def classical_exactcover_solver(A, w=None, num_threads=4):
nrows, ncolumns = np.shape(A)
if w is None:
w = np.ones(ncolumns)
assert(len(w) == ncolumns)
assert(sum(w >= 0))
model = CyLPModel()
# Decision variables, one for each cover
x = model.addVariable('x', ncolumns, isInt=True)
# Adding the box contraints
model += 0 <= x <= 1
# Adding the cover constraints
# Sum_j x_ij == 1
for i in range(nrows):
model += CyLPArray(A[i,:]) * x == 1
# Adding the objective function
model.objective = CyLPArray(w) * x
lp = CyClpSimplex(model)
lp.logLevel = 0
lp.optimizationDirection = 'min'
mip = lp.getCbcModel()
mip.logLevel = 0
# Setting number of threads
mip.numberThreads = num_threads
mip.solve()
return mip.objectiveValue, [int(i) for i in mip.primalVariableSolution['x']]
def test_Sparse(self):
model = CyLPModel()
x = model.addVariable('x', 3)
y = model.addVariable('y', 2)
A = csc_matrixPlus(([1, 2, 1, 1], ([0, 0, 1, 1], [0, 1, 0, 2])),
shape=(2, 3))
B = csc_matrixPlus(([1, 1], ([0, 1], [0, 2])), shape=(2, 3))
D = np.matrix([[1., 2.], [0, 1]])
a = CyLPArray([5, 2.5])
b = CyLPArray([4.2, 3])
x_u = CyLPArray([2., 3.5])
model.addConstraint(A * x <= a)
model.addConstraint(2 <= B * x + D * y <= b)
model.addConstraint(y >= 0)
model.addConstraint(1.1 <= x[1:3] <= x_u)
c = CyLPArray([1., -2., 3.])
model.objective = c * x + 2 * y[0] + 2 * y[1]
s = CyClpSimplex(model)
s.primal()
sol = np.concatenate(
(s.primalVariableSolution['x'], s.primalVariableSolution['y']))
self.assertTrue(
(abs(sol - np.array([0.2, 2, 1.1, 0, 0.9])) <= 10**-6).all())
def test(self):
model = CyLPModel()
x = model.addVariable('x', 3)
A = np.matrix([[1,2,3], [1,1,1]])
b = CyLPArray([5, 3])
model.addConstraint(A * x == b)
model.addConstraint(x >= 0)
model.objective = 1*x[0] + 1*x[1] + 1.1 * x[2]
# Solve it a first time
s = CyClpSimplex(model)
s.primal()
sol = s.primalVariableSolution['x']
self.assertTrue((abs(sol - np.array([1,2,0]) ) <= 10**-6).all())
# Add a cut
s.addConstraint(x[0] >= 1.1)
s.primal()
sol = s.primalVariableSolution['x']
self.assertTrue((abs(sol - np.array([1.1, 1.8, 0.1]) ) <= 10**-6).all())
# Change the objective function
c = csr_matrixPlus([[1, 10, 1.1]]).T
s.objective = c.T * x
s.primal()
sol = s.primalVariableSolution['x']
self.assertTrue((abs(sol - np.array([2, 0, 1]) ) <= 10**-6).all())
def test_Sparse(self):
model = CyLPModel()
x = model.addVariable('x', 3)
y = model.addVariable('y', 2)
A = csc_matrixPlus(([1, 2, 1, 1], ([0, 0, 1, 1], [0, 1, 0, 2])), shape=(2, 3))
B = csc_matrixPlus(([1, 1], ([0, 1], [0, 2])), shape=(2, 3))
D = np.matrix([[1., 2.],[0, 1]])
a = CyLPArray([5, 2.5])
b = CyLPArray([4.2, 3])
x_u= CyLPArray([2., 3.5])
model.addConstraint(A*x <= a)
model.addConstraint(2 <= B * x + D * y <= b)
model.addConstraint(y >= 0)
model.addConstraint(1.1 <= x[1:3] <= x_u)
c = CyLPArray([1., -2., 3.])
model.objective = c * x + 2 * y[0] + 2 * y[1]
s = CyClpSimplex(model)
s.primal()
sol = np.concatenate((s.primalVariableSolution['x'],
s.primalVariableSolution['y']))
self.assertTrue((abs(sol -
np.array([0.2, 2, 1.1, 0, 0.9]) ) <= 10**-6).all())
def setUp(self):
'Test remove constraint'
model = CyLPModel()
x = model.addVariable('x', 3)
y = model.addVariable('y', 2)
A = csc_matrixPlus(([1, 2, 1, 1], ([0, 0, 1, 1], [0, 1, 0, 2])), shape=(2, 3))
B = csc_matrixPlus(([1, 1], ([0, 1], [0, 2])), shape=(2, 3))
D = np.matrix([[1., 2.],[0, 1]])
a = CyLPArray([3, 2.5])
b = CyLPArray([4.2, 3])
x_u= CyLPArray([2., 3.5])
model.addConstraint(A * x <= a, 'res1')
model.addConstraint(2 <= B * x + D * y <= b, 'res2')
model.addConstraint(y >= 0)
model.addConstraint(1.1 <= x[1:3] <= x_u)
model.addConstraint(x[0] >= 0.1)
c = CyLPArray([1., -2., 3.])
model.objective = c * x + 2 * y[0] + 2 * y[1]
s = CyClpSimplex(model)
self.s = s
self.x = x
self.y = y
def setUp(self):
'Test remove constraint'
model = CyLPModel()
x = model.addVariable('x', 3)
y = model.addVariable('y', 2)
A = csc_matrixPlus(([1, 2, 1, 1], ([0, 0, 1, 1], [0, 1, 0, 2])),
shape=(2, 3))
B = csc_matrixPlus(([1, 1], ([0, 1], [0, 2])), shape=(2, 3))
D = np.matrix([[1., 2.], [0, 1]])
a = CyLPArray([3, 2.5])
b = CyLPArray([4.2, 3])
x_u = CyLPArray([2., 3.5])
model.addConstraint(A * x <= a, 'res1')
model.addConstraint(2 <= B * x + D * y <= b, 'res2')
model.addConstraint(y >= 0)
model.addConstraint(1.1 <= x[1:3] <= x_u)
model.addConstraint(x[0] >= 0.1)
c = CyLPArray([1., -2., 3.])
model.objective = c * x + 2 * y[0] + 2 * y[1]
s = CyClpSimplex(model)
self.s = s
self.x = x
self.y = y
def test(self):
model = CyLPModel()
x = model.addVariable('x', 3)
A = np.matrix([[1, 2, 3], [1, 1, 1]])
b = CyLPArray([5, 3])
model.addConstraint(A * x == b)
model.addConstraint(x >= 0)
model.objective = 1 * x[0] + 1 * x[1] + 1.1 * x[2]
# Solve it a first time
s = CyClpSimplex(model)
s.primal()
sol = s.primalVariableSolution['x']
self.assertTrue((abs(sol - np.array([1, 2, 0])) <= 10**-6).all())
# Add a cut
s.addConstraint(x[0] >= 1.1)
s.primal()
sol = s.primalVariableSolution['x']
self.assertTrue((abs(sol - np.array([1.1, 1.8, 0.1])) <= 10**-6).all())
# Change the objective function
c = csr_matrixPlus([[1, 10, 1.1]]).T
s.objective = c.T * x
s.primal()
sol = s.primalVariableSolution['x']
self.assertTrue((abs(sol - np.array([2, 0, 1])) <= 10**-6).all())
def branch_and_bound(G, num_threads=4):
N = len(G)
model = CyLPModel()
# Decision variables, one for each node
x = model.addVariable('x', N, isInt=True)
# Adjacency matrix (possibly weighted)
W = nx.to_numpy_matrix(G)
z_ind = dict()
ind = 0
w = []
for i in range(N):
j_range = range(N)
if (not nx.is_directed(G)):
# Reduced range for undirected graphs
j_range = range(i, N)
for j in j_range:
if (W[i,j] == 0):
continue
if (i not in z_ind):
z_ind[i] = dict()
z_ind[i][j] = ind
w.append(W[i,j])
ind += 1
# Aux variables, one for each edge
z = model.addVariable('z', len(w), isInt=True)
# Adding the box contraints
model += 0 <= x <= 1
model += 0 <= z <= 1
# Adding the cutting constraints
# If x_i == x_j then z_ij = 0
# If x_i != x_j then z_ij = 1
for i in z_ind:
for j in z_ind[i]:
model += z[z_ind[i][j]] - x[i] - x[j] <= 0
model += z[z_ind[i][j]] + x[i] + x[j] <= 2
# Adding the objective function
model.objective = CyLPArray(w) * z
lp = CyClpSimplex(model)
lp.logLevel = 0
lp.optimizationDirection = 'max'
mip = lp.getCbcModel()
mip.logLevel = 0
# Setting number of threads
mip.numberThreads = num_threads
mip.solve()
return mip.objectiveValue, [int(i) for i in mip.primalVariableSolution['x']]
def solve_cylp(self, verbose: bool = True, **kwargs):
""" Inspired by the cvxpy cbc layer, ty :) """
from cylp.cy import CyClpSimplex
from cylp.py.modeling.CyLPModel import CyLPModel, CyLPArray
cons = self.combine_cons()
n = int(self.next_var_idx - 1) # Number of variables.
# Maximize c@x s.t. A@x <= b (variable bounds done by constraints)
c = self.objective.rawdense().squeeze()[
1:n + 1] # Objective coefficients, no constants.
A = cons.raw()[:, 1:n + 1] # Constraint coefficients.
b = cons[:, 0].rawdense().squeeze() * -1.0 # Constraint constants.
model = CyLPModel()
x = model.addVariable("x", n) # Variables
model.objective = c
# I hate this so much. Casting A to a matrix causes A.__mul__ to be
# be called, which raises NotImplemented, so then x.__rmul__ is called
# which gets the job done. Using np.matmul or np.dot doesn't
# trigger x.__rmul__
# model.addConstraint(np.matrix(A) * x <= CyLPArray(b)) # Works
model.addConstraint(x.__rmul__(A) <= CyLPArray(b))
model = CyClpSimplex(model) # Convert model
model.logLevel = 0 if not verbose else model.logLevel
is_integer_model = not np.isclose(self.int_vars.sum(), 0)
if is_integer_model:
model.setInteger(x[np.argwhere(self.int_vars)])
cbcModel = model.getCbcModel()
cbcModel.solve()
status = cbcModel.status
solmodel = cbcModel
else:
status = model.initialSolve()
solmodel = model
sol_x = np.hstack( # Pad back to original shape
(
[1.0], # Special constant 1.0 variable.
solmodel.primalVariableSolution["x"], # Actual solution
np.zeros(self.max_vars - n - 1), # Unused vars
))
solution = {
"status": status,
"primal": sol_x,
"value": solmodel.objectiveValue
}
return solution, solution["primal"]
def test_onlyBounds(self):
model = CyLPModel()
x = model.addVariable('x', 3)
y = model.addVariable('y', 2)
model += y >= 1
model += 2 <= x <= 4
c = CyLPArray([1., -2., 3.])
model.objective = c * x + 2 * y[0] + 2 * y[1]
s = CyClpSimplex(model)
s.primal()
sol = np.concatenate(
(s.primalVariableSolution['x'], s.primalVariableSolution['y']))
self.assertTrue((abs(sol - np.array([2, 4, 2, 1, 1])) <= 10**-6).all())
def test_onlyBounds(self):
model = CyLPModel()
x = model.addVariable('x', 3)
y = model.addVariable('y', 2)
model += y >= 1
model += 2 <= x <= 4
c = CyLPArray([1., -2., 3.])
model.objective = c * x + 2 * y[0] + 2 * y[1]
s = CyClpSimplex(model)
s.primal()
sol = np.concatenate((s.primalVariableSolution['x'],
s.primalVariableSolution['y']))
self.assertTrue((abs(sol -
np.array([2, 4, 2, 1, 1]) ) <= 10**-6).all())
def LP_solver_cylp(A_Matrix, B_vectors, weights, really_verbose=False):
"""
Solve the Linear Programming problem given in Giangrande et al, 2012 using
the CyLP module.
Parameters
----------
A_Matrix : matrix
Row augmented A matrix, see :py:func:`construct_A_matrix`
B_vectors : matrix
Matrix containing B vectors, see :py:func:`construct_B_vectors`
weights : array
Weights.
really_verbose : bool
True to print CLP messaging. False to suppress.
Returns
-------
soln : array
Solution to LP problem.
See Also
--------
LP_solver_cvxopt : Solve LP problem using the CVXOPT module.
LP_solver_pyglpk : Solve LP problem using the PyGLPK module.
