:
# (1) z_1_a <= w_1
# (2) z_1_a <= y_a
# (3) z_1_a >= w_1 + y_a - 1
m.constraint('c_1_a_1', Expr.sub(z_1_a, w_1), Domain.lessThan(0.0))
m.constraint('c_1_a_2', Expr.sub(z_1_a, y_a), Domain.lessThan(0.0))
m.constraint('c_1_a_3', Expr.sub(z_1_a, Expr.add([w_1, y_a])),
Domain.greaterThan(-1.0))
m.constraint('c_1_b_1', Expr.sub(z_1_b, w_1), Domain.lessThan(0.0))
m.constraint('c_1_b_2', Expr.sub(z_1_b, y_b), Domain.lessThan(0.0))
m.constraint('c_1_b_3', Expr.sub(z_1_b, Expr.add([w_1, y_b])),
Domain.greaterThan(-1.0))
m.constraint('c_1_c', Expr.sub(0.0, Expr.add([w_1, y_c])),
Domain.greaterThan(-1.0))
m.constraint('c_1_d', Expr.sub(0.0, Expr.add([w_1, y_d])),
Domain.greaterThan(-1.0))
m.constraint('c_2_a_1', Expr.sub(z_2_a, w_2), Domain.lessThan(0.0))
# clique or incur its own cost.
q_2_b = m.variable('q_2_b', *binary)
q_2_c = m.variable('q_2_c', *binary)
q_2_d = m.variable('q_2_d', *binary)
q_3_b = m.variable('q_3_b', *binary)
q_3_c = m.variable('q_3_c', *binary)
q_3_d = m.variable('q_3_d', *binary)
# Inclusion of an image and a command means that image must
# use all command invocation from the clique.
# For instance:
# (1) z_1_a <= w_1
# (2) z_1_a <= y_a
# (3) z_1_a >= w_1 + y_a - 1
m.constraint('c_1_a_1', Expr.sub(z_1_a, w_1), Domain.lessThan(0.0))
m.constraint('c_1_a_2', Expr.sub(z_1_a, y_a), Domain.lessThan(0.0))
m.constraint('c_1_a_3', Expr.sub(z_1_a, Expr.add([w_1, y_a])), Domain.greaterThan(-1.0))
m.constraint('c_1_b_1', Expr.sub(z_1_b, w_1), Domain.lessThan(0.0))
m.constraint('c_1_b_2', Expr.sub(z_1_b, y_b), Domain.lessThan(0.0))
m.constraint('c_1_b_3', Expr.sub(z_1_b, Expr.add([w_1, y_b])), Domain.greaterThan(-1.0))
m.constraint('c_1_c', Expr.sub(0.0, Expr.add([w_1, y_c])), Domain.greaterThan(-1.0))
m.constraint('c_1_d', Expr.sub(0.0, Expr.add([w_1, y_d])), Domain.greaterThan(-1.0))
m.constraint('c_2_a_1', Expr.sub(z_2_a, w_2), Domain.lessThan(0.0))
m.constraint('c_2_a_2', Expr.sub(z_2_a, y_a), Domain.lessThan(0.0))
m.constraint('c_2_a_3', Expr.sub(z_2_a, Expr.add([w_2, y_a])), Domain.greaterThan(-1.0))
m.constraint('c_2_b_1', Expr.sub(z_2_b, w_2), Domain.lessThan(0.0))
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)
x_123_b_23_cd = m.variable('x_123_b_23_cd', *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, x_123_b]), Domain.equalsTo(1.0))
m.constraint('c_2_a', Expr.add([x_2_a]), Domain.equalsTo(1.0))
m.constraint('c_2_b', Expr.add([x_2_b, x_23_bcd, x_123_b]), Domain.equalsTo(1.0))
m.constraint('c_2_c', Expr.add([x_2_c, x_23_bcd, x_123_b_23_cd]), Domain.equalsTo(1.0))
m.constraint('c_2_d', Expr.add([x_2_d, x_23_bcd, x_123_b_23_cd]), Domain.equalsTo(1.0))
m.constraint('c_3_b', Expr.add([x_3_b, x_23_bcd, x_123_b]), Domain.equalsTo(1.0))
m.constraint('c_3_c', Expr.add([x_3_c, x_23_bcd, x_123_b_23_cd]), Domain.equalsTo(1.0))
m.constraint('c_3_d', Expr.add([x_3_d, x_23_bcd, x_123_b_23_cd]), Domain.equalsTo(1.0))
# Add dependency constraints for sub-cliques.
m.constraint('d_123_b_23_cd', Expr.sub(x_123_b, x_123_b_23_cd), Domain.greaterThan(0.0))
