def solve(A, rhs, ct=None, logLevel=0):
s = CyClpSimplex()
s.logLevel = logLevel
lp_dim = A.shape[1]
x = s.addVariable('x', lp_dim)
A = np.matrix(A)
rhs = CyLPArray(rhs)
s += A * x >= rhs
s += x[lp_dim - 1] >= 0
s.objective = x[lp_dim - 1]
nnz = np.count_nonzero(A)
logging.debug(f"TASK SIZE XCOUNT: {lp_dim} GXCOUNT: {len(rhs)}")
s.primal()
k = list(s.primalConstraintSolution.keys())[0]
k2 = list(s.dualConstraintSolution.keys())[0]
q = s.dualConstraintSolution[k2]
logging.debug(f"{s.getStatusString()} objective: {s.objectiveValue}")
logging.debug(
f"nonzeros rhs: {np.count_nonzero(s.primalConstraintSolution[k])}")
logging.debug(
f"nonzeros dual: {np.count_nonzero(s.dualConstraintSolution[k2])}")
basis = s.getBasisStatus()
print("Basis[0]")
print(basis[0])
print("basis[1]")
print(basis[1])
np.savetxt("out", basis[1])
print("#" * 100)
s = CyClpSimplex()
s.logLevel = logLevel
lp_dim = A.shape[1]
x = s.addVariable('x', lp_dim)
A = np.matrix(A)
rhs = CyLPArray(rhs)
s += A * x >= rhs
s += x[lp_dim - 1] >= 0
s.objective = x[lp_dim - 1]
nnz = np.count_nonzero(A)
logging.debug(f"TASK SIZE XCOUNT: {lp_dim} GXCOUNT: {len(rhs)}")
s.setBasisStatus(*basis)
s.primal()
return s.primalVariableSolution['x']
def solve(A, rhs, ct=None, logLevel=0, extnd=False, basis=False, mps_file=None):
s = CyClpSimplex()
s.logLevel = logLevel
lp_dim = A.shape[1]
x = s.addVariable('x', lp_dim)
A = np.matrix(A)
rhs = CyLPArray(rhs)
s += A * x >= rhs
s += x[lp_dim - 1] >= 0
s.objective = x[lp_dim - 1]
nnz = np.count_nonzero(A)
if not mps_file is None:
s.writeMps(mps_file)
return None
logging.debug(f"TASK SIZE XCOUNT: {lp_dim} GXCOUNT: {len(rhs)}")
s.primal()
k = list(s.primalConstraintSolution.keys())[0]
k2 =list(s.dualConstraintSolution.keys())[0]
q = s.dualConstraintSolution[k2]
logging.debug(f"{s.getStatusString()} objective: {s.objectiveValue}")
logging.debug(f"nonzeros rhs: {np.count_nonzero(s.primalConstraintSolution[k])}")
logging.debug(f"nonzeros dual: {np.count_nonzero(s.dualConstraintSolution[k2])}")
if extnd and not basis:
return s.primalVariableSolution['x'],s.primalConstraintSolution[k],s.dualConstraintSolution[k2]
elif not extnd and basis:
basis = s.getBasisStatus()
return s.primalVariableSolution['x'],*basis
else:
return s.primalVariableSolution['x']
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 __init__(self: T,
lp: CyClpSimplex,
integerIndices: List[int],
lower_bound: Union[float, int] = -float('inf'),
b_idx: int = None,
b_dir: str = None,
b_val: float = None,
depth=0):
"""
:param lp: model object simplex is run against
:param integerIndices: indices of variables we aim to find integer solutions
:param lower_bound: starting lower bound on optimal objective value
for the minimization problem in this node
:param b_idx: index of the branching variable
:param b_dir: direction of branching
:param b_val: initial value of the branching variable
:param depth: how deep in the tree this node is
"""
assert isinstance(lp, CyClpSimplex), 'lp must be CyClpSimplex instance'
assert all(0 <= idx < lp.nVariables and isinstance(idx, int)
for idx in integerIndices), 'indices must match variables'
assert len(set(integerIndices)) == len(integerIndices), \
'indices must be distinct'
assert isinstance(lower_bound, float) or isinstance(lower_bound, int), \
'lower bound must be a float or an int'
assert (b_dir is None) == (b_idx is None) == (b_val is None), \
'none are none or all are none'
assert b_idx in integerIndices or b_idx is None, \
'branch index corresponds to integer variable if it exists'
assert b_dir in ['up', 'down'] or b_dir is None, \
'we can only round a variable up or down when branching'
if b_val is not None:
good_down = 0 < b_val - lp.variablesUpper[b_idx] < 1
good_up = 0 < lp.variablesLower[b_idx] - b_val < 1
assert (b_dir == 'down' and good_down) or \
(b_dir == 'up' and good_up), 'branch val should be within 1 of both bounds'
assert isinstance(depth,
int) and depth >= 0, 'depth is a positive integer'
lp.logLevel = 0
self._lp = lp
self._integerIndices = integerIndices
self.lower_bound = lower_bound
self.objective_value = None
self.solution = None
self.lp_feasible = None
self.unbounded = None
self.mip_feasible = None
self._epsilon = .0001
self._b_dir = b_dir
self._b_idx = b_idx
self._b_val = b_val
self.depth = depth
self.search_method = 'best first'
self.branch_method = 'most fractional'
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 computePriceSweep(thisSlice,chunkNum, qpid, qresult):
myLength = thisSlice.shape[1]
myPID = multiprocessing.current_process().pid
# Add our process id to the list of process ids
while qpid.empty():
time.sleep(0.01)
pidList = qpid.get()
pidList.append(myPID)
qpid.put(pidList)
storagePriceSet = np.arange(1.0,20.1,0.25)
storagePriceSet = np.arange(1.0,3.1,1)
eff_round = 0.9 # Round-trip efficiency
E_min = 0
E_max = 1
# Endogenous parameters; calculated automatically
(eff_in, eff_out) = [np.sqrt(eff_round)] *2 # Properly account for the round trip efficiency of storage
P_max = E_max/eff_in # Max discharge power at grid intertie, e.g max limit for C_i
P_min = -1*E_max/eff_out # Max charge power at grid intertie, e.g. min D_i
# Create a set of zero-filled dataframes for storing results
resultIndex = pd.MultiIndex.from_product([thisSlice.index,['size','kwhPassed','profit']])
results = pd.DataFrame(index = resultIndex, columns=storagePriceSet)