"""
from cylp.cy.CyClpSimplex import CyClpSimplex
from cylp.py.modeling.CyLPModel import CyLPModel, CyLPArray
n_gates = weights.shape[1] // 2
n_rays = B_vectors.shape[0]
soln = np.zeros([n_rays, n_gates])
# Create CyLPModel and initialize it
model = CyLPModel()
G = np.matrix(A_Matrix)
h = CyLPArray(np.empty(B_vectors.shape[1]))
x = model.addVariable('x', G.shape[1])
model.addConstraint(G * x >= h)
#c = CyLPArray(np.empty(weights.shape[1]))
c = CyLPArray(np.squeeze(weights[0]))
model.objective = c * x
# import model in solver
s = CyClpSimplex(model)
# disable logging
if not really_verbose:
s.logLevel = 0
for raynum in range(n_rays):
# set new B_vector values for actual ray
s.setRowLowerArray(np.squeeze(np.asarray(B_vectors[raynum])))
# set new weights (objectives) for actual ray
#s.setObjectiveArray(np.squeeze(np.asarray(weights[raynum])))
# solve with dual method, it is faster
s.dual()
# extract primal solution
soln[raynum, :] = s.primalVariableSolution['x'][n_gates:2 * n_gates]
# apply smoothing filter on a per scan basis
soln = smooth_and_trim_scan(soln, window_len=5, window='sg_smooth')
return soln
def LP_solver_cylp_mp(A_Matrix,
B_vectors,
weights,
really_verbose=False,
proc=1):
"""
Solve the Linear Programming problem given in Giangrande et al, 2012 using
the CyLP module using multiple processes.
Parameters
----------
A_Matrix : matrix
Row augmented A matrix, see :py:func:`construct_A_matrix`
B_vectors : matrix
Matrix containing B vectors, see :py:func:`construct_B_vectors`
weights : array
Weights.
really_verbose : bool
True to print CLP messaging. False to suppress.
proc : int
Number of worker processes.
Returns
-------
soln : array
Solution to LP problem.
See Also
--------
LP_solver_cvxopt : Solve LP problem using the CVXOPT module.
LP_solver_pyglpk : Solve LP problem using the PyGLPK module.
LP_solver_cylp : Solve LP problem using the CyLP module using single
process.
"""
from cylp.cy.CyClpSimplex import CyClpSimplex
from cylp.py.modeling.CyLPModel import CyLPModel, CyLPArray
import multiprocessing as mp
n_gates = weights.shape[1] // 2
n_rays = B_vectors.shape[0]
soln = np.zeros([n_rays, n_gates])
# Create CyLPModel and initialize it
model = CyLPModel()
G = np.matrix(A_Matrix)
h = CyLPArray(np.empty(B_vectors.shape[1]))
x = model.addVariable('x', G.shape[1])
model.addConstraint(G * x >= h)
c = CyLPArray(np.empty(weights.shape[1]))
#c = CyLPArray(np.squeeze(weights[0]))
model.objective = c * x
chunksize = int(n_rays / proc)
# check if equal sized chunks can be distributed to worker processes
if n_rays % chunksize != 0:
print("Problem of %d rays cannot be split to %d worker processes!\n\r"
"Fallback to 1 process!" % (n_rays, proc))
chunksize = n_rays # fall back to one process
proc = 1
print("Calculating with %d processes, %d rays per chunk" %
(proc, chunksize))
def worker(model, B_vectors, weights, ray, chunksize, out_q):
"""
The worker function, invoked in a process.
The results are placed in a dictionary that's pushed to a queue.
"""
outdict = {}
iray = int(ray / chunksize)
outdict[iray] = solve_cylp(model, B_vectors, weights, ray, chunksize)
out_q.put(outdict)
# Queue for LP solutions
out_q = mp.Queue()
procs = []
# fire off worker processes
for raynum in range(0, n_rays, chunksize):
p = mp.Process(target=worker,
args=(model, B_vectors, weights, raynum, chunksize,
out_q))
procs.append(p)
p.start()
# collecting results
resultdict = {}
for raynum in range(0, n_rays, chunksize):
resultdict.update(out_q.get())
# Wait for all worker processes to finish
for p in procs:
p.join()
# copy results in output array
for raynum in range(0, int(n_rays / chunksize)):
soln[raynum * chunksize:raynum * chunksize +
chunksize, :] = (resultdict[raynum])
# apply smoothing filter to output array
soln = smooth_and_trim_scan(soln, window_len=5, window='sg_smooth')
return soln
def Single_Year_Stage_II(puf, Stage_I_factors, Stage_II_targets, year, tol):
length = len(puf.s006)
print("Preparing coefficient matrix...")
s006 = np.where(puf.e02400>0,
puf.s006*Stage_I_factors[year]["APOPSNR"]/100,
puf.s006*Stage_I_factors[year]["ARETS"]/100)
single_return = np.where((puf.mars==1) & (puf.filer==1), s006, 0)
joint_return = np.where(((puf.mars==2)|(puf.mars==3)) & (puf.filer==1), s006, 0)
hh_return = np.where((puf.mars==4) & (puf.filer==1),s006,0)
return_w_SS = np.where((puf.e02400>0) & (puf.filer==1),s006,0)
dependent_exempt_num = (puf.xocah+puf.xocawh+puf.xoodep+puf.xopar)*s006
interest = puf.e00300*s006
dividend = puf.e00600*s006
biz_income = np.where(puf.e00900>0, puf.e00900, 0)*s006
biz_loss = np.where(puf.e00900<0, -puf.e00900, 0)*s006
cap_gain = np.where((puf.p23250+puf.p22250)>0, (puf.p23250+puf.p22250), 0)*s006
annuity_pension = puf.e01700*s006
sch_e_income = np.where(puf.e02000>0, puf.e02000, 0)*s006
sch_e_loss = np.where(puf.e02000<0, -puf.e02000, 0)*s006
ss_income = puf.e02400*s006
unemployment_comp = puf.e02300*s006
# Wage distribution
wage_1 = np.where(puf.e00100<=0, puf.e00200,0)*s006
wage_2 = np.where((puf.e00100>0)&(puf.e00100<=10000), puf.e00200,0)*s006
wage_3 = np.where((puf.e00100>10000)&(puf.e00100<=20000), puf.e00200,0)*s006
wage_4 = np.where((puf.e00100>20000)&(puf.e00100<=30000), puf.e00200,0)*s006
wage_5 = np.where((puf.e00100>30000)&(puf.e00100<=40000), puf.e00200,0)*s006
wage_6 = np.where((puf.e00100>40000)&(puf.e00100<=50000), puf.e00200,0)*s006
wage_7 = np.where((puf.e00100>50000)&(puf.e00100<=75000), puf.e00200,0)*s006
wage_8 = np.where((puf.e00100>75000)&(puf.e00100<=100000), puf.e00200,0)*s006
wage_9 = np.where((puf.e00100>100000)&(puf.e00100<=200000), puf.e00200,0)*s006
wage_10 = np.where((puf.e00100>200000)&(puf.e00100<=500000), puf.e00200,0)*s006
wage_11 = np.where((puf.e00100>500000)&(puf.e00100<=1000000), puf.e00200,0)*s006
wage_12 = np.where((puf.e00100>1000000), puf.e00200,0)*s006
# Set up the matrix
One_half_LHS = np.vstack((single_return, joint_return, hh_return, return_w_SS,
dependent_exempt_num, interest, dividend,
biz_income,biz_loss, cap_gain, annuity_pension,
sch_e_income, sch_e_loss, ss_income, unemployment_comp,
wage_1, wage_2, wage_3, wage_4, wage_5, wage_6,
wage_7, wage_8, wage_9, wage_10, wage_11, wage_12))
# Coefficients for r and s
A1 = np.matrix(One_half_LHS)
A2 = np.matrix(-One_half_LHS)
print("Preparing targets for ", year)
APOPN = Stage_I_factors[year]["APOPN"]
b = []
b.append(Stage_II_targets[year]['Single Returns']-single_return.sum())
b.append(Stage_II_targets[year]['Joint Returns']-joint_return.sum())
b.append(Stage_II_targets[year]['Head of Household Returns']-hh_return.sum())
b.append(Stage_II_targets[year]['Number of Returns w/ Gross Security Income']-return_w_SS.sum())
b.append(Stage_II_targets[year]['Number of Dependent Exemptions'] - dependent_exempt_num.sum())
AINTS = Stage_I_factors[year]["AINTS"]
INTEREST = Stage_II_targets[year]['Taxable Interest Income']*APOPN/AINTS*1000-interest.sum()
ADIVS = Stage_I_factors[year]["ADIVS"]
DIVIDEND = Stage_II_targets[year]['Ordinary Dividends']*APOPN/ADIVS*1000 - dividend.sum()
ASCHCI = Stage_I_factors[year]["ASCHCI"]
BIZ_INCOME = Stage_II_targets[year]['Business Income (Schedule C)']*APOPN/ASCHCI*1000 - biz_income.sum()
ASCHCL = Stage_I_factors[year]["ASCHCL"]
BIZ_LOSS = Stage_II_targets[year]['Business Loss (Schedule C)']*APOPN/ASCHCL*1000 - biz_loss.sum()
ACGNS = Stage_I_factors[year]["ACGNS"]
CAP_GAIN = Stage_II_targets[year]['Net Capital Gains in AGI']*APOPN/ACGNS*1000 - cap_gain.sum()
ATXPY = Stage_I_factors[year]["ATXPY"]
ANNUITY_PENSION = Stage_II_targets[year]['Taxable Pensions and Annuities']*APOPN/ATXPY*1000 - annuity_pension.sum()
ASCHEI = Stage_I_factors[year]["ASCHEI"]
SCH_E_INCOME = Stage_II_targets[year]["Supplemental Income (Schedule E)"]*APOPN/ASCHEI*1000 - sch_e_income.sum()
ASCHEL = Stage_I_factors[year]["ASCHEL"]
SCH_E_LOSS = Stage_II_targets[year]["Supplemental Loss (Schedule E)"]*APOPN/ASCHEL*1000 - sch_e_loss.sum()
ASOCSEC = Stage_I_factors[year]["ASOCSEC"]
APOPSNR = Stage_I_factors[year]["APOPSNR"]
SS_INCOME = Stage_II_targets[year]["Gross Social Security Income"]*APOPSNR/ASOCSEC*1000 - ss_income.sum()
AUCOMP = Stage_I_factors[year]["AUCOMP"]
UNEMPLOYMENT_COMP = Stage_II_targets[year]["Unemployment Compensation"]*APOPN/AUCOMP*1000 - unemployment_comp.sum()
AWAGE = Stage_I_factors[year]["AWAGE"]
WAGE_1 = Stage_II_targets[year]["Wages and Salaries: Zero or Less"]*APOPN/AWAGE*1000 - wage_1.sum()
WAGE_2 = Stage_II_targets[year]["Wages and Salaries: $1 Less Than $10,000"]*APOPN/AWAGE*1000 - wage_2.sum()
WAGE_3 = Stage_II_targets[year]["Wages and Salaries: $10,000 Less Than $20,000"]*APOPN/AWAGE*1000 - wage_3.sum()
WAGE_4 = Stage_II_targets[year]["Wages and Salaries: $20,000 Less Than $30,000"]*APOPN/AWAGE*1000 - wage_4.sum()
WAGE_5 = Stage_II_targets[year]["Wages and Salaries: $30,000 Less Than $40,000"]*APOPN/AWAGE*1000 - wage_5.sum()
WAGE_6 = Stage_II_targets[year]["Wages and Salaries: $40,000 Less Than $50,000"]*APOPN/AWAGE*1000 - wage_6.sum()
WAGE_7 = Stage_II_targets[year]["Wages and Salaries: $50,000 Less Than $75,000"]*APOPN/AWAGE*1000 - wage_7.sum()
WAGE_8 = Stage_II_targets[year]["Wages and Salaries: $75,000 Less Than $100,000"]*APOPN/AWAGE*1000 - wage_8.sum()
WAGE_9 = Stage_II_targets[year]["Wages and Salaries: $100,000 Less Than $200,000"]*APOPN/AWAGE*1000 - wage_9.sum()
WAGE_10 = Stage_II_targets[year]["Wages and Salaries: $200,000 Less Than $500,000"]*APOPN/AWAGE*1000 - wage_10.sum()
WAGE_11 = Stage_II_targets[year]["Wages and Salaries: $500,000 Less Than $1 Million"]*APOPN/AWAGE*1000 - wage_11.sum()
WAGE_12 = Stage_II_targets[year]["Wages and Salaries: $1 Million and Over"]*APOPN/AWAGE*1000 - wage_12.sum()
temp = [INTEREST,DIVIDEND, BIZ_INCOME, BIZ_LOSS, CAP_GAIN, ANNUITY_PENSION, SCH_E_INCOME, SCH_E_LOSS, SS_INCOME, UNEMPLOYMENT_COMP,
WAGE_1,WAGE_2, WAGE_3,WAGE_4, WAGE_5, WAGE_6, WAGE_7,WAGE_8,WAGE_9, WAGE_10, WAGE_11, WAGE_12]
for m in temp:
b.append(m)
targets = CyLPArray(b)
print("Targets for year ", year, " is ", targets)
LP = CyLPModel()
r = LP.addVariable('r', length)
s = LP.addVariable('s', length)
print("Adding constraints")
LP.addConstraint(r >=0, "positive r")
LP.addConstraint(s >=0, "positive s")
LP.addConstraint(r + s <= tol, "abs upperbound")
c = CyLPArray((np.ones(length)))
LP.objective = c * r + c * s
LP.addConstraint(A1 * r + A2 * s == targets, "Aggregates")
print("Setting up the LP model")
model = CyClpSimplex(LP)
print("Solving LP......")
model.initialSolve()
print("DONE!!")
z = np.empty([length])
z = (1+model.primalVariableSolution['r'] - model.primalVariableSolution['s'])*s006 * 100
return z
def classical_maxkcut_solver(G, num_partitions, num_threads=4):
# G: NetworkX graph
# num_partitions: the number partitions or groups in which we should
# subdivide the nodes (i.e., the value of K)
N = len(G)
model = CyLPModel()
# Decision variables, one for each node
x = model.addVariable('x', num_partitions * N, isInt=True)
# Adjacency matrix (possibly weighted)
W = nx.to_numpy_matrix(G)
z_ind = dict()
ind = 0
w = []
for i in range(N):
j_range = range(N)
if (not nx.is_directed(G)):
# Reduced range for undirected graphs
j_range = range(i, N)
for j in j_range:
if (W[i, j] == 0):
continue
if (i not in z_ind):
z_ind[i] = dict()
z_ind[i][j] = ind
w.append(W[i, j])
ind += 1
# Aux variables, one for each edge
z = model.addVariable('z', len(w), isInt=True)
# Adding the box contraints
model += 0 <= x <= 1
model += 0 <= z <= 1
# Adding the selection constraints
for i in range(N):
indices = [i + k * N for k in range(num_partitions)]
model += x[indices].sum() == 1
# Adding the cutting constraints
for i in z_ind:
for j in z_ind[i]:
for k in range(num_partitions):
shift = k * N
model += z[z_ind[i][j]] + x[i + shift] + x[j + shift] <= 2
model += z[z_ind[i][j]] + x[i + shift] - x[j + shift] >= 0
model += z[z_ind[i][j]] - x[i + shift] + x[j + shift] >= 0
# Adding the objective function
model.objective = CyLPArray(w) * z
lp = CyClpSimplex(model)
lp.logLevel = 0
lp.optimizationDirection = 'max'
mip = lp.getCbcModel()
mip.logLevel = 0
# Setting number of threads
mip.numberThreads = num_threads
mip.solve()
sol = [int(i) for i in mip.primalVariableSolution['x']]
sol_formatted = []
for i in range(N):
indices = [i + k * N for k in range(num_partitions)]
for j in range(num_partitions):
if (sol[indices[j]] == 1):
sol_formatted.append(j)
break
assert (len(sol_formatted) == N)
return mip.objectiveValue, sol_formatted
def Single_Year_Stage_II(puf, Stage_I_factors, Stage_II_targets, year, tol):
length = len(puf.s006)
print("Preparing coefficient matrix...")
s006 = np.where(puf.e02400>0,
puf.s006*Stage_I_factors[year]["APOPSNR"]/100,
puf.s006*Stage_I_factors[year]["ARETS"]/100)
single_return = np.where(puf.mars==1, s006, 0)
joint_return = np.where((puf.mars==2)|(puf.mars==3), s006, 0)
hh_return = np.where(puf.mars==4,s006,0)
return_w_SS = np.where(puf.e02400>0,s006,0)
dependent_exempt_num = (puf.xocah+puf.xocawh+puf.xoodep+puf.xopar)*s006
interest = puf.e00300*s006
dividend = puf.e00600*s006
biz_income = np.where(puf.e00900>0, puf.e00900, 0)*s006
biz_loss = np.where(puf.e00900<0, -puf.e00900, 0)*s006
cap_gain = np.where(puf.e01000>0, puf.e01000, 0)*s006
annuity_pension = puf.e01700*s006
sch_e_income = np.where(puf.e02000>0, puf.e02000, 0)*s006
sch_e_loss = np.where(puf.e02000<0, -puf.e02000, 0)*s006
ss_income = puf.e02400*s006
unemployment_comp = puf.e02300*s006
# Wage distribution
wage_1 = np.where(puf.e00100<=0, puf.e00200,0)*s006
wage_2 = np.where((puf.e00100>0)&(puf.e00100<=10000), puf.e00200,0)*s006
wage_3 = np.where((puf.e00100>10000)&(puf.e00100<=20000), puf.e00200,0)*s006
wage_4 = np.where((puf.e00100>20000)&(puf.e00100<=30000), puf.e00200,0)*s006
wage_5 = np.where((puf.e00100>30000)&(puf.e00100<=40000), puf.e00200,0)*s006
wage_6 = np.where((puf.e00100>40000)&(puf.e00100<=50000), puf.e00200,0)*s006
wage_7 = np.where((puf.e00100>50000)&(puf.e00100<=75000), puf.e00200,0)*s006
wage_8 = np.where((puf.e00100>75000)&(puf.e00100<=100000), puf.e00200,0)*s006
wage_9 = np.where((puf.e00100>100000)&(puf.e00100<=200000), puf.e00200,0)*s006
wage_10 = np.where((puf.e00100>200000)&(puf.e00100<=500000), puf.e00200,0)*s006
wage_11 = np.where((puf.e00100>500000)&(puf.e00100<=1000000), puf.e00200,0)*s006
wage_12 = np.where((puf.e00100>1000000), puf.e00200,0)*s006
# Set up the matrix
One_half_LHS = np.vstack((single_return, joint_return, hh_return, return_w_SS,
dependent_exempt_num, interest, dividend,
biz_income,biz_loss, cap_gain, annuity_pension,
sch_e_income, sch_e_loss, ss_income, unemployment_comp,
wage_1, wage_2, wage_3, wage_4, wage_5, wage_6,
wage_7, wage_8, wage_9, wage_10, wage_11, wage_12))
# Coefficients for r and s
A1 = np.matrix(One_half_LHS)
A2 = np.matrix(-One_half_LHS)
print("Preparing targets for ", year)
APOPN = Stage_I_factors[year]["APOPN"]
b = []
b.append(Stage_II_targets[year]['Single']-single_return.sum())
b.append(Stage_II_targets[year]['Joint']-joint_return.sum())
b.append(Stage_II_targets[year]['HH']-hh_return.sum())
b.append(Stage_II_targets[year]['SS_return']-return_w_SS.sum())
b.append(Stage_II_targets[year]['Dep_return'] - dependent_exempt_num.sum())
AINTS = Stage_I_factors[year]["AINTS"]
INTEREST = Stage_II_targets[year]['INTS']*APOPN/AINTS*1000-interest.sum()
ADIVS = Stage_I_factors[year]["ADIVS"]
DIVIDEND = Stage_II_targets[year]['DIVS']*APOPN/ADIVS*1000 - dividend.sum()
ASCHCI = Stage_I_factors[year]["ASCHCI"]
BIZ_INCOME = Stage_II_targets[year]['SCHCI']*APOPN/ASCHCI*1000 - biz_income.sum()
ASCHCL = Stage_I_factors[year]["ASCHCL"]
BIZ_LOSS = Stage_II_targets[year]['SCHCL']*APOPN/ASCHCL*1000 - biz_loss.sum()
ACGNS = Stage_I_factors[year]["ACGNS"]
CAP_GAIN = Stage_II_targets[year]['CGNS']*APOPN/ACGNS*1000 - cap_gain.sum()
ATXPY = Stage_I_factors[year]["ATXPY"]
ANNUITY_PENSION = Stage_II_targets[year]['Pension']*APOPN/ATXPY*1000 - annuity_pension.sum()
ASCHEI = Stage_I_factors[year]["ASCHEI"]
SCH_E_INCOME = Stage_II_targets[year]["SCHEI"]*APOPN/ASCHEI*1000 - sch_e_income.sum()
ASCHEL = Stage_I_factors[year]["ASCHEL"]
SCH_E_LOSS = Stage_II_targets[year]["SCHEL"]*APOPN/ASCHEL*1000 - sch_e_loss.sum()
ASOCSEC = Stage_I_factors[year]["ASOCSEC"]
APOPSNR = Stage_I_factors[year]["APOPSNR"]
SS_INCOME = Stage_II_targets[year]["SS"]*APOPSNR/ASOCSEC*1000 - ss_income.sum()
AUCOMP = Stage_I_factors[year]["AUCOMP"]
UNEMPLOYMENT_COMP = Stage_II_targets[year]["UCOMP"]*APOPN/AUCOMP*1000 - unemployment_comp.sum()
AWAGE = Stage_I_factors[year]["AWAGE"]
WAGE_1 = Stage_II_targets[year]["WAGE_1"]*APOPN/AWAGE*1000 - wage_1.sum()
WAGE_2 = Stage_II_targets[year]["WAGE_2"]*APOPN/AWAGE*1000 - wage_2.sum()
WAGE_3 = Stage_II_targets[year]["WAGE_3"]*APOPN/AWAGE*1000 - wage_3.sum()
WAGE_4 = Stage_II_targets[year]["WAGE_4"]*APOPN/AWAGE*1000 - wage_4.sum()
WAGE_5 = Stage_II_targets[year]["WAGE_5"]*APOPN/AWAGE*1000 - wage_5.sum()
WAGE_6 = Stage_II_targets[year]["WAGE_6"]*APOPN/AWAGE*1000 - wage_6.sum()
WAGE_7 = Stage_II_targets[year]["WAGE_7"]*APOPN/AWAGE*1000 - wage_7.sum()
WAGE_8 = Stage_II_targets[year]["WAGE_8"]*APOPN/AWAGE*1000 - wage_8.sum()
WAGE_9 = Stage_II_targets[year]["WAGE_9"]*APOPN/AWAGE*1000 - wage_9.sum()
WAGE_10 = Stage_II_targets[year]["WAGE_10"]*APOPN/AWAGE*1000 - wage_10.sum()
WAGE_11 = Stage_II_targets[year]["WAGE_11"]*APOPN/AWAGE*1000 - wage_11.sum()
WAGE_12 = Stage_II_targets[year]["WAGE_12"]*APOPN/AWAGE*1000 - wage_12.sum()
temp = [INTEREST,DIVIDEND, BIZ_INCOME, BIZ_LOSS, CAP_GAIN, ANNUITY_PENSION, SCH_E_INCOME, SCH_E_LOSS, SS_INCOME, UNEMPLOYMENT_COMP,
WAGE_1,WAGE_2, WAGE_3,WAGE_4, WAGE_5, WAGE_6, WAGE_7,WAGE_8,WAGE_9, WAGE_10, WAGE_11, WAGE_12]
for m in temp:
b.append(m)
targets = CyLPArray(b)
print("Targets for year ", year, " is ", targets)
LP = CyLPModel()
r = LP.addVariable('r', length)
s = LP.addVariable('s', length)
print("Adding constraints")
LP.addConstraint(r >=0, "positive r")
LP.addConstraint(s >=0, "positive s")
LP.addConstraint(r + s <= tol, "abs upperbound")
c = CyLPArray((np.ones(length)))
LP.objective = c * r + c * s
LP.addConstraint(A1 * r + A2 * s == targets, "Aggregates")
print("Setting up the LP model")
model = CyClpSimplex(LP)
print("Solving LP......")
model.initialSolve()
print("DONE!!")
z = np.empty([length])
z = (1+model.primalVariableSolution['r'] - model.primalVariableSolution['s'])*s006
return z
def BranchAndBound(T, CONSTRAINTS, VARIABLES, OBJ, MAT, RHS,
branch_strategy=MOST_FRACTIONAL,
search_strategy=DEPTH_FIRST,
complete_enumeration=False,
display_interval=None,
binary_vars=True,
solver='dynamic',
rel_param=(4, 3, 1 / 6, 5),
more_return=False
):
"""
solver:
dynamic - initialSolve
primalSimplex - initialPrimalSolve
dualSimplex - initialDualSolve
Parameter Tuple for Reliability Branching
rel_param = (eta_rel,gamma,mu,lambda):
eta_rel = 0 - psesudocost branching
eta_rel = 1 - psesudocost branching with strong branching initialization
eta_rel = 4,8 - best performing reliability branching rules
eta_rel = inifity - strong branching
gamma - max number of simplex iterations in score calculation
mu - score factor, a number between 0 and 1. Paper uses 1/6
lambda - if max score is not updated for lambda
consecutive iterations, stop.
