# 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)
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