obj2 = [
Expr.mul(c, z) for c, z in [
# Individual image/command pairs
(r['A'], z_1_a),
(r['B'], z_1_b),
(r['A'], z_2_a),
(r['B'], z_2_b),
(r['C'], z_2_c),
(r['D'], z_2_d),
(r['B'], z_3_b),
(r['C'], z_3_c),
(r['D'], z_3_d),
]
]
m.objective('w', ObjectiveSense.Maximize,
Expr.sub(Expr.add(obj2), Expr.add(obj1)))
m.setLogHandler(sys.stdout)
m.solve()
print
print 'Images:'
print '\tw_1 = %.0f' % w_1.level()[0]
print '\tw_2 = %.0f' % w_2.level()[0]
print '\tw_3 = %.0f' % w_3.level()[0]
print
print 'Commands:'
print '\ty_a = %.0f' % y_a.level()[0]
print '\ty_b = %.0f' % y_b.level()[0]
print '\ty_c = %.0f' % y_c.level()[0]
print '\ty_d = %.0f' % y_d.level()[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),
]]
m.objective('w', ObjectiveSense.Minimize, Expr.add(obj))
m.setLogHandler(sys.stdout)
m.solve()
print
print 'Image 1:'
print '\tx_1_a = %.0f' % x_1_a.level()[0]
print '\tx_1_b = %.0f' % x_1_b.level()[0]
print
print 'Image 2:'
print '\tx_2_a = %.0f' % x_2_a.level()[0]
print '\tx_2_b = %.0f' % x_2_b.level()[0]
print '\tx_2_c = %.0f' % x_2_c.level()[0]
print '\tx_2_d = %.0f' % x_2_d.level()[0]
print
# Eliminated intersections between cliques.
m.constraint('e1', Expr.add([x_23_bcd, x_123_b]), Domain.lessThan(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),
# Cliques
(r['B'] + r['C'] + r['D'], x_23_bcd),
(r['B'], x_123_b),
(r['C'] + r['D'], x_123_b_23_cd),
]]
m.objective('w', ObjectiveSense.Minimize, Expr.add(obj))
m.setLogHandler(sys.stdout)
m.solve()
print
print 'Image 1:'
print '\tx_1_a = %.0f' % x_1_a.level()[0]
print '\tx_1_b = %.0f' % x_1_b.level()[0]
print
print 'Image 2:'
print '\tx_2_a = %.0f' % x_2_a.level()[0]
print '\tx_2_b = %.0f' % x_2_b.level()[0]
print '\tx_2_c = %.0f' % x_2_c.level()[0]
print '\tx_2_d = %.0f' % x_2_d.level()[0]
print
(r['A'], z_1_a), (r['B'], z_1_b),
(r['A'], z_2_a),
]]
obj3 = [Expr.mul(c, z) for c, z in [
# Individual image/command pairs for commands that are now run alone
(r['B'], q_2_b), (r['C'], q_2_c), (r['D'], q_2_d),
(r['B'], q_3_b), (r['C'], q_3_c), (r['D'], q_3_d),
]]
obj4 = [Expr.mul(c, y) for c, y in [
# Commands taken out of the existing cliques
(r['B'], n_b), (r['C'], n_c), (r['D'], n_d)
]]
m.objective('w', ObjectiveSense.Maximize,
Expr.sub(Expr.add(obj2 + obj4), Expr.add(obj1 + obj3))
)
m.setLogHandler(sys.stdout)
m.solve()
print
print 'Images:'
print '\tw_1 = %.0f' % w_1.level()[0]
print '\tw_2 = %.0f' % w_2.level()[0]
print '\tw_3 = %.0f' % w_3.level()[0]
print
print 'Commands:'
print '\ty_a = %.0f' % y_a.level()[0]
print '\ty_b = %.0f' % y_b.level()[0]
print '\ty_c = %.0f' % y_c.level()[0]
m.constraint('c_3_d_1', Expr.sub(z_3_d, w_3), Domain.lessThan(0.0))
m.constraint('c_3_d_2', Expr.sub(z_3_d, y_d), Domain.lessThan(0.0))
m.constraint('c_3_d_3', Expr.sub(z_3_d, Expr.add([w_3, y_d])), Domain.greaterThan(-1.0))
# Maximize the amount we can improve our objective by adding a new clique.
obj1 = [Expr.mul(c, y) for c, y in [
(r['A'], y_a), (r['B'], y_b), (r['C'], y_c), (r['D'], y_d)
]]
obj2 = [Expr.mul(c, z) for c, z in [
# Individual image/command pairs
(r['A'], z_1_a), (r['B'], z_1_b),
(r['A'], z_2_a), (r['B'], z_2_b), (r['C'], z_2_c), (r['D'], z_2_d),
(r['B'], z_3_b), (r['C'], z_3_c), (r['D'], z_3_d),
]]
m.objective('w', ObjectiveSense.Maximize, Expr.sub(Expr.add(obj2), Expr.add(obj1)))
m.setLogHandler(sys.stdout)
m.solve()
print
print 'Images:'
print '\tw_1 = %.0f' % w_1.level()[0]
print '\tw_2 = %.0f' % w_2.level()[0]
print '\tw_3 = %.0f' % w_3.level()[0]
print
print 'Commands:'
print '\ty_a = %.0f' % y_a.level()[0]
print '\ty_b = %.0f' % y_b.level()[0]
print '\ty_c = %.0f' % y_c.level()[0]
print '\ty_d = %.0f' % y_d.level()[0]
(r['D'], q_2_d),
(r['B'], q_3_b),
(r['C'], q_3_c),
(r['D'], q_3_d),
]
]
obj4 = [
Expr.mul(c, y) for c, y in [
# Commands taken out of the existing cliques
(r['B'], n_b),
(r['C'], n_c),
(r['D'], n_d)
]
]
m.objective('w', ObjectiveSense.Maximize,
Expr.sub(Expr.add(obj2 + obj4), Expr.add(obj1 + obj3)))
m.setLogHandler(sys.stdout)
m.solve()
print
print 'Images:'
print '\tw_1 = %.0f' % w_1.level()[0]
print '\tw_2 = %.0f' % w_2.level()[0]
print '\tw_3 = %.0f' % w_3.level()[0]
print
print 'Commands:'
print '\ty_a = %.0f' % y_a.level()[0]
print '\ty_b = %.0f' % y_b.level()[0]
print '\ty_c = %.0f' % y_c.level()[0]
print '\ty_d = %.0f' % y_d.level()[0]
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