# Eliminated intersections between cliques.
m.constraint('e1', Expr.add([x_23_bcd, x_123_b]), Domain.lessThan(1.0))
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)
# 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))
m.constraint('c_2_b', Expr.add([x_2_b, x_23_bcd]), Domain.equalsTo(1.0))
m.constraint('c_2_c', Expr.add([x_2_c, x_23_bcd]), Domain.equalsTo(1.0))
m.constraint('c_2_d', Expr.add([x_2_d, x_23_bcd]), Domain.equalsTo(1.0))
m.constraint('c_3_b', Expr.add([x_3_b, x_23_bcd]), Domain.equalsTo(1.0))
m.constraint('c_3_c', Expr.add([x_3_c, x_23_bcd]), Domain.equalsTo(1.0))
m.constraint('c_3_d', Expr.add([x_3_d, x_23_bcd]), Domain.equalsTo(1.0))
# Minimize resources required to construct all images.
obj = [Expr.mul(c, x) for c, x in [
# Individual image/command pairs
(r['A'], x_1_a), (r['B'], x_1_b),
(r['A'], x_2_a), (r['B'], x_2_b), (r['C'], x_2_c), (r['D'], x_2_d),
(r['B'], x_3_b), (r['C'], x_3_c), (r['D'], x_3_d),
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)
# 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))
m.constraint('c_2_b', Expr.add([x_2_b, x_23_bcd]), Domain.equalsTo(1.0))
m.constraint('c_2_c', Expr.add([x_2_c, x_23_bcd]), Domain.equalsTo(1.0))
m.constraint('c_2_d', Expr.add([x_2_d, x_23_bcd]), Domain.equalsTo(1.0))
m.constraint('c_3_b', Expr.add([x_3_b, x_23_bcd]), Domain.equalsTo(1.0))
m.constraint('c_3_c', Expr.add([x_3_c, x_23_bcd]), Domain.equalsTo(1.0))
m.constraint('c_3_d', Expr.add([x_3_d, x_23_bcd]), Domain.equalsTo(1.0))
# Minimize resources required to construct all images.
obj = [
Expr.mul(c, x) for c, x in [
# Individual image/command pairs
(r['A'], x_1_a),
(r['B'], x_1_b),
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)
x_123_b_23_cd = m.variable('x_123_b_23_cd', *binary)
x_12_a = m.variable('x_12_a', *binary)
# Each command must be run once for each image.
m.constraint('c_1_a', Expr.add([x_1_a, x_12_a]), Domain.equalsTo(1.0))
m.constraint('c_1_b', Expr.add([x_1_b, x_123_b]), Domain.equalsTo(1.0))
m.constraint('c_2_a', Expr.add([x_2_a, x_12_a]), Domain.equalsTo(1.0))
m.constraint('c_2_b', Expr.add([x_2_b, x_23_bcd, x_123_b]), Domain.equalsTo(1.0))
m.constraint('c_2_c', Expr.add([x_2_c, x_23_bcd, x_123_b_23_cd]), Domain.equalsTo(1.0))
m.constraint('c_2_d', Expr.add([x_2_d, x_23_bcd, x_123_b_23_cd]), Domain.equalsTo(1.0))
m.constraint('c_3_b', Expr.add([x_3_b, x_23_bcd, x_123_b]), Domain.equalsTo(1.0))
m.constraint('c_3_c', Expr.add([x_3_c, x_23_bcd, x_123_b_23_cd]), Domain.equalsTo(1.0))
m.constraint('c_3_d', Expr.add([x_3_d, x_23_bcd, x_123_b_23_cd]), Domain.equalsTo(1.0))
# Add dependency constraints for sub-cliques.
m.constraint('d_123_b_23_cd', Expr.sub(x_123_b, x_123_b_23_cd), Domain.greaterThan(0.0))
# Eliminated intersections between cliques.
m.constraint('e1', Expr.add([x_23_bcd, x_123_b]), Domain.lessThan(1.0))
m.constraint('e2', Expr.add([x_12_a, x_123_b]), Domain.lessThan(1.0))
# 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))
m.constraint('c_2_b', Expr.add([x_2_b]), Domain.equalsTo(1.0))
m.constraint('c_2_c', Expr.add([x_2_c]), Domain.equalsTo(1.0))
m.constraint('c_2_d', Expr.add([x_2_d]), Domain.equalsTo(1.0))
m.constraint('c_3_b', Expr.add([x_3_b]), Domain.equalsTo(1.0))
m.constraint('c_3_c', Expr.add([x_3_c]), Domain.equalsTo(1.0))
m.constraint('c_3_d', Expr.add([x_3_d]), Domain.equalsTo(1.0))
# Minimize resources required to construct all images.
obj = [
Expr.mul(c, x) for c, x in [
# Individual image/command pairs
(r['A'], x_1_a),
(r['B'], x_1_b),
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