more_return:
False - return maximizer and max
True - also return a dict of stats(time, tree size, LP solved)
"""
ACTUAL_BRANCH_STRATEGY = branch_strategy
# reliability branching parameters
eta_rel, gamma, mu, lam = rel_param
# hybrid branching parameters
total_num_pivot = average_num_pivot = 0
# translate problems into cylp format
cyOBJ = CyLPArray([-val for val in OBJ.values()])
cyMAT = np.matrix([MAT[v] for v in VARIABLES]).T
cyRHS = CyLPArray(RHS)
OBJ = cyOBJ
MAT = cyMAT
RHS = cyRHS
if T.get_layout() == 'dot2tex':
cluster_attrs = {'name': 'Key', 'label': r'\text{Key}', 'fontsize': '12'}
T.add_node('C', label=r'\text{Candidate}', style='filled',
color='yellow', fillcolor='yellow')
T.add_node('I', label=r'\text{Infeasible}', style='filled',
color='orange', fillcolor='orange')
T.add_node('S', label=r'\text{Solution}', style='filled',
color='lightblue', fillcolor='lightblue')
T.add_node('P', label=r'\text{Pruned}', style='filled',
color='red', fillcolor='red')
T.add_node('PC', label=r'\text{Pruned}$\\ $\text{Candidate}', style='filled',
color='red', fillcolor='yellow')
else:
cluster_attrs = {'name': 'Key', 'label': 'Key', 'fontsize': '12'}
T.add_node('C', label='Candidate', style='filled',
color='yellow', fillcolor='yellow')
T.add_node('I', label='Infeasible', style='filled',
color='orange', fillcolor='orange')
T.add_node('S', label='Solution', style='filled',
color='lightblue', fillcolor='lightblue')
T.add_node('P', label='Pruned', style='filled',
color='red', fillcolor='red')
T.add_node('PC', label='Pruned \n Candidate', style='filled',
color='red', fillcolor='yellow')
T.add_edge('C', 'I', style='invisible', arrowhead='none')
T.add_edge('I', 'S', style='invisible', arrowhead='none')
T.add_edge('S', 'P', style='invisible', arrowhead='none')
T.add_edge('P', 'PC', style='invisible', arrowhead='none')
T.create_cluster(['C', 'I', 'S', 'P', 'PC'], cluster_attrs)
# The initial lower bound
LB = -INFINITY
# The number of LP's solved, and the number of nodes solved
node_count = 1
iter_count = 0
lp_count = 0 # The problems that are fully solved during
# Reliability and Hybrid branching is also couned here
# For reliability branching
half_solved = 0 # record number problems been halfly solved when calculate scores
full_solved = 0 # record number problems been fully solved when calculate scores
numVars = len(VARIABLES)
# List of incumbent solution variable values
opt = dict([(i, 0) for i in range(len(VARIABLES))])
pseudo_u = dict((i, (-OBJ[i], 0)) for i in range(len(VARIABLES)))
pseudo_d = dict((i, (-OBJ[i], 0)) for i in range(len(VARIABLES)))
print("===========================================")
print("Starting Branch and Bound")
if branch_strategy == MOST_FRACTIONAL:
print("Most fractional variable")
elif branch_strategy == FIXED_BRANCHING:
print("Fixed order")
elif branch_strategy == PSEUDOCOST_BRANCHING:
print("Pseudocost brancing")
elif branch_strategy == RELIABILITY_BRANCHING:
print("Reliability branching")
elif branch_strategy == HYBRID:
print('Hybrid strong/pseduocost branching')
else:
print("Unknown branching strategy %s" % branch_strategy)
if search_strategy == DEPTH_FIRST:
print("Depth first search strategy")
elif search_strategy == BEST_FIRST:
print("Best first search strategy")
elif search_strategy == BEST_ESTIMATE:
print("Best estimate search strategy")
else:
print("Unknown search strategy %s" % search_strategy)
print("===========================================")
# List of candidate nodes
Q = PriorityQueue()
# The current tree depth
cur_depth = 0
cur_index = 0
# Timer
timer = time.time()
Q.push(0, -INFINITY, (0, None, None, None, None, None, None))
# Branch and Bound Loop
while not Q.isEmpty():
# maximum allowed strong branch performed
if branch_strategy == HYBRID and cur_depth > max(int(len(VARIABLES) * 0.2), 5):
branch_strategy = PSEUDOCOST_BRANCHING
print("Switch from strong branch to psedocost branch")
infeasible = False
integer_solution = False
(cur_index, parent, relax, branch_var, branch_var_value, sense,
rhs) = Q.pop()
if cur_index is not 0:
cur_depth = T.get_node_attr(parent, 'level') + 1
else:
cur_depth = 0
print("")
print("----------------------------------------------------")
print("")
if LB > -INFINITY:
print("Node: %s, Depth: %s, LB: %s" % (cur_index, cur_depth, LB))
else:
print("Node: %s, Depth: %s, LB: %s" % (cur_index, cur_depth, "None"))
if relax is not None and relax <= LB:
print("Node pruned immediately by bound")
T.set_node_attr(parent, 'color', 'red')
continue
# ====================================
# LP Relaxation
# ====================================
# Compute lower bound by LP relaxation
prob = CyLPModel()
if binary_vars:
x = prob.addVariable('x', dim=len(VARIABLES))
prob += 0 <= x <= 1
else:
x = prob.addVariable('x', dim=len(VARIABLES))
prob.objective = OBJ * x
prob += MAT * x <= RHS
# Fix all prescribed variables
branch_vars = []
if cur_index is not 0:
sys.stdout.write("Branching variables: ")
branch_vars.append(branch_var)
if sense == '>=':
prob += x[branch_var] >= rhs
else:
prob += x[branch_var] <= rhs
print('x_{}'.format(branch_var), end=' ')
pred = parent
while not str(pred) == '0':
pred_branch_var = T.get_node_attr(pred, 'branch_var')
pred_rhs = T.get_node_attr(pred, 'rhs')
pred_sense = T.get_node_attr(pred, 'sense')
if pred_sense == '<=':
prob += x[pred_branch_var] <= pred_rhs
else:
prob += x[pred_branch_var] >= pred_rhs
print(pred_branch_var, end=' ')
branch_vars.append(pred_branch_var)
pred = T.get_node_attr(pred, 'parent')
print()
# Solve the LP relaxation
s = CyClpSimplex(prob)
if solver == 'primalSimplex':
s.initialPrimalSolve()
elif solver == 'dualSimplex':
s.initialDualSolve()
else:
s.initialSolve()
lp_count = lp_count + 1
total_num_pivot += s.iteration
average_num_pivot = total_num_pivot / lp_count
# Check infeasibility
# -1 - unknown e.g. before solve or if postSolve says not optimal
# 0 - optimal
# 1 - primal infeasible
# 2 - dual infeasible
# 3 - stopped on iterations or time
# 4 - stopped due to errors
# 5 - stopped by event handler (virtual int ClpEventHandler::event())
infeasible = (s.getStatusCode() in [1, 2])
# Print status
if infeasible:
print("LP Solved, status: Infeasible")
else:
print("LP Solved, status: %s, obj: %s" % (s.getStatusString(),
s.objectiveValue))
if(s.getStatusCode() == 0):
relax = -round(s.objectiveValue,7)
# Update pseudocost
if branch_var != None:
if sense == '<=':
pseudo_d[branch_var] = (
old_div((pseudo_d[branch_var][0] * pseudo_d[branch_var][1] +
old_div((T.get_node_attr(parent, 'obj') - relax),
(branch_var_value - rhs))),
(pseudo_d[branch_var][1] + 1)),
pseudo_d[branch_var][1] + 1)
else:
pseudo_u[branch_var] = (
old_div((pseudo_u[branch_var][0] * pseudo_d[branch_var][1] +
old_div((T.get_node_attr(parent, 'obj') - relax),
(rhs - branch_var_value))),
(pseudo_u[branch_var][1] + 1)),
pseudo_u[branch_var][1] + 1)
var_values = dict([(i, round(s.primalVariableSolution['x'][i],7))
for i in range(len(VARIABLES))])
integer_solution = 1
for i in range(len(VARIABLES)):
if (abs(round(var_values[i]) - var_values[i]) > .001):
integer_solution = 0
break
# Determine integer_infeasibility_count and
# Integer_infeasibility_sum for scatterplot and such
integer_infeasibility_count = 0
integer_infeasibility_sum = 0.0
for i in range(len(VARIABLES)):
if (var_values[i] not in set([0, 1])):
integer_infeasibility_count += 1
integer_infeasibility_sum += min([var_values[i],
1.0 - var_values[i]])
if (integer_solution and relax > LB):
LB = relax
for i in range(len(VARIABLES)):
# These two have different data structures first one
# list, second one dictionary
opt[i] = var_values[i]
print("New best solution found, objective: %s" % relax)
for i in range(len(VARIABLES)):
if var_values[i] > 0:
print("%s = %s" % (i, var_values[i]))
elif (integer_solution and relax <= LB):
print("New integer solution found, objective: %s" % relax)
for i in range(len(VARIABLES)):
if var_values[i] > 0:
print("%s = %s" % (i, var_values[i]))
else:
print("Fractional solution:")
for i in range(len(VARIABLES)):
if var_values[i] > 0:
print("x%s = %s" % (i, var_values[i]))
# For complete enumeration
if complete_enumeration:
relax = LB - 1
else:
relax = INFINITY
if integer_solution:
print("Integer solution")
BBstatus = 'S'
status = 'integer'
color = 'lightblue'
elif infeasible:
print("Infeasible node")
BBstatus = 'I'
status = 'infeasible'
color = 'orange'
elif not complete_enumeration and relax <= LB:
print("Node pruned by bound (obj: %s, UB: %s)" % (relax, LB))
BBstatus = 'P'
status = 'fathomed'
color = 'red'
elif cur_depth >= numVars:
print("Reached a leaf")
BBstatus = 'fathomed'
status = 'L'
else:
BBstatus = 'C'
status = 'candidate'
color = 'yellow'
if BBstatus is 'I':
if T.get_layout() == 'dot2tex':
label = '\text{I}'
else:
label = 'I'
else:
label = "%.1f" % relax
if iter_count == 0:
if status is not 'candidate':
integer_infeasibility_count = None
integer_infeasibility_sum = None
if status is 'fathomed':
if T._incumbent_value is None:
print('WARNING: Encountered "fathom" line before ' +
'first incumbent.')
T.AddOrUpdateNode(0, None, None, 'candidate', relax,
integer_infeasibility_count,
integer_infeasibility_sum,
label=label,
obj=relax, color=color,
style='filled', fillcolor=color)
if status is 'integer':
T._previous_incumbent_value = T._incumbent_value
T._incumbent_value = relax
T._incumbent_parent = -1
T._new_integer_solution = True
# #Currently broken
# if ETREE_INSTALLED and T.attr['display'] == 'svg':
# T.write_as_svg(filename = "node%d" % iter_count,
# nextfile = "node%d" % (iter_count + 1),
# highlight = cur_index)
else:
_direction = {'<=': 'L', '>=': 'R'}
if status is 'infeasible':
integer_infeasibility_count = T.get_node_attr(parent,
'integer_infeasibility_count')
integer_infeasibility_sum = T.get_node_attr(parent,
'integer_infeasibility_sum')
relax = T.get_node_attr(parent, 'lp_bound')
elif status is 'fathomed':
if T._incumbent_value is None:
print('WARNING: Encountered "fathom" line before' +
' first incumbent.')
print(' This may indicate an error in the input file.')
elif status is 'integer':
integer_infeasibility_count = None
integer_infeasibility_sum = None
T.AddOrUpdateNode(cur_index, parent, _direction[sense],
status, relax,
integer_infeasibility_count,
integer_infeasibility_sum,
branch_var=branch_var,
branch_var_value=var_values[branch_var],
sense=sense, rhs=rhs, obj=relax,
color=color, style='filled',
label=label, fillcolor=color)
if status is 'integer':
T._previous_incumbent_value = T._incumbent_value
T._incumbent_value = relax
T._incumbent_parent = parent
T._new_integer_solution = True
# Currently Broken
# if ETREE_INSTALLED and T.attr['display'] == 'svg':
# T.write_as_svg(filename = "node%d" % iter_count,
# prevfile = "node%d" % (iter_count - 1),
# nextfile = "node%d" % (iter_count + 1),
# highlight = cur_index)
if T.get_layout() == 'dot2tex':
_dot2tex_label = {'>=': ' \geq ', '<=': ' \leq '}
T.set_edge_attr(parent, cur_index, 'label',
str(branch_var) + _dot2tex_label[sense] +
str(rhs))
else:
T.set_edge_attr(parent, cur_index, 'label',
str(branch_var) + sense + str(rhs))
iter_count += 1
if BBstatus == 'C':
# Branching:
# Choose a variable for branching
branching_var = None
if branch_strategy == FIXED_BRANCHING:
# fixed order
for i in range(len(VARIABLES)):
frac = min(var_values[i] - math.floor(var_values[i]),
math.ceil(var_values[i]) - var_values[i])
if (frac > 0):
min_frac = frac
branching_var = i
# TODO(aykut): understand this break
break
elif branch_strategy == MOST_FRACTIONAL:
# most fractional variable
min_frac = -1
for i in range(len(VARIABLES)):
frac = min(var_values[i] - math.floor(var_values[i]),
math.ceil(var_values[i]) - var_values[i])
if (frac > min_frac):
min_frac = frac
branching_var = i
elif branch_strategy == PSEUDOCOST_BRANCHING:
scores = {}
for i in range(len(VARIABLES)):
# find the fractional solutions
if abs(var_values[i] - math.floor(var_values[i])) > 1e-8:
scores[i] = min(pseudo_u[i][0] * (math.ceil(var_values[i])
- var_values[i]),
pseudo_d[i][0] * (var_values[i]
- math.floor(var_values[i])))
# sort the dictionary by value
branching_var = sorted(list(scores.items()), key=lambda x: x[1])[-1][0]
elif branch_strategy == RELIABILITY_BRANCHING:
# Calculating Scores
# The algorithm in paper is different from the one in Grumpy
# I will try to use paper notations
scores = {}
for i in range(len(VARIABLES)):
# find the fractional solutions
if abs(var_values[i] - math.floor(var_values[i])) > 1e-8:
qp = pseudo_u[i][0] * (math.ceil(var_values[i])
- var_values[i]) # q^+
qm = pseudo_d[i][0] * (var_values[i]
- math.floor(var_values[i])) # q^^-
scores[i] = (1 - mu) * min(qm, qp) + mu * max(qm, qp)
# sort the dictionary by value
candidate_vars = [en[0] for en in sorted(list(scores.items()), key=lambda x: x[1], reverse=True)]
no_change = 0 # number of iterations that maximum of scores is not changed
smax = scores[candidate_vars[0]] # current maximum of scores
for i in candidate_vars:
if min(pseudo_d[i][1], pseudo_u[i][1]) < eta_rel:
qp = pseudo_u[i][0] * (math.ceil(var_values[i]) - var_values[i]) # q^+
qm = pseudo_d[i][0] * (var_values[i] - math.floor(var_values[i])) # q^^-
# left subproblem/down direction
s_left = CyClpSimplex(prob)
s_left += x[i] <= math.floor(var_values[i])
s_left.maxNumIteration = gamma # solve for fixed number of iterations
s_left.dual()
if s_left.getStatusCode() == 0:
qm = relax + s_left.objectiveValue # use a more reliable source to update q^-
full_solved = full_solved + 1
lp_count = lp_count + 1 # If the LP is fully solved, counter plus one
elif s_left.getStatusCode() == 3:
qm = relax + s_left.objectiveValue # use a more reliable source to update q^-
half_solved = half_solved + 1
# right subproblem/up direction
s_right = CyClpSimplex(prob)
s_right += x[i] >= math.ceil(var_values[i])
s_right.maxNumIteration = gamma # solve for fixed number of iterations
s_right.dual()
if s_right.getStatusCode() == 0:
qp = relax + s_right.objectiveValue # use a more reliable source to update q^+
full_solved = full_solved + 1
lp_count = lp_count + 1 # If the LP is fully solved, counter plus one
elif s_right.getStatusCode() == 3:
qp = relax + s_right.objectiveValue # use a more reliable source to update q^+
half_solved = half_solved + 1
scores[i] = (1 - mu) * min(qm, qp) + mu * max(qm, qp)
if (smax == scores[i]):
no_change += 1
elif (smax <= scores[i]):
no_change = 0
smax = scores[i]
else:
no_change = 0
if no_change >= lam:
break
branching_var = sorted(list(scores.items()), key=lambda x: x[1])[-1][0]
elif branch_strategy == HYBRID:
scores = {}
for i in range(len(VARIABLES)):
# find the fractional solutions
if abs(var_values[i] - math.floor(var_values[i])) > 1e-8:
scores[i] = min(pseudo_u[i][0] * (math.ceil(var_values[i])
- var_values[i]),
pseudo_d[i][0] * (var_values[i]
- math.floor(var_values[i])))
candidate_vars = [en[0] for en in sorted(list(scores.items()), key=lambda x: x[1], reverse=True)]
restricted_candidate_vars = candidate_vars[:max(1, int(0.5 * len(candidate_vars)))]
# print("Subset of candidate variables:")
# print(restricted_candidate_vars)
best_progress = 0
branch_candidate = None
for i in restricted_candidate_vars:
s = CyClpSimplex(prob)
s += math.floor(var_values[i]) <= x[i] <= math.ceil(var_values[i])
s.maxNumIteration = average_num_pivot * 2
s.dual()
if s.getStatusCode() == 0:
lp_count += 1
progress = relax - (-s.objectiveValue)
if (progress - best_progress) > 1e-8:
branch_candidate = i
best_progress = progress
if branch_candidate is None:
branch_candidate = restricted_candidate_vars[0]
branching_var = branch_candidate
else:
print("Unknown branching strategy %s" % branch_strategy)
exit()
if branching_var is not None:
print("Branching on variable %s" % branching_var)
# Create new nodes
if search_strategy == DEPTH_FIRST:
priority = (-cur_depth - 1, -cur_depth - 1)
elif search_strategy == BEST_FIRST:
priority = (-relax, -relax)
elif search_strategy == BEST_ESTIMATE:
priority = (-relax - pseudo_d[branching_var][0] *
(math.floor(var_values[branching_var]) - var_values[branching_var]),
-relax + pseudo_u[branching_var][0] *
(math.ceil(var_values[branching_var]) - var_values[branching_var]))
node_count += 1
Q.push(node_count, priority[0], (node_count, cur_index, relax, branching_var,
var_values[branching_var],
'<=', math.floor(var_values[branching_var])))
node_count += 1
Q.push(node_count, priority[1], (node_count, cur_index, relax, branching_var,
var_values[branching_var],
'>=', math.ceil(var_values[branching_var])))
T.set_node_attr(cur_index, color, 'green')
if T.root is not None and display_interval is not None and\
iter_count % display_interval == 0:
T.display(count=iter_count)
timer = int(math.ceil((time.time() - timer) * 1000))
print("")
print("===========================================")
print("Branch and bound completed in %sms" % timer)
print("Strategy: %s" % ACTUAL_BRANCH_STRATEGY)
if complete_enumeration:
print("Complete enumeration")
print("%s nodes visited " % node_count)
print("%s LP's solved" % lp_count)
print("===========================================")
print("Optimal solution")
# print optimal solution
for i in range(len(VARIABLES)):
if opt[i] > 0:
print("x%s = %s" % (i, opt[i]))
print("Objective function value")
print(LB)
print("===========================================")
if T.attr['display'] is not 'off':
T.display(count=iter_count)
T._lp_count = lp_count
if more_return:
stat = {'Time': timer, 'Size': node_count, 'LP Solved': lp_count}
if branch_strategy == RELIABILITY_BRANCHING:
stat['LP Solved for Bounds'] = lp_count - full_solved
stat['Halfly Solved'] = half_solved
stat['Fully Solved'] = full_solved
return opt, LB, stat
return opt, LB
def get_model_quality_estimate_clp(settings, n, k, node_pos, node_val,
num_iterations):
"""Compute an estimate of model quality using LPs with Clp.
Computes an estimate of model quality, performing
cross-validation. This version does not use all interpolation
nodes, but rather only the best num_iterations ones, and it uses a
sequence of LPs instead of a brute-force calculation. It should be
much faster than the brute-force calculation, as each LP in the
sequence requires only two pivots. The solver is COIN-OR Clp.
Parameters
----------
settings : :class:`rbfopt_settings.RbfSettings`
Global and algorithmic settings.
n : int
Dimension of the problem, i.e. the space where the point lives.
k : int
Number of nodes, i.e. interpolation points.
node_pos : 2D numpy.ndarray[float]
Location of current interpolation nodes (one on each row).
node_val : 1D numpy.ndarray[float]
List of values of the function at the nodes.
num_iterations : int
Number of nodes on which quality should be tested.
Returns
-------
float
An estimate of the leave-one-out cross-validation error, which
can be interpreted as a measure of model quality.
Raises
------
RuntimeError
If the LPs cannot be solved.
ValueError
If some settings are not supported.
"""
assert(isinstance(node_pos, np.ndarray))
assert(isinstance(node_val, np.ndarray))
assert(isinstance(settings, RbfSettings))
assert(len(node_val) == k)
assert(len(node_pos) == k)
assert(num_iterations <= k)
assert(cpx_available)
# We cannot find a leave-one-out interpolant if the following
# condition is not met.
assert(k > n + 1)
# Get size of polynomial part of the matrix (p) and sign of obj
# function (sign)
if (ru.get_degree_polynomial(settings) == 1):
p = n + 1
sign = 1
elif (ru.get_degree_polynomial(settings) == 0):
p = 1
sign = -1
else:
raise ValueError('RBF type ' + settings.rbf + ' not supported')
# Sort interpolation nodes by increasing objective function value
sorted_idx = node_val.argsort()
# Initialize the arrays used for the cross-validation
cv_node_pos = node_pos[sorted_idx]
cv_node_val = node_val[sorted_idx]
# Compute the RBF matrix, and the two submatrices of interest
Amat = ru.get_rbf_matrix(settings, n, k, cv_node_pos)
Phimat = Amat[:k, :k]
Pmat = Amat[:k, k:]
identity = np.matrix(np.identity(k))
# Instantiate model
model = CyLPModel()
# Add variables: lambda, h, slacks
rbf_lambda = model.addVariable('rbf_lambda', k)
rbf_h = model.addVariable('rbf_h', p)
slack = model.addVariable('slack', k)
# Add constraints: interpolation conditions, unisolvence
F = CyLPArray(cv_node_val)
zeros = CyLPArray([0] * p)
ones = CyLPArray([1] * p)
if (p > 1):
# We can use matrix form
model += (Phimat * rbf_lambda + Pmat * rbf_h + identity * slack == F)
model += (Pmat.transpose() * rbf_lambda == zeros)
else:
# Workaround for one dimensional variables: one row at a time
for i in range(k):
model += Phimat[i, :] * rbf_lambda + rbf_h + slack[i] == F[i]
model += (Pmat.transpose() * rbf_lambda == zeros)
# Add objective
obj = CyLPArray([sign*val for val in node_val])
model.objective = obj * rbf_lambda
# Create LP, suppress output, and set bounds
lp = clp.CyClpSimplex(model)
lp.logLevel = 0
infinity = lp.getCoinInfinity()
for i in range(k + p):
lp.setColumnLower(i, -infinity)
lp.setColumnUpper(i, infinity)
for i in range(k):
lp.setColumnLower(k + p + i, 0.0)
lp.setColumnUpper(k + p + i, 0.0)
# Estimate of the model error
loo_error = 0.0
for i in range(num_iterations):
# Fix lambda[i] to zero
lp.setColumnLower(i, 0.0)
lp.setColumnUpper(i, 0.0)
# Set slack[i] to unconstrained
lp.setColumnLower(k + p + i, -infinity)
lp.setColumnUpper(k + p + i, infinity)
lp.dual(startFinishOptions = 'sx')
if (not lp.getStatusCode() == 0):
raise RuntimeError('Could not solve LP with Clp, status ' +
lp.getStatusString())
lambda_sol = lp.primalVariableSolution['rbf_lambda'].tolist()
h_sol = lp.primalVariableSolution['rbf_h'].tolist()
# Compute value of the interpolant at the removed node
predicted_val = ru.evaluate_rbf(settings, cv_node_pos[i], n, k,
cv_node_pos, lambda_sol, h_sol)
# Update leave-one-out error
loo_error += abs(predicted_val - cv_node_val[i])
# Fix lambda[i] to zero
lp.setColumnLower(i, -infinity)
lp.setColumnUpper(i, infinity)
# Set slack[i] to unconstrained
lp.setColumnLower(k + p + i, 0.0)
lp.setColumnUpper(k + p + i, 0.0)
return loo_error/num_iterations
def LP_solver_cylp_mp(A_Matrix, B_vectors, weights, really_verbose=False,
proc=1):
"""
Solve the Linear Programming problem given in Giangrande et al, 2012 using
the CyLP module using multiple processes.
Parameters
----------
A_Matrix : matrix
Row augmented A matrix, see :py:func:`construct_A_matrix`
B_vectors : matrix
Matrix containing B vectors, see :py:func:`construct_B_vectors`
weights : array
Weights.
really_verbose : bool
True to print CLP messaging. False to suppress.
proc : int
Number of worker processes.
Returns
-------
soln : array
Solution to LP problem.
See Also
--------
LP_solver_cvxopt : Solve LP problem using the CVXOPT module.
LP_solver_pyglpk : Solve LP problem using the PyGLPK module.
LP_solver_cylp : Solve LP problem using the CyLP module using single
process.
"""
from cylp.cy.CyClpSimplex import CyClpSimplex
from cylp.py.modeling.CyLPModel import CyLPModel, CyLPArray
import multiprocessing as mp
n_gates = weights.shape[1] // 2
n_rays = B_vectors.shape[0]
soln = np.zeros([n_rays, n_gates])
# Create CyLPModel and initialize it
model = CyLPModel()
G = np.matrix(A_Matrix)
h = CyLPArray(np.empty(B_vectors.shape[1]))
x = model.addVariable('x', G.shape[1])
model.addConstraint(G * x >= h)
c = CyLPArray(np.empty(weights.shape[1]))
#c = CyLPArray(np.squeeze(weights[0]))
model.objective = c * x
chunksize = int(n_rays/proc)
# check if equal sized chunks can be distributed to worker processes
if n_rays % chunksize != 0:
print("Problem of %d rays cannot be split to %d worker processes!\n\r"
"Fallback to 1 process!" % (n_rays, proc))
chunksize = n_rays # fall back to one process
proc = 1
print("Calculating with %d processes, %d rays per chunk" %
(proc, chunksize))
def worker(model, B_vectors, weights, ray, chunksize, out_q):
"""
The worker function, invoked in a process.
The results are placed in a dictionary that's pushed to a queue.
"""
outdict = {}
iray = int(ray/chunksize)
outdict[iray] = solve_cylp(model, B_vectors, weights, ray, chunksize)
out_q.put(outdict)
# Queue for LP solutions
out_q = mp.Queue()
procs = []
# fire off worker processes
for raynum in range(0, n_rays, chunksize):
p = mp.Process(target=worker, args=(
model, B_vectors, weights, raynum, chunksize, out_q))
procs.append(p)
p.start()
# collecting results
resultdict = {}
for raynum in range(0, n_rays, chunksize):
resultdict.update(out_q.get())
# Wait for all worker processes to finish
for p in procs:
p.join()
# copy results in output array
for raynum in range(0, int(n_rays / chunksize)):
soln[raynum * chunksize:raynum * chunksize + chunksize, :] = (
resultdict[raynum])
# apply smoothing filter to output array
soln = smooth_and_trim_scan(soln, window_len=5, window='sg_smooth')
return soln
def solve_lp_for_year(puf, Stage_I_factors, Stage_II_targets, year, tol):
puf_length = len(puf.s006)
print("Preparing coefficient matrix for year {} .....".format(year))
s006 = np.where(puf.e02400 > 0,
puf.s006 * Stage_I_factors[year]["APOPSNR"] / 100,
puf.s006 * Stage_I_factors[year]["ARETS"] / 100)
single_return = np.where((puf.mars == 1) & (puf.filer == 1), s006, 0)
joint_return = np.where(
((puf.mars == 2) | (puf.mars == 3)) & (puf.filer == 1), s006, 0)
hh_return = np.where((puf.mars == 4) & (puf.filer == 1), s006, 0)
return_w_SS = np.where((puf.e02400 > 0) & (puf.filer == 1), s006, 0)
dependent_exempt_num = (puf.xocah + puf.xocawh + puf.xoodep +
puf.xopar) * s006
interest = puf.e00300 * s006
dividend = puf.e00600 * s006
biz_income = np.where(puf.e00900 > 0, puf.e00900, 0) * s006
biz_loss = np.where(puf.e00900 < 0, -puf.e00900, 0) * s006
cap_gain = np.where(
(puf.p23250 + puf.p22250) > 0, puf.p23250 + puf.p22250, 0) * s006
annuity_pension = puf.e01700 * s006
sch_e_income = np.where(puf.e02000 > 0, puf.e02000, 0) * s006
sch_e_loss = np.where(puf.e02000 < 0, -puf.e02000, 0) * s006
ss_income = np.where(puf.filer == 1, puf.e02400, 0) * s006
unemployment_comp = puf.e02300 * s006
# Wage distribution
wage_1 = np.where(puf.e00100 <= 0, puf.e00200, 0) * s006
wage_2 = np.where(
(puf.e00100 > 0) & (puf.e00100 <= 10000), puf.e00200, 0) * s006
wage_3 = np.where(
(puf.e00100 > 10000) & (puf.e00100 <= 20000), puf.e00200, 0) * s006
wage_4 = np.where(
(puf.e00100 > 20000) & (puf.e00100 <= 30000), puf.e00200, 0) * s006
wage_5 = np.where(
(puf.e00100 > 30000) & (puf.e00100 <= 40000), puf.e00200, 0) * s006
wage_6 = np.where(
(puf.e00100 > 40000) & (puf.e00100 <= 50000), puf.e00200, 0) * s006
wage_7 = np.where(
(puf.e00100 > 50000) & (puf.e00100 <= 75000), puf.e00200, 0) * s006
wage_8 = np.where(
(puf.e00100 > 75000) & (puf.e00100 <= 100000), puf.e00200, 0) * s006
wage_9 = np.where(
(puf.e00100 > 100000) & (puf.e00100 <= 200000), puf.e00200, 0) * s006
wage_10 = np.where(
(puf.e00100 > 200000) & (puf.e00100 <= 500000), puf.e00200, 0) * s006
wage_11 = np.where(
(puf.e00100 > 500000) & (puf.e00100 <= 1000000), puf.e00200, 0) * s006
wage_12 = np.where(puf.e00100 > 1000000, puf.e00200, 0) * s006
# Set up the matrix
One_half_LHS = np.vstack(
(single_return, joint_return, hh_return, return_w_SS,
dependent_exempt_num, interest, dividend, biz_income, biz_loss,
cap_gain, annuity_pension, sch_e_income, sch_e_loss, ss_income,
unemployment_comp, wage_1, wage_2, wage_3, wage_4, wage_5, wage_6,
wage_7, wage_8, wage_9, wage_10, wage_11, wage_12))
# Coefficients for r and s
A1 = np.matrix(One_half_LHS)
A2 = np.matrix(-One_half_LHS)
print("Preparing targets for year {} .....".format(year))
APOPN = Stage_I_factors[year]["APOPN"]
b = []
b.append(Stage_II_targets[year]["Single Returns"] - single_return.sum())
b.append(Stage_II_targets[year]["Joint Returns"] - joint_return.sum())
target_name = "Head of Household Returns"
b.append(Stage_II_targets[year][target_name] - hh_return.sum())
target_name = "Number of Returns w/ Gross Security Income"
b.append(Stage_II_targets[year][target_name] - return_w_SS.sum())
target_name = "Number of Dependent Exemptions"
b.append(Stage_II_targets[year][target_name] - dependent_exempt_num.sum())
AINTS = Stage_I_factors[year]["AINTS"]
INTEREST = (Stage_II_targets[year]["Taxable Interest Income"] * APOPN /
AINTS * 1000 - interest.sum())
ADIVS = Stage_I_factors[year]["ADIVS"]
DIVIDEND = (
Stage_II_targets[year]["Ordinary Dividends"] * APOPN / ADIVS * 1000 -
dividend.sum())
ASCHCI = Stage_I_factors[year]["ASCHCI"]
BIZ_INCOME = (Stage_II_targets[year]["Business Income (Schedule C)"] *
APOPN / ASCHCI * 1000 - biz_income.sum())
ASCHCL = Stage_I_factors[year]["ASCHCL"]
BIZ_LOSS = (Stage_II_targets[year]["Business Loss (Schedule C)"] * APOPN /
ASCHCL * 1000 - biz_loss.sum())
ACGNS = Stage_I_factors[year]["ACGNS"]
CAP_GAIN = (Stage_II_targets[year]["Net Capital Gains in AGI"] * APOPN /
ACGNS * 1000 - cap_gain.sum())
ATXPY = Stage_I_factors[year]["ATXPY"]
target_name = "Taxable Pensions and Annuities"
ANNUITY_PENSION = (
Stage_II_targets[year][target_name] * APOPN / ATXPY * 1000 -
annuity_pension.sum())
ASCHEI = Stage_I_factors[year]["ASCHEI"]
target_name = "Supplemental Income (Schedule E)"
SCH_E_INCOME = (
Stage_II_targets[year][target_name] * APOPN / ASCHEI * 1000 -
sch_e_income.sum())
ASCHEL = Stage_I_factors[year]["ASCHEL"]
SCH_E_LOSS = (Stage_II_targets[year]["Supplemental Loss (Schedule E)"] *
APOPN / ASCHEL * 1000 - sch_e_loss.sum())
ASOCSEC = Stage_I_factors[year]["ASOCSEC"]
APOPSNR = Stage_I_factors[year]["APOPSNR"]
SS_INCOME = (Stage_II_targets[year]["Gross Social Security Income"] *
APOPSNR / ASOCSEC * 1000 - ss_income.sum())
AUCOMP = Stage_I_factors[year]["AUCOMP"]
UNEMPLOYMENT_COMP = (Stage_II_targets[year]["Unemployment Compensation"] *
APOPN / AUCOMP * 1000 - unemployment_comp.sum())
AWAGE = Stage_I_factors[year]["AWAGE"]
target_name = "Wages and Salaries: Zero or Less"
WAGE_1 = (Stage_II_targets[year][target_name] * APOPN / AWAGE * 1000 -
wage_1.sum())
target_name = "Wages and Salaries: $1 Less Than $10,000"
WAGE_2 = (Stage_II_targets[year][target_name] * APOPN / AWAGE * 1000 -
wage_2.sum())
target_name = "Wages and Salaries: $10,000 Less Than $20,000"
WAGE_3 = (Stage_II_targets[year][target_name] * APOPN / AWAGE * 1000 -
wage_3.sum())
target_name = "Wages and Salaries: $20,000 Less Than $30,000"
WAGE_4 = (Stage_II_targets[year][target_name] * APOPN / AWAGE * 1000 -
wage_4.sum())
target_name = "Wages and Salaries: $30,000 Less Than $40,000"
WAGE_5 = (Stage_II_targets[year][target_name] * APOPN / AWAGE * 1000 -
wage_5.sum())
target_name = "Wages and Salaries: $40,000 Less Than $50,000"
WAGE_6 = (Stage_II_targets[year][target_name] * APOPN / AWAGE * 1000 -
wage_6.sum())
target_name = "Wages and Salaries: $50,000 Less Than $75,000"
WAGE_7 = (Stage_II_targets[year][target_name] * APOPN / AWAGE * 1000 -
wage_7.sum())
target_name = "Wages and Salaries: $75,000 Less Than $100,000"
WAGE_8 = (Stage_II_targets[year][target_name] * APOPN / AWAGE * 1000 -
wage_8.sum())
target_name = "Wages and Salaries: $100,000 Less Than $200,000"
WAGE_9 = (Stage_II_targets[year][target_name] * APOPN / AWAGE * 1000 -
wage_9.sum())
target_name = "Wages and Salaries: $200,000 Less Than $500,000"
WAGE_10 = (Stage_II_targets[year][target_name] * APOPN / AWAGE * 1000 -
wage_10.sum())
target_name = "Wages and Salaries: $500,000 Less Than $1 Million"
WAGE_11 = (Stage_II_targets[year][target_name] * APOPN / AWAGE * 1000 -
wage_11.sum())
target_name = "Wages and Salaries: $1 Million and Over"
WAGE_12 = (Stage_II_targets[year][target_name] * APOPN / AWAGE * 1000 -
wage_12.sum())
temp = [
INTEREST, DIVIDEND, BIZ_INCOME, BIZ_LOSS, CAP_GAIN, ANNUITY_PENSION,
SCH_E_INCOME, SCH_E_LOSS, SS_INCOME, UNEMPLOYMENT_COMP, WAGE_1, WAGE_2,
WAGE_3, WAGE_4, WAGE_5, WAGE_6, WAGE_7, WAGE_8, WAGE_9, WAGE_10,
WAGE_11, WAGE_12
]
for m in temp:
b.append(m)
targets = CyLPArray(b)
print("Targets for year {} are:".format(year))
print(targets)
LP = CyLPModel()
r = LP.addVariable("r", puf_length)
s = LP.addVariable("s", puf_length)
print("Adding constraints for year {} .....".format(year))
LP.addConstraint(r >= 0, "positive r")
LP.addConstraint(s >= 0, "positive s")
LP.addConstraint(r + s <= tol, "abs upperbound")
c = CyLPArray((np.ones(puf_length)))
LP.objective = c * r + c * s
LP.addConstraint(A1 * r + A2 * s == targets, "Aggregates")
print("Setting up the LP model for year {} .....".format(year))
model = CyClpSimplex(LP)
print("Solving LP for year {} .....".format(year))
model.initialSolve()
print("DONE solving LP for year {}".format(year))
z = np.empty([puf_length])
z = (1.0 + model.primalVariableSolution["r"] -
model.primalVariableSolution["s"]) * s006 * 100
return z
def BranchAndBoundCylp(T, CONSTRAINTS, VARIABLES, OBJ, MAT, RHS,
branch_strategy=MOST_FRACTIONAL,
search_strategy=DEPTH_FIRST,
complete_enumeration=False,
display_interval=None,
binary_vars=True):
if T.get_layout() == 'dot2tex':
cluster_attrs = {'name':'Key', 'label':r'\text{Key}', 'fontsize':'12'}
T.add_node('C', label = r'\text{Candidate}', style = 'filled',
color = 'yellow', fillcolor = 'yellow')
T.add_node('I', label = r'\text{Infeasible}', style = 'filled',
color = 'orange', fillcolor = 'orange')
T.add_node('S', label = r'\text{Solution}', style = 'filled',
color = 'lightblue', fillcolor = 'lightblue')
T.add_node('P', label = r'\text{Pruned}', style = 'filled',
color = 'red', fillcolor = 'red')
T.add_node('PC', label = r'\text{Pruned}$\\ $\text{Candidate}', style = 'filled',
color = 'red', fillcolor = 'yellow')
else:
cluster_attrs = {'name':'Key', 'label':'Key', 'fontsize':'12'}
T.add_node('C', label = 'Candidate', style = 'filled',
color = 'yellow', fillcolor = 'yellow')
T.add_node('I', label = 'Infeasible', style = 'filled',
color = 'orange', fillcolor = 'orange')
T.add_node('S', label = 'Solution', style = 'filled',
color = 'lightblue', fillcolor = 'lightblue')
T.add_node('P', label = 'Pruned', style = 'filled',
color = 'red', fillcolor = 'red')
T.add_node('PC', label = 'Pruned \n Candidate', style = 'filled',
color = 'red', fillcolor = 'yellow')
T.add_edge('C', 'I', style = 'invisible', arrowhead = 'none')
T.add_edge('I', 'S', style = 'invisible', arrowhead = 'none')
T.add_edge('S', 'P', style = 'invisible', arrowhead = 'none')
T.add_edge('P', 'PC', style = 'invisible', arrowhead = 'none')
T.create_cluster(['C', 'I', 'S', 'P', 'PC'], cluster_attrs)
# Change to CyLP format
cyOBJ = CyLPArray([-val for val in OBJ.values()]) # CyLP takes min
cyMAT = np.matrix([MAT[v] for v in VARIABLES]).T
cyRHS = CyLPArray(RHS)
# The initial lower bound
LB = -INFINITY
# The number of LP's solved, and the number of nodes solved
node_count = 1
iter_count = 0
lp_count = 0
numCons = len(CONSTRAINTS)
numVars = len(VARIABLES)
# List of incumbent solution variable values
opt = dict([(i, 0) for i in VARIABLES])
pseudo_u = dict((i, (OBJ[i], 0)) for i in VARIABLES)
pseudo_d = dict((i, (OBJ[i], 0)) for i in VARIABLES)
print("===========================================")
print("Starting Branch and Bound")
if branch_strategy == MOST_FRACTIONAL:
print("Most fractional variable")
elif branch_strategy == FIXED_BRANCHING:
print("Fixed order")
elif branch_strategy == PSEUDOCOST_BRANCHING:
print("Pseudocost brancing")
else:
print("Unknown branching strategy %s" %branch_strategy)
if search_strategy == DEPTH_FIRST:
print("Depth first search strategy")
elif search_strategy == BEST_FIRST:
print("Best first search strategy")
else:
print("Unknown search strategy %s" %search_strategy)
print("===========================================")
# List of candidate nodes
Q = PriorityQueue()
# The current tree depth
cur_depth = 0
cur_index = 0
# Timer
timer = time.time()
Q.push(0, -INFINITY, (0, None, None, None, None, None, None))
# Branch and Bound Loop
while not Q.isEmpty():
infeasible = False
integer_solution = False
(cur_index, parent, relax, branch_var, branch_var_value, sense,
rhs) = Q.pop()
if cur_index is not 0:
cur_depth = T.get_node_attr(parent, 'level') + 1
else:
cur_depth = 0
print("")
print("----------------------------------------------------")
print("")
if LB > -INFINITY:
print("Node: %s, Depth: %s, LB: %s" %(cur_index,cur_depth,LB))
else:
print("Node: %s, Depth: %s, LB: %s" %(cur_index,cur_depth,"None"))
if relax is not None and relax <= LB:
print("Node pruned immediately by bound")
T.set_node_attr(parent, 'color', 'red')
continue
#====================================
# LP Relaxation
#====================================
# Compute lower bound by LP relaxation
prob = CyLPModel()
# CyLP do not allow change variable object without model
if binary_vars:
var = prob.addVariable('x', dim=len(VARIABLES))
prob += 0 <= var <= 1
else:
var = prob.addVariable('x', dim=len(VARIABLES))
prob += 0 <= var # To avoid random generated problems be unbounded
prob += cyMAT * var <= RHS
prob.objective = cyOBJ * var
s = CyClpSimplex(prob)
# Fix all prescribed variables
branch_vars = []
if cur_index is not 0:
sys.stdout.write("Branching variables: ")
branch_vars.append(branch_var)
if sense == '>=':
prob += var[int(branch_var[1:])] >= rhs # slice the name for index
else:
prob += var[int(branch_var[1:])] <= rhs # slice the name for index
print(branch_var, end=' ')
pred = parent
while not str(pred) == '0':
pred_branch_var = T.get_node_attr(pred, 'branch_var')
pred_rhs = T.get_node_attr(pred, 'rhs')
pred_sense = T.get_node_attr(pred, 'sense')
if pred_sense == '<=':
prob += var[int(pred_branch_var[1:])] <= pred_rhs
else:
prob += var[int(pred_branch_var[1:])] >= pred_rhs
print(pred_branch_var, end=' ')
branch_vars.append(pred_branch_var)
pred = T.get_node_attr(pred, 'parent')
print()
# Solve the LP relaxation
s = CyClpSimplex(prob)
s.initialSolve()
lp_count = lp_count +1
if (s.getStatusCode() < 0):
print('%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%')
print(lp_count)
print(s.getStatusCode())
print(s.primal())
print(s.objectiveValue)
print(s.primalVariableSolution)
print('%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%')
# Check infeasibility
#-1 - unknown e.g. before solve or if postSolve says not optimal
#0 - optimal
#1 - primal infeasible
#2 - dual infeasible
#3 - stopped on iterations or time
#4 - stopped due to errors
#5 - stopped by event handler (virtual int ClpEventHandler::event())
infeasible = (s.getStatusCode() in [-1,1,3,4,5])
# Print status
if infeasible:
print("LP Solved, status: Infeasible")
else:
print("LP Solved, status: %s, obj: %s" %(s.getStatusString(),-s.objectiveValue))
if(s.getStatusCode() == 0):
relax = -s.objectiveValue
# Update pseudocost
if branch_var != None:
if sense == '<=':
pseudo_d[branch_var] = (
old_div((pseudo_d[branch_var][0]*pseudo_d[branch_var][1] +
old_div((T.get_node_attr(parent, 'obj') - relax),
(branch_var_value - rhs))),(pseudo_d[branch_var][1]+1)),
pseudo_d[branch_var][1]+1)
else:
pseudo_u[branch_var] = (
old_div((pseudo_u[branch_var][0]*pseudo_d[branch_var][1] +
old_div((T.get_node_attr(parent, 'obj') - relax),
(rhs - branch_var_value))),(pseudo_u[branch_var][1]+1)),
pseudo_u[branch_var][1]+1)
var_values = dict([(i, s.primalVariableSolution['x'][int(i[1:])]) for i in VARIABLES])
integer_solution = 1
for i in VARIABLES:
if (abs(round(var_values[i]) - var_values[i]) > .001):
integer_solution = 0
break
# Determine integer_infeasibility_count and
# Integer_infeasibility_sum for scatterplot and such
integer_infeasibility_count = 0
integer_infeasibility_sum = 0.0
for i in VARIABLES:
if (var_values[i] not in set([0,1])):
integer_infeasibility_count += 1
integer_infeasibility_sum += min([var_values[i],
1.0-var_values[i]])
if (integer_solution and relax>LB):
LB = relax
for i in VARIABLES:
# These two have different data structures first one
#list, second one dictionary
opt[i] = var_values[i]
print("New best solution found, objective: %s" %relax)
for i in VARIABLES:
if var_values[i] > 0:
print("%s = %s" %(i, var_values[i]))
elif (integer_solution and relax<=LB):
print("New integer solution found, objective: %s" %relax)
for i in VARIABLES:
if var_values[i] > 0:
print("%s = %s" %(i, var_values[i]))
else:
print("Fractional solution:")
for i in VARIABLES:
if var_values[i] > 0:
print("%s = %s" %(i, var_values[i]))
#For complete enumeration
if complete_enumeration:
relax = LB - 1
else:
relax = INFINITY
if integer_solution:
print("Integer solution")
BBstatus = 'S'
status = 'integer'
color = 'lightblue'
elif infeasible:
print("Infeasible node")
BBstatus = 'I'
status = 'infeasible'
color = 'orange'
elif not complete_enumeration and relax <= LB:
print("Node pruned by bound (obj: %s, UB: %s)" %(relax,LB))
BBstatus = 'P'
status = 'fathomed'
color = 'red'
elif cur_depth >= numVars :
print("Reached a leaf")
BBstatus = 'fathomed'
status = 'L'
else:
BBstatus = 'C'
status = 'candidate'
color = 'yellow'
if BBstatus is 'I':
if T.get_layout() == 'dot2tex':
label = '\text{I}'
else:
label = 'I'
else:
label = "%.1f"%relax
if iter_count == 0:
if status is not 'candidate':
integer_infeasibility_count = None
integer_infeasibility_sum = None
if status is 'fathomed':
if T._incumbent_value is None:
print('WARNING: Encountered "fathom" line before '+\
'first incumbent.')
T.AddOrUpdateNode(0, None, None, 'candidate', relax,
integer_infeasibility_count,
integer_infeasibility_sum,
label = label,
obj = relax, color = color,
style = 'filled', fillcolor = color)
if status is 'integer':
T._previous_incumbent_value = T._incumbent_value
T._incumbent_value = relax
T._incumbent_parent = -1
T._new_integer_solution = True
# #Currently broken
# if ETREE_INSTALLED and T.attr['display'] == 'svg':
# T.write_as_svg(filename = "node%d" % iter_count,
# nextfile = "node%d" % (iter_count + 1),
# highlight = cur_index)
else:
_direction = {'<=':'L', '>=':'R'}
if status is 'infeasible':
integer_infeasibility_count = T.get_node_attr(parent,
'integer_infeasibility_count')
integer_infeasibility_sum = T.get_node_attr(parent,
'integer_infeasibility_sum')
relax = T.get_node_attr(parent, 'lp_bound')
elif status is 'fathomed':
if T._incumbent_value is None:
print('WARNING: Encountered "fathom" line before'+\
' first incumbent.')
print(' This may indicate an error in the input file.')
elif status is 'integer':
integer_infeasibility_count = None
integer_infeasibility_sum = None
T.AddOrUpdateNode(cur_index, parent, _direction[sense],\
status, relax,\
integer_infeasibility_count,\
integer_infeasibility_sum,\
branch_var = branch_var,\
branch_var_value = var_values[branch_var],\
sense = sense, rhs = rhs, obj = relax,\
color = color, style = 'filled',\
label = label, fillcolor = color)
if status is 'integer':
T._previous_incumbent_value = T._incumbent_value
T._incumbent_value = relax
T._incumbent_parent = parent
T._new_integer_solution = True
# Currently Broken
# if ETREE_INSTALLED and T.attr['display'] == 'svg':
# T.write_as_svg(filename = "node%d" % iter_count,
# prevfile = "node%d" % (iter_count - 1),
# nextfile = "node%d" % (iter_count + 1),
# highlight = cur_index)
if T.get_layout() == 'dot2tex':
_dot2tex_label = {'>=':' \geq ', '<=':' \leq '}
T.set_edge_attr(parent, cur_index, 'label',\
str(branch_var) + _dot2tex_label[sense] +\
str(rhs))
else:
T.set_edge_attr(parent, cur_index, 'label',\
str(branch_var) + sense + str(rhs))
iter_count += 1
if BBstatus == 'C':
# Branching:
# Choose a variable for branching
branching_var = None
if branch_strategy == FIXED_BRANCHING:
#fixed order
for i in VARIABLES:
frac = min(s.primalVariableSolution['x'][int(i[1:])]-math.floor(s.primalVariableSolution['x'][int(i[1:])]),\
math.ceil(s.primalVariableSolution['x'][int(i[1:])]) - s.primalVariableSolution['x'][int(i[1:])])
if (frac > 0):
min_frac = frac
branching_var = i
# TODO(aykut): understand this break
break
elif branch_strategy == MOST_FRACTIONAL:
#most fractional variable
min_frac = -1
for i in VARIABLES:
frac = min(s.primalVariableSolution['x'][int(i[1:])]-math.floor(s.primalVariableSolution['x'][int(i[1:])]),\
math.ceil(s.primalVariableSolution['x'][int(i[1:])])- s.primalVariableSolution['x'][int(i[1:])])
if (frac> min_frac):
min_frac = frac
branching_var = i
elif branch_strategy == PSEUDOCOST_BRANCHING:
scores = {}
for i in VARIABLES:
# find the fractional solutions
if (s.primalVariableSolution['x'][int(i[1:])] - math.floor(s.primalVariableSolution['x'][int(i[1:])])) != 0:
scores[i] = min(pseudo_u[i][0]*(1-s.primalVariableSolution['x'][int(i[1:])]),\
pseudo_d[i][0]*s.primalVariableSolution['x'][int(i[1:])])
# sort the dictionary by value
branching_var = sorted(list(scores.items()),
key=lambda x : x[1])[-1][0]
else:
print("Unknown branching strategy %s" %branch_strategy)
exit()
if branching_var is not None:
print("Branching on variable %s" %branching_var)
#Create new nodes
if search_strategy == DEPTH_FIRST:
priority = (-cur_depth - 1, -cur_depth - 1)
elif search_strategy == BEST_FIRST:
priority = (-relax, -relax)
elif search_strategy == BEST_ESTIMATE:
priority = (-relax - pseudo_d[branching_var][0]*\
(math.floor(s.primalVariableSolution['x'][int(branching_var[1:])]) -\
s.primalVariableSolution['x'][int(branching_var[1:])]),\
-relax + pseudo_u[branching_var][0]*\
(math.ceil(s.primalVariableSolution['x'][int(branching_var[1:])]) -\
s.primalVariableSolution['x'][int(branching_var[1:])]))
node_count += 1
Q.push(node_count, priority[0], (node_count, cur_index, relax, branching_var,
var_values[branching_var],
'<=', math.floor(s.primalVariableSolution['x'][int(branching_var[1:])])))
node_count += 1
Q.push(node_count, priority[1], (node_count, cur_index, relax, branching_var,
var_values[branching_var],
'>=', math.ceil(s.primalVariableSolution['x'][int(branching_var[1:])])))
T.set_node_attr(cur_index, color, 'green')
if T.root is not None and display_interval is not None and\
iter_count%display_interval == 0:
T.display(count=iter_count)
timer = int(math.ceil((time.time()-timer)*1000))
print("")
print("===========================================")
print("Branch and bound completed in %sms" %timer)
print("Strategy: %s" %branch_strategy)
if complete_enumeration:
print("Complete enumeration")
print("%s nodes visited " %node_count)
print("%s LP's solved" %lp_count)
print("===========================================")
print("Optimal solution")
#print optimal solution
for i in sorted(VARIABLES):
if opt[i] > 0:
print("%s = %s" %(i, opt[i]))
print("Objective function value")
print(LB)
print("===========================================")
if T.attr['display'] is not 'off':
T.display(count=iter_count)
T._lp_count = lp_count
return LB,opt
def LP_solver_cylp(A_Matrix, B_vectors, weights, really_verbose=False):
"""
Solve the Linear Programming problem given in Giangrande et al, 2012 using
the CyLP module.