# Create clean problem matrices - needs efficiency and length!
(A, b, A_eq, b_eq) = createABMatrices(myLength, delta_T, eff_in, eff_out, P_min, P_max, E_min, E_max)
# Define model:
coolStart = CyClpSimplex()
coolStart.logLevel = 0
x_var = coolStart.addVariable('x',myLength*3+2)
# Add constraints to model:
coolStart += A * x_var <= b.toarray()
coolStart += A_eq * x_var == b_eq.toarray()
newIDs = [] # this holds the names of nodes which we've recently processed
def dumpResults():
results.dropna(axis=0,how='all').to_csv('Data/priceSweepResults_pid'+str(myPID)+'temp.csv' )
# Make sure that the results queue hasn't been checked out by somebody else
while qresult.empty():
time.sleep(0.01)
resultList = qresult.get()
resultList[chunkNum] = resultList[chunkNum] + newIDs
qresult.put(resultList)
for i in range(thisSlice.shape[0]):
## Set up prices
myNodeName = thisSlice.index[i]
energyPrice = thisSlice.loc[myNodeName,:] / 1000.0 # Price $/kWh as array
# if (np.random.random(1)[0] < 0.05):
# sys.exit(1) # Randomly kill the process
c = np.concatenate([[0.0],[0.0]*(myLength+1),energyPrice,energyPrice],axis=0) #placeholder; No cost for storage state; charged for what we consume, get paid for what we discharge
#[[storagePricePlaceholder],[0]*(myLength+1),myPrice,myPrice],axis=1)
c_clp = CyLPArray(c)
sweepStartTime = time.time()
for myStoragePrice in storagePriceSet:
c_clp[0] = myStoragePrice * simulationYears
coolStart.objective = c_clp * x_var
# Run the model
coolStart.primal()
# Results- Rows are Nodes, indexed by name. Columns are Storage price, indexed by price
x_out = coolStart.primalVariableSolution['x']
results.loc[(myNodeName,'size'), myStoragePrice] = x_out[0]
results.loc[(myNodeName,'profit'), myStoragePrice] = np.dot(-c, x_out)
results.loc[(myNodeName,'kwhPassed'),myStoragePrice] = sum(x_out[2+myLength : 2+myLength*2]) * eff_in # Note: this is the net power pulled from the grid, not the number of cycles when the system is unconstrained
storagePriceSet = storagePriceSet[::-1] # Reverse the price set so that we start from the same price for the next node to make warm-start more effective
newIDs.append(myNodeName)
if (i+1)%5==0:
dumpResults() # Write the results to file, and then also update the process Queue with the
newIDs = []
# The results should now be all done!
dumpResults()
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 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]
n = c.shape[0]
solver_cache = cached_data[self.name()]
# Problem
model = CyClpSimplex()
# Variables
x = model.addVariable('x', n)
if self.is_mip(data):
for i in data[s.BOOL_IDX]:
model.setInteger(x[i])
for i in data[s.INT_IDX]:
model.setInteger(x[i])
# Constraints
# eq
model += A[0:dims[s.EQ_DIM], :] * x == 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 <= b[leq_start:leq_end]
# no boolean vars available in cbc -> model as int + restrict to [0,1]
if self.is_mip(data):
for i in data[s.BOOL_IDX]:
model += 0 <= x[i] <= 1
# Objective
model.objective = c
# Build model & solve
status = None
if self.is_mip(data):
cbcModel = model.getCbcModel() # need to convert model
if not verbose:
cbcModel.logLevel = 0
# Add cut-generators (optional)
for cut_name, cut_func in six.iteritems(self.SUPPORTED_CUT_GENERATORS):
if cut_name in solver_opts and solver_opts[cut_name]:
module = importlib.import_module("cylp.cy.CyCgl")
funcToCall = getattr(module, cut_func)
cut_gen = funcToCall()
cbcModel.addCutGