def splitCuts(lp, integerIndices = None, sense = '>=', sol = None,
max_coeff = 1):
A = lp.coefMatrix
b = CyLPArray(lp.constraintsUpper)
if integerIndices is None:
integerIndices = range(lp.nVariables)
if sol is None:
sol = lp.primalVariableSolution['x']
s = A*sol - b
best = lp.getCoinInfinity()
best_theta = None
for theta in [0.1, 0.2, 0.3, 0.4, 0.5]:
sp = CyLPModel()
u = sp.addVariable('u', lp.nConstraints, isInt = False)
v = sp.addVariable('v', lp.nConstraints, isInt = False)
pi = sp.addVariable('pi', lp.nVariables, isInt = True)
pi0 = sp.addVariable('pi0', 1, isInt = True)
sp += pi + A.transpose()*u - A.transpose()*v == 0
sp += pi0 + b*u - b*v == theta - 1
if sense == '<=':
sp += u >= 0
sp += v >= 0
else:
#TODO this direction is not debugged
# Is this all we need?
sp += u <= 0
sp += v <= 0
sp.objective = (theta-1)*s*u - theta*s*v
for i in xrange(lp.nVariables):
if i in integerIndices:
sp += -max_coeff <= pi[i] <= max_coeff
else:
sp[i] += pi[i] == 0
cbcModel = CyClpSimplex(sp).getCbcModel()
cbcModel.logLevel = 0
#cbcModel.maximumSeconds = 5
cbcModel.solve()
if debug_print:
print theta, cbcModel.objectiveValue
print cbcModel.primalVariableSolution['pi'],
print cbcModel.primalVariableSolution['pi0']
if cbcModel.objectiveValue < best:
best = cbcModel.objectiveValue
multu = cbcModel.primalVariableSolution['u']
disjunction = cbcModel.primalVariableSolution['pi']
rhs = cbcModel.primalVariableSolution['pi0']
best_theta = theta
if best_theta is not None:
alpha = A.transpose()*multu + best_theta*disjunction
if sense == '<=':
beta = np.dot(lp.constraintsUpper, multu) + best_theta*rhs
else:
beta = np.dot(lp.constraintsLower, multu) + best_theta*rhs
if (abs(alpha) > 1e-6).any():
return [(alpha, beta)]
return []
cuts = []
for rowInd in range(s.nConstraints):
basicVarInd = bv[rowInd]
if basicVarInd < clpModel.nVariables and intInds[
basicVarInd] and not rhsIsInt[rowInd]:
coef, b = gomoryCut(clpModel, rowInd)
if b is not None:
#print 'Adding cut: ', coef, '>=', b
expr = CyLPArray(coef) * x >= b
cuts.append(expr)
return cuts
if __name__ == '__main__':
m = CyLPModel()
firstExample = False
if (firstExample):
x = m.addVariable('x', 2, isInt=True)
A = np.matrix([[7., -2.], [0., 1], [2., -2]])
b = CyLPArray([14, 3, 3])
m += A * x <= b
m += x >= 0
c = CyLPArray([-4, 1])
m.objective = c * x
s = CyClpSimplex(m)
def disjunctionToCut(lp, pi, pi0, integerIndices = None, sense = '>=',
sol = None, debug_print = False, use_cylp = True):
me = "cglp_cuts: "
if sol is None:
sol = lp.primalVariableSolution['x']
infinity = lp.getCoinInfinity()
if debug_print:
print(me, "constraints sense = ", sense)
print(me, "con lower bounds = ", lp.constraintsLower)
print(me, "con upper bounds = ", lp.constraintsUpper)
print(me, "con matrix = ", lp.coefMatrix.toarray())
print(me, "vars lower bounds = ", lp.variablesLower)
print(me, "vars upper bounds = ", lp.variablesUpper)
print(me, "Assuming objective is to minimize")
print(me, "objective = ", lp.objective)
print(me, "infinity = ", infinity)
print(me, "current point = ", sol)
print(me, "pi = ", pi)
print(me, "pi0 = ", pi0)
A = lp.coefMatrix.toarray()
#c = lp.objective
## Convert to >= if the problem is in <= form.
if sense == '<=':
b = deepcopy(lp.constraintsUpper)
b = -1.0*b
A = -1.0*A
else:
b = deepcopy(lp.constraintsLower)
#Add bounds on variables as explicit constraints
for i in range(lp.nCols):
e = np.zeros((1, lp.nCols))
if lp.variablesUpper[i] < infinity:
b.resize(b.size+1, refcheck = False)
e[0, i] = -1.0
b[-1] = -1.0*lp.variablesUpper[i]
A = np.vstack((A, e))
if lp.variablesLower[i] > -infinity:
b.resize(b.size+1, refcheck = False)
e[0, i] = 1.0
b[-1] = lp.variablesLower[i]
A = np.vstack((A, e))
A = csc_matrixPlus(A)
############################################################################
## There are two given LPs:
## s.t. Ax >= b s.t. Ax >= b
## -pi.x >= -pi_0 pi.x >= pi_0+1
## A, b, c, pi, pi_0 are given
##
## CGLP: alpha.x >= beta should be valid for both LPs above
##
## min alpha.x* - beta
## uA - u0.pi = alpha
## vA + v0.pi = alpha
## ub - u0.pi_0 >= beta
## vb + v0.(pi_0 + 1) >= beta
## u0 + v0 = 1
## u, v, u0, v0 >= 0
## if min value comes out < 0, then (alpha.x >= beta) is a cut.
############################################################################
b = CyLPArray(b)
pi = CyLPArray(pi)
Atran = A.transpose()
if use_cylp:
sp = CyLPModel()
u = sp.addVariable('u', A.shape[0], isInt = False)
v = sp.addVariable('v', A.shape[0], isInt = False)
u0 = sp.addVariable('u0', 1, isInt = False)
v0 = sp.addVariable('v0', 1, isInt = False)
alpha = sp.addVariable('alpha', lp.nVariables, isInt = False)
beta = sp.addVariable('beta', 1, isInt = False)
for i in range(A.shape[1]):
sp += alpha[i] - sum(Atran[i,j]*u[j] for j in range(A.shape[0])) + pi[i]*u0 == 0
for i in range(A.shape[1]):
sp += alpha[i] - sum(Atran[i,j]*v[j] for j in range(A.shape[0])) - pi[i]*v0 == 0
sp += beta - b*u + pi0*u0 <= 0
sp += beta - b*v - (pi0 + 1)*v0 <= 0
sp += u0 + v0 == 1
if sense == '<=':
sp += u >= 0
sp += v >= 0
sp += u0 >= 0
sp += v0 >= 0
else:
#TODO this direction is not debugged
# Is this all we need?
sp += u <= 0
sp += v <= 0
sp += u0 <= 0
sp += v0 <= 0
sp.objective = sum(sol[i]*alpha[i] for i in range(A.shape[1])) - beta
cbcModel = CyClpSimplex(sp).getCbcModel()
cbcModel.logLevel = 0
#cbcModel.maximumSeconds = 5
cbcModel.solve()
beta = cbcModel.primalVariableSolution['beta'][0]
alpha = cbcModel.primalVariableSolution['alpha']
u = cbcModel.primalVariableSolution['u']
v = cbcModel.primalVariableSolution['v']
u0 = cbcModel.primalVariableSolution['u0'][0]
v0 = cbcModel.primalVariableSolution['v0'][0]
if debug_print:
print('Objective Value: ', cbcModel.objectiveValue)
print('alpha: ', alpha, 'alpha*sol: ', np.dot(alpha, sol))
print('beta: ', beta)
print('Violation of cut: ', np.dot(alpha, sol) - beta)
else:
CG = AbstractModel()
CG.u = Var(list(range(A.shape[0])), domain=NonNegativeReals,
bounds = (0.0, None))
CG.v = Var(list(range(A.shape[0])), domain=NonNegativeReals,
bounds = (0.0, None))
CG.u0 = Var(domain=NonNegativeReals, bounds = (0.0, None))
CG.v0 = Var(domain=NonNegativeReals, bounds = (0.0, None))
CG.alpha = Var(list(range(A.shape[0])), domain=Reals,
bounds = (None, None))
CG.beta = Var(domain=Reals, bounds = (None, None))
## Constraints
def pi_rule_left(CG, i):
x = float(pi[i])
return(sum(Atran[i, j]*CG.u[j] for j in range(A.shape[0])) -
x*CG.u0 - CG.alpha[i] == 0.0)
CG.pi_rule_left = Constraint(list(range(A.shape[1])), rule=pi_rule_left)
def pi_rule_right(CG, i):
x = float(pi[i])
return(sum(Atran[i, j]*CG.v[j] for j in range(A.shape[0])) +
x*CG.v0 - CG.alpha[i] == 0.0)
CG.pi_rule_right = Constraint(list(range(A.shape[1])), rule=pi_rule_right)
def pi0_rule_left(CG):
return(sum(b[j]*CG.u[j] for j in range(A.shape[0])) -
pi0*CG.u0 - CG.beta >= 0.0)
CG.pi0_rule_left = Constraint(rule=pi0_rule_left)
def pi0_rule_right(CG):
return(sum(b[j]*CG.v[j] for j in range(A.shape[0])) +
(pi0 + 1)*CG.v0 - CG.beta >= 0.0)
CG.pi0_rule_right = Constraint(rule=pi0_rule_right)
def normalization_rule(CG):
return(CG.u0 + CG.v0 == 1.0)
CG.normalization_rule = Constraint(rule=normalization_rule)
def objective_rule(CG):
return(sum(sol[i]*CG.alpha[i] for i in range(A.shape[1])) -
CG.beta)
CG.objective = Objective(sense=minimize, rule=objective_rule)
opt = SolverFactory("cbc")
instance = CG.create_instance()
#instance.pprint()
#instance.write("foo.nl", format = "nl")
#opt.options['bonmin.bb_log_level'] = 5
#opt.options['bonmin.bb_log_interval'] = 1
results = opt.solve(instance, tee=False)
#results = opt.solve(instance)
instance.solutions.load_from(results)
beta = instance.beta.value
alpha = np.array([instance.alpha[i].value
for i in range(lp.nVariables)])
violation = beta - np.dot(alpha, sol)
if debug_print:
print(me, 'Beta: ', beta)
print(me, 'alpha: ', alpha)
print(me, 'Violation of cut: ', violation)
if violation > 0.001:
if (sense == ">="):
return [(alpha, beta)]
else:
return [(-alpha, -beta)]
return []
rhsIsInt = map(isInt, rhs)
cuts = []
for rowInd in xrange(s.nConstraints):
basicVarInd = bv[rowInd]
if basicVarInd < clpModel.nVariables and intInds[basicVarInd] and not rhsIsInt[rowInd]:
coef, b = gomoryCut(clpModel, rowInd)
if b is not None:
#print 'Adding cut: ', coef, '>=', b
expr = CyLPArray(coef) * x >= b
cuts.append(expr)
return cuts
if __name__ == '__main__':
m = CyLPModel()
firstExample = False
if (firstExample):
x = m.addVariable('x', 2, isInt=True)
A = np.matrix([[7., -2.],[0., 1], [2., -2]])
b = CyLPArray([14, 3, 3])
m += A * x <= b
m += x >= 0
c = CyLPArray([-4, 1])
m.objective = c * x
s = CyClpSimplex(m)
def disjunctionToCut(m, pi, pi0, debug_print=False, use_cylp=True, eps=EPS):
'''Generate the most violated valid inequality from a given disjunction'''
me = "cglp_cuts: "
lp = m.lp
sol = lp.primalVariableSolution['x']
if debug_print:
print(me, "constraints sense = ", m.sense)
print(me, "matrix = ")
print(m.A)
print(me, "rhs = ", m.b)
print(me, "vars lower bounds = ", lp.variablesLower)
print(me, "vars upper bounds = ", lp.variablesUpper)
print(me, "objective = ", lp.objective)
print(me, "current solution = ", sol)
print(me, "pi = ", pi)
print(me, "pi0 = ", pi0)
############################################################################
## There are two given LPs:
## s.t. Ax >= b s.t. Ax >= b
## -pi.x >= -pi_0 pi.x >= pi_0+1
## A, b, c, pi, pi_0 are given
##
## CGLP: alpha.x >= beta should be valid for both LPs above
##
## min alpha.x* - beta
## uA - u0.pi = alpha
## vA + v0.pi = alpha
## ub - u0.pi_0 >= beta
## vb + v0.(pi_0 + 1) >= beta
## u0 + v0 = 1
## u, v, u0, v0 >= 0
## if min value comes out < 0, then (alpha.x >= beta) is a cut.
############################################################################
pi = CyLPArray(pi)
Atran = m.A.transpose()
b = CyLPArray(m.b)
numRows, numCols = m.A.shape
if use_cylp:
sp = CyLPModel()
u = sp.addVariable('u', numRows, isInt=False)
v = sp.addVariable('v', numRows, isInt=False)
u0 = sp.addVariable('u0', 1, isInt=False)
v0 = sp.addVariable('v0', 1, isInt=False)
alpha = sp.addVariable('alpha', lp.nVariables, isInt=False)
beta = sp.addVariable('beta', 1, isInt=False)
#This should be as simple as this, but it doesn't work.
#Maybe a bug in CyLP?
#sp += alpha - Atran*u - pi*u0 == 0
#sp += alpha - Atran*v + pi*v0 == 0
for i in range(numCols):
sp += alpha[i] - sum(Atran[i, j] * u[j]
for j in range(numRows)) - pi[i] * u0 == 0
for i in range(numCols):
sp += alpha[i] - sum(Atran[i, j] * v[j]
for j in range(numRows)) + pi[i] * v0 == 0
if m.sense == '<=':
sp += beta - b * u - pi0 * u0 >= 0
sp += beta - b * v + (pi0 + 1) * v0 >= 0
else:
sp += beta - b * u - pi0 * u0 <= 0
sp += beta - b * v + (pi0 + 1) * v0 <= 0
sp += u0 + v0 == 1
sp += u >= 0
sp += v >= 0
sp += u0 >= 0
sp += v0 >= 0
if m.sense == '<=':
sp.objective = sum(-sol[i] * alpha[i]
for i in range(numCols)) + beta
else:
#This direction is not debugged
sp.objective = sum(sol[i] * alpha[i]
for i in range(numCols)) - beta
cglp = CyClpSimplex(sp)
# If we want to solve it as an MILP
# cglp = CyClpSimplex(sp).getCbcModel()
#cglp.writeLp('lp.lp')
cglp.logLevel = 0
cglp.primal(startFinishOptions='x')
# Solve as MILP
# cglp.solve()
beta = cglp.primalVariableSolution['beta'][0]
alpha = cglp.primalVariableSolution['alpha']
u = cglp.primalVariableSolution['u']
v = cglp.primalVariableSolution['v']
u0 = cglp.primalVariableSolution['u0'][0]
v0 = cglp.primalVariableSolution['v0'][0]
if debug_print:
print(me, 'Objective Value: ', cglp.objectiveValue)
if debug_print:
print(me, 'u: ', u)
print(me, 'v: ', v)
print(me, 'u0: ', u0)
print(me, 'v0: ', v0)
else:
CG = AbstractModel()
CG.u = Var(list(range(numRows)),
domain=NonNegativeReals,
bounds=(0.0, None))
CG.v = Var(list(range(numRows)),
domain=NonNegativeReals,
bounds=(0.0, None))
CG.u0 = Var(domain=NonNegativeReals, bounds=(0.0, None))
CG.v0 = Var(domain=NonNegativeReals, bounds=(0.0, None))
CG.alpha = Var(list(range(numRows)), domain=Reals, bounds=(None, None))
CG.beta = Var(domain=Reals, bounds=(None, None))
## Constraints
def pi_rule_left(CG, i):
x = float(pi[i])
return (sum(Atran[i, j] * CG.u[j] for j in range(numRows)) -
x * CG.u0 - CG.alpha[i] == 0.0)
CG.pi_rule_left = Constraint(list(range(numCols)), rule=pi_rule_left)
def pi_rule_right(CG, i):
x = float(pi[i])
return (sum(Atran[i, j] * CG.v[j] for j in range(numRows)) +
x * CG.v0 - CG.alpha[i] == 0.0)
CG.pi_rule_right = Constraint(list(range(numCols)), rule=pi_rule_right)
if m.sense == '<=':
def pi0_rule_left(CG):
return (sum(b[j] * CG.u[j]
for j in range(numRows)) - pi0 * CG.u0 - CG.beta <=
0.0)
CG.pi0_rule_left = Constraint(rule=pi0_rule_left)
def pi0_rule_right(CG):
return (sum(b[j] * CG.v[j] for j in range(numRows)) +
(pi0 + 1) * CG.v0 - CG.beta <= 0.0)
CG.pi0_rule_right = Constraint(rule=pi0_rule_right)
else:
def pi0_rule_left(CG):
return (sum(b[j] * CG.u[j]
for j in range(numRows)) - pi0 * CG.u0 - CG.beta >=
0.0)
CG.pi0_rule_left = Constraint(rule=pi0_rule_left)
def pi0_rule_right(CG):
return (sum(b[j] * CG.v[j] for j in range(numRows)) +
(pi0 + 1) * CG.v0 - CG.beta >= 0.0)
CG.pi0_rule_right = Constraint(rule=pi0_rule_right)
def normalization_rule(CG):
return (CG.u0 + CG.v0 == 1.0)
CG.normalization_rule = Constraint(rule=normalization_rule)
def objective_rule(CG):
return (sum(sol[i] * CG.alpha[i]
for i in range(numCols)) - CG.beta)
if m.sense == '<=':
CG.objective = Objective(sense=maximize, rule=objective_rule)
else:
CG.objective = Objective(sense=minimize, rule=objective_rule)
opt = SolverFactory("cbc")
instance = CG.create_instance()
#instance.pprint()
#instance.write("foo.nl", format = "nl")
#opt.options['bonmin.bb_log_level'] = 5
#opt.options['bonmin.bb_log_interval'] = 1
results = opt.solve(instance, tee=False)
#results = opt.solve(instance)
instance.solutions.load_from(results)
beta = instance.beta.value
alpha = np.array(
[instance.alpha[i].value for i in range(lp.nVariables)])
violation = beta - np.dot(alpha, sol)
if debug_print:
print(me, 'Beta: ', beta)
print(me, 'alpha: ', alpha)
print(me, 'Violation of cut: ', violation)
if np.abs(violation) > 10**(-eps):
return [(alpha, beta)]
print('No violated cuts found solving CGLP', violation)
return []
def maxViolationSplitCuts(lp, integerIndices = None, sense = '>=', sol = None,
max_coeff = 1):
#Warning: At the moment, you must put bound constraints in explicitly for split cuts
A = lp.coefMatrix
if sense == '<=':
b = CyLPArray(lp.constraintsUpper)
else:
b = CyLPArray(lp.constraintsLower)
if integerIndices is None:
integerIndices = range(lp.nVariables)
if sol is None:
sol = lp.primalVariableSolution['x']
s = A*sol - b
best = lp.getCoinInfinity()
best_theta = None
for theta in [0.01, 0.02, 0.03, 0.04, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5]:
sp = CyLPModel()
u = sp.addVariable('u', lp.nConstraints, isInt = False)
v = sp.addVariable('v', lp.nConstraints, isInt = False)
pi = sp.addVariable('pi', lp.nVariables, isInt = True)
pi0 = sp.addVariable('pi0', 1, isInt = True)
sp += pi + A.transpose()*u - A.transpose()*v == 0
sp += pi0 + b*u - b*v == theta - 1
if sense == '<=':
sp += u >= 0
sp += v >= 0
else:
#TODO this direction is not debugged
# Is this all we need?
sp += u <= 0
sp += v <= 0
sp.objective = (theta-1)*s*u - theta*s*v
for i in xrange(lp.nVariables):
if i in integerIndices:
sp += -max_coeff <= pi[i] <= max_coeff
else:
sp[i] += pi[i] == 0
cbcModel = CyClpSimplex(sp).getCbcModel()
cbcModel.logLevel = 0
#cbcModel.maximumSeconds = 5
cbcModel.solve()
if debug_print:
#print 'Theta: ', theta,
#print 'Objective Value: ', cbcModel.objectiveValue - theta*(1-theta)
#print 'pi: ', cbcModel.primalVariableSolution['pi']
#print 'pi0: ', cbcModel.primalVariableSolution['pi0']
multu = cbcModel.primalVariableSolution['u']
disjunction = cbcModel.primalVariableSolution['pi']
rhs = cbcModel.primalVariableSolution['pi0']
alpha = A.transpose()*multu + theta*disjunction
beta = np.dot(b, multu) + theta*rhs
#print 'alpha: ', alpha, 'alpha*sol: ', np.dot(alpha, sol)
#print 'beta: ', beta
#print 'Violation of cut: ', np.dot(alpha, sol) - beta
if cbcModel.objectiveValue - theta*(1-theta) < best:
best = cbcModel.objectiveValue - theta*(1-theta)
best_multu = cbcModel.primalVariableSolution['u']
best_multv = cbcModel.primalVariableSolution['v']
best_disjunction = cbcModel.primalVariableSolution['pi']
best_rhs = cbcModel.primalVariableSolution['pi0']
best_theta = theta
if best_theta is not None:
alpha = A.transpose()*best_multu + best_theta*best_disjunction
beta = np.dot(b, best_multu) + best_theta*best_rhs
if debug_print:
print 'Violation of cut: ', np.dot(alpha, sol) - beta
print 'pi: ', best_disjunction
print 'pi0: ', best_rhs
print 'theta: ', best_theta
if (abs(alpha) > 1e-6).any():
return [(alpha, beta)]
return []
def disjunctionToCut(lp,
pi,
pi0,
integerIndices=None,
sense='>=',
sol=None,
debug_print=False,
use_cylp=True):
me = "cglp_cuts: "
if sol is None:
sol = lp.primalVariableSolution['x']
infinity = lp.getCoinInfinity()
if debug_print:
print(me, "constraints sense = ", sense)
print(me, "con lower bounds = ", lp.constraintsLower)
print(me, "con upper bounds = ", lp.constraintsUpper)
print(me, "con matrix = ", lp.coefMatrix.toarray())
print(me, "vars lower bounds = ", lp.variablesLower)
print(me, "vars upper bounds = ", lp.variablesUpper)
print(me, "Assuming objective is to minimize")
print(me, "objective = ", lp.objective)
print(me, "infinity = ", infinity)
print(me, "current point = ", sol)
print(me, "pi = ", pi)
print(me, "pi0 = ", pi0)
A = lp.coefMatrix.toarray()
#c = lp.objective
## Convert to >= if the problem is in <= form.
if sense == '<=':
b = deepcopy(lp.constraintsUpper)
b = -1.0 * b
A = -1.0 * A
else:
b = deepcopy(lp.constraintsLower)
#Add bounds on variables as explicit constraints
for i in range(lp.nCols):
e = np.zeros((1, lp.nCols))
if lp.variablesUpper[i] < infinity:
b.resize(b.size + 1, refcheck=False)
e[0, i] = -1.0
b[-1] = -1.0 * lp.variablesUpper[i]
A = np.vstack((A, e))
if lp.variablesLower[i] > -infinity:
b.resize(b.size + 1, refcheck=False)
e[0, i] = 1.0
b[-1] = lp.variablesLower[i]
A = np.vstack((A, e))
A = csc_matrixPlus(A)
############################################################################
## There are two given LPs:
## s.t. Ax >= b s.t. Ax >= b
## -pi.x >= -pi_0 pi.x >= pi_0+1
## A, b, c, pi, pi_0 are given
##
## CGLP: alpha.x >= beta should be valid for both LPs above
##
## min alpha.x* - beta
## uA - u0.pi = alpha
## vA + v0.pi = alpha
## ub - u0.pi_0 >= beta
## vb + v0.(pi_0 + 1) >= beta
## u0 + v0 = 1
## u, v, u0, v0 >= 0
## if min value comes out < 0, then (alpha.x >= beta) is a cut.
############################################################################
b = CyLPArray(b)
pi = CyLPArray(pi)
Atran = A.transpose()
if use_cylp:
sp = CyLPModel()
u = sp.addVariable('u', A.shape[0], isInt=False)
v = sp.addVariable('v', A.shape[0], isInt=False)
u0 = sp.addVariable('u0', 1, isInt=False)
v0 = sp.addVariable('v0', 1, isInt=False)
alpha = sp.addVariable('alpha', lp.nVariables, isInt=False)
beta = sp.addVariable('beta', 1, isInt=False)
for i in range(A.shape[1]):
sp += alpha[i] - sum(Atran[i, j] * u[j]
for j in range(A.shape[0])) + pi[i] * u0 == 0
for i in range(A.shape[1]):
sp += alpha[i] - sum(Atran[i, j] * v[j]
for j in range(A.shape[0])) - pi[i] * v0 == 0
sp += beta - b * u + pi0 * u0 <= 0
sp += beta - b * v - (pi0 + 1) * v0 <= 0
sp += u0 + v0 == 1
if sense == '<=':
sp += u >= 0
sp += v >= 0
sp += u0 >= 0
sp += v0 >= 0
else:
#TODO this direction is not debugged
# Is this all we need?
sp += u <= 0
sp += v <= 0
sp += u0 <= 0
sp += v0 <= 0
sp.objective = sum(sol[i] * alpha[i] for i in range(A.shape[1])) - beta
cbcModel = CyClpSimplex(sp).getCbcModel()
cbcModel.logLevel = 0
#cbcModel.maximumSeconds = 5
cbcModel.solve()
beta = cbcModel.primalVariableSolution['beta'][0]
alpha = cbcModel.primalVariableSolution['alpha']
u = cbcModel.primalVariableSolution['u']
v = cbcModel.primalVariableSolution['v']
u0 = cbcModel.primalVariableSolution['u0'][0]
v0 = cbcModel.primalVariableSolution['v0'][0]
if debug_print:
print('Objective Value: ', cbcModel.objectiveValue)
print('alpha: ', alpha, 'alpha*sol: ', np.dot(alpha, sol))
print('beta: ', beta)
print('Violation of cut: ', np.dot(alpha, sol) - beta)
else:
CG = AbstractModel()
CG.u = Var(list(range(A.shape[0])),
domain=NonNegativeReals,
bounds=(0.0, None))
CG.v = Var(list(range(A.shape[0])),
domain=NonNegativeReals,
bounds=(0.0, None))
CG.u0 = Var(domain=NonNegativeReals, bounds=(0.0, None))
CG.v0 = Var(domain=NonNegativeReals, bounds=(0.0, None))
CG.alpha = Var(list(range(A.shape[0])),
domain=Reals,
bounds=(None, None))
CG.beta = Var(domain=Reals, bounds=(None, None))
## Constraints
def pi_rule_left(CG, i):
x = float(pi[i])
return (sum(Atran[i, j] * CG.u[j] for j in range(A.shape[0])) -
x * CG.u0 - CG.alpha[i] == 0.0)
CG.pi_rule_left = Constraint(list(range(A.shape[1])),
rule=pi_rule_left)
def pi_rule_right(CG, i):
x = float(pi[i])
return (sum(Atran[i, j] * CG.v[j] for j in range(A.shape[0])) +
x * CG.v0 - CG.alpha[i] == 0.0)
CG.pi_rule_right = Constraint(list(range(A.shape[1])),
rule=pi_rule_right)
def pi0_rule_left(CG):
return (sum(b[j] * CG.u[j]
for j in range(A.shape[0])) - pi0 * CG.u0 - CG.beta >=
0.0)
CG.pi0_rule_left = Constraint(rule=pi0_rule_left)
def pi0_rule_right(CG):
return (sum(b[j] * CG.v[j] for j in range(A.shape[0])) +
(pi0 + 1) * CG.v0 - CG.beta >= 0.0)
CG.pi0_rule_right = Constraint(rule=pi0_rule_right)
def normalization_rule(CG):
return (CG.u0 + CG.v0 == 1.0)
CG.normalization_rule = Constraint(rule=normalization_rule)
def objective_rule(CG):
return (sum(sol[i] * CG.alpha[i]
for i in range(A.shape[1])) - CG.beta)
CG.objective = Objective(sense=minimize, rule=objective_rule)
opt = SolverFactory("cbc")
instance = CG.create_instance()
#instance.pprint()
#instance.write("foo.nl", format = "nl")
#opt.options['bonmin.bb_log_level'] = 5
#opt.options['bonmin.bb_log_interval'] = 1
results = opt.solve(instance, tee=False)
#results = opt.solve(instance)
instance.solutions.load_from(results)
beta = instance.beta.value
alpha = np.array(
[instance.alpha[i].value for i in range(lp.nVariables)])
violation = beta - np.dot(alpha, sol)
if debug_print:
print(me, 'Beta: ', beta)
print(me, 'alpha: ', alpha)
print(me, 'Violation of cut: ', violation)
if violation > 0.001:
if (sense == ">="):
return [(alpha, beta)]
else:
return [(-alpha, -beta)]
return []