Parameters
----------
A_Matrix : matrix
Row augmented A matrix, see :py:func:`construct_A_matrix`
B_vectors : matrix
Matrix containing B vectors, see :py:func:`construct_B_vectors`
weights : array
Weights.
really_verbose : bool
True to print CLP messaging. False to suppress.
Returns
-------
soln : array
Solution to LP problem.
See Also
--------
LP_solver_cvxopt : Solve LP problem using the CVXOPT module.
LP_solver_pyglpk : Solve LP problem using the PyGLPK module.
"""
from cylp.cy.CyClpSimplex import CyClpSimplex
from cylp.py.modeling.CyLPModel import CyLPModel, CyLPArray
n_gates = weights.shape[1] // 2
n_rays = B_vectors.shape[0]
soln = np.zeros([n_rays, n_gates])
# Create CyLPModel and initialize it
model = CyLPModel()
G = np.matrix(A_Matrix)
h = CyLPArray(np.empty(B_vectors.shape[1]))
x = model.addVariable('x', G.shape[1])
model.addConstraint(G * x >= h)
#c = CyLPArray(np.empty(weights.shape[1]))
c = CyLPArray(np.squeeze(weights[0]))
model.objective = c * x
# import model in solver
s = CyClpSimplex(model)
# disable logging
if not really_verbose:
s.logLevel = 0
for raynum in range(n_rays):
# set new B_vector values for actual ray
s.setRowLowerArray(np.squeeze(np.asarray(B_vectors[raynum])))
# set new weights (objectives) for actual ray
#s.setObjectiveArray(np.squeeze(np.asarray(weights[raynum])))
# solve with dual method, it is faster
s.dual()
# extract primal solution
soln[raynum, :] = s.primalVariableSolution['x'][n_gates: 2 * n_gates]
# apply smoothing filter on a per scan basis
soln = smooth_and_trim_scan(soln, window_len=5, window='sg_smooth')
return soln
def solve_via_data(self, data, warm_start, verbose, solver_opts, solver_cache=None):
# Import basic modelling tools of cylp
from cylp.cy import CyClpSimplex
from cylp.py.modeling.CyLPModel import CyLPModel, CyLPArray
c = data[s.C]
b = data[s.B]
A = data[s.A]
dims = dims_to_solver_dict(data[s.DIMS])
n = c.shape[0]
# Problem
model = CyLPModel()
# Variables
x = model.addVariable('x', n)
# Constraints
# eq
model += A[0:dims[s.EQ_DIM], :] * x == CyLPArray(b[0:dims[s.EQ_DIM]])
# leq
leq_start = dims[s.EQ_DIM]
leq_end = dims[s.EQ_DIM] + dims[s.LEQ_DIM]
model += A[leq_start:leq_end, :] * x <= CyLPArray(b[leq_start:leq_end])
# Objective
model.objective = c
# Convert model
model = CyClpSimplex(model)
# No boolean vars available in Cbc -> model as int + restrict to [0,1]
if data[s.BOOL_IDX] or data[s.INT_IDX]:
# Mark integer- and binary-vars as "integer"
model.setInteger(x[data[s.BOOL_IDX]])
model.setInteger(x[data[s.INT_IDX]])
# Restrict binary vars only
idxs = data[s.BOOL_IDX]
n_idxs = len(idxs)
model.setColumnLowerSubset(np.arange(n_idxs, dtype=np.int32),
np.array(idxs, np.int32),
np.zeros(n_idxs))
model.setColumnUpperSubset(np.arange(n_idxs, dtype=np.int32),
np.array(idxs, np.int32),
np.ones(n_idxs))
# Verbosity Clp
if not verbose:
model.logLevel = 0
# Build model & solve
status = None
if data[s.BOOL_IDX] or data[s.INT_IDX]:
# Convert model
cbcModel = model.getCbcModel()
for key, value in solver_opts.items():
setattr(cbcModel, key, value)
# Verbosity Cbc
if not verbose:
cbcModel.logLevel = 0
# cylp: /cylp/cy/CyCbcModel.pyx#L134
# Call CbcMain. Solve the problem using the same parameters used by
# CbcSolver. Equivalent to solving the model from the command line
# using cbc's binary.
cbcModel.solve()
status = cbcModel.status
else:
# cylp: /cylp/cy/CyClpSimplex.pyx
# Run CLP's initialSolve. It does a presolve and uses primal or dual
# Simplex to solve a problem.
status = model.initialSolve()
solution = {}
if data[s.BOOL_IDX] or data[s.INT_IDX]:
solution["status"] = self.STATUS_MAP_MIP[status]
solution["primal"] = cbcModel.primalVariableSolution['x']
solution["value"] = cbcModel.objectiveValue
else:
solution["status"] = self.STATUS_MAP_LP[status]
solution["primal"] = model.primalVariableSolution['x']
solution["value"] = model.objectiveValue
return solution
def solve(self, objective, constraints, cached_data,
warm_start, verbose, solver_opts):
"""Returns the result of the call to the solver.
Parameters
----------
objective : LinOp
The canonicalized objective.
constraints : list
The list of canonicalized cosntraints.
cached_data : dict
A map of solver name to cached problem data.
warm_start : bool
Not used.
verbose : bool
Should the solver print output?
solver_opts : dict
Additional arguments for the solver.
Returns
-------
tuple
(status, optimal value, primal, equality dual, inequality dual)
"""
# Import basic modelling tools of cylp
from cylp.cy import CyClpSimplex
from cylp.py.modeling.CyLPModel import CyLPModel, CyLPArray
# Get problem data
data = self.get_problem_data(objective, constraints, cached_data)
c = data[s.C]
b = data[s.B]
A = data[s.A]
dims = data[s.DIMS]
data[s.BOOL_IDX] = solver_opts[s.BOOL_IDX]
data[s.INT_IDX] = solver_opts[s.INT_IDX]
n = c.shape[0]
# Problem
model = CyLPModel()
# Variables
x = model.addVariable('x', n)
# Constraints
# eq
model += A[0:dims[s.EQ_DIM], :] * x == CyLPArray(b[0:dims[s.EQ_DIM]])
# leq
leq_start = dims[s.EQ_DIM]
leq_end = dims[s.EQ_DIM] + dims[s.LEQ_DIM]
model += A[leq_start:leq_end, :] * x <= CyLPArray(b[leq_start:leq_end])
# Objective
model.objective = c
# Convert model
model = CyClpSimplex(model)
# No boolean vars available in Cbc -> model as int + restrict to [0,1]
if self.is_mip(data):
# Mark integer- and binary-vars as "integer"
model.setInteger(x[data[s.BOOL_IDX]])
model.setInteger(x[data[s.INT_IDX]])
# Restrict binary vars only
idxs = data[s.BOOL_IDX]
n_idxs = len(idxs)
model.setColumnLowerSubset(np.arange(n_idxs, dtype=np.int32),
np.array(idxs, np.int32),
np.zeros(n_idxs))
model.setColumnUpperSubset(np.arange(n_idxs, dtype=np.int32),
np.array(idxs, np.int32),
np.ones(n_idxs))
# Verbosity Clp
if not verbose:
model.logLevel = 0
# Build model & solve
status = None
if self.is_mip(data):
# Convert model
cbcModel = model.getCbcModel()
# Verbosity Cbc
if not verbose:
cbcModel.logLevel = 0
# cylp: /cylp/cy/CyCbcModel.pyx#L134
# Call CbcMain. Solve the problem using the same parameters used by
# CbcSolver. Equivalent to solving the model from the command line
# using cbc's binary.
cbcModel.solve()
status = cbcModel.status
else:
# cylp: /cylp/cy/CyClpSimplex.pyx
# Run CLP's initialSolve. It does a presolve and uses primal or dual
# Simplex to solve a problem.
status = model.initialSolve()
results_dict = {}
results_dict["status"] = status
if self.is_mip(data):
results_dict["x"] = cbcModel.primalVariableSolution['x']
results_dict["obj_value"] = cbcModel.objectiveValue
else:
results_dict["x"] = model.primalVariableSolution['x']
results_dict["obj_value"] = model.objectiveValue
return self.format_results(results_dict, data, cached_data)
def get_model_quality_estimate_clp(settings, n, k, node_pos, node_val,
num_iterations):
"""Compute an estimate of model quality using LPs with Clp.
Computes an estimate of model quality, performing
cross-validation. This version does not use all interpolation
nodes, but rather only the best num_iterations ones, and it uses a
sequence of LPs instead of a brute-force calculation. It should be
much faster than the brute-force calculation, as each LP in the
sequence requires only two pivots. The solver is COIN-OR Clp.
Parameters
----------
settings : rbfopt_settings.RbfSettings
Global and algorithmic settings.
n : int
Dimension of the problem, i.e. the space where the point lives.
k : int
Number of nodes, i.e. interpolation points.
node_pos : List[List[float]]
Location of current interpolation nodes.
node_val : List[float]
List of values of the function at the nodes.
num_iterations : int
Number of nodes on which quality should be tested.
Returns
-------
float
An estimate of the leave-one-out cross-validation error, which
can be interpreted as a measure of model quality.
Raises
------
RuntimeError
If the LPs cannot be solved.
ValueError
If some settings are not supported.
"""
assert(isinstance(settings, RbfSettings))
assert(len(node_val)==k)
assert(len(node_pos)==k)
assert(num_iterations <= k)
assert(cpx_available)
# We cannot find a leave-one-out interpolant if the following
# condition is not met.
assert(k > n + 1)
# Get size of polynomial part of the matrix (p) and sign of obj
# function (sign)
if (ru.get_degree_polynomial(settings) == 1):
p = n + 1
sign = 1
elif (ru.get_degree_polynomial(settings) == 0):
p = 1
sign = -1
else:
raise ValueError('RBF type ' + settings.rbf + ' not supported')
# Sort interpolation nodes by increasing objective function value
sorted_list = sorted([(node_val[i], node_pos[i]) for i in range(k)])
# Initialize the arrays used for the cross-validation
cv_node_pos = [sorted_list[i][1] for i in range(k)]
cv_node_val = [sorted_list[i][0] for i in range(k)]
# Compute the RBF matrix, and the two submatrices of interest
Amat = ru.get_rbf_matrix(settings, n, k, cv_node_pos)
Phimat = Amat[:k, :k]
Pmat = Amat[:k, k:]
identity = np.matrix(np.identity(k))
# Instantiate model
model = CyLPModel()
# Add variables: lambda, h, slacks
rbf_lambda = model.addVariable('rbf_lambda', k)
rbf_h = model.addVariable('rbf_h', p)
slack = model.addVariable('slack', k)
# Add constraints: interpolation conditions, unisolvence
F = CyLPArray(cv_node_val)
zeros = CyLPArray([0] * p)
ones = CyLPArray([1] * p)
if (p > 1):
# We can use matrix form
model += (Phimat * rbf_lambda + Pmat * rbf_h + identity * slack == F)
model += (Pmat.transpose() * rbf_lambda == zeros)
else:
# Workaround for one dimensional variables: one row at a time
for i in range(k):
model += Phimat[i, :] * rbf_lambda + rbf_h + slack[i] == F[i]
model += (Pmat.transpose() * rbf_lambda == zeros)
# Add objective
obj = CyLPArray([sign*val for val in node_val])
model.objective = obj * rbf_lambda
# Create LP, suppress output, and set bounds
lp = clp.CyClpSimplex(model)
lp.logLevel = 0
infinity = lp.getCoinInfinity()
for i in range(k + p):
lp.setColumnLower(i, -infinity)
lp.setColumnUpper(i, infinity)
for i in range(k):
lp.setColumnLower(k + p + i, 0.0)
lp.setColumnUpper(k + p + i, 0.0)
# Estimate of the model error
loo_error = 0.0
for i in range(num_iterations):
# Fix lambda[i] to zero
lp.setColumnLower(i, 0.0)
lp.setColumnUpper(i, 0.0)
# Set slack[i] to unconstrained
lp.setColumnLower(k + p + i, -infinity)
lp.setColumnUpper(k + p + i, infinity)
lp.dual(startFinishOptions = 'sx')
if (not lp.getStatusCode() == 0):
raise RuntimeError('Could not solve LP with Clp, status ' +
lp.getStatusString())
lambda_sol = lp.primalVariableSolution['rbf_lambda'].tolist()
h_sol = lp.primalVariableSolution['rbf_h'].tolist()
# Compute value of the interpolant at the removed node
predicted_val = ru.evaluate_rbf(settings, cv_node_pos[i], n, k,
cv_node_pos, lambda_sol, h_sol)
# Update leave-one-out error
loo_error += abs(predicted_val - cv_node_val[i])
# Fix lambda[i] to zero
lp.setColumnLower(i, -infinity)
lp.setColumnUpper(i, infinity)
# Set slack[i] to unconstrained
lp.setColumnLower(k + p + i, 0.0)
lp.setColumnUpper(k + p + i, 0.0)
return loo_error/num_iterations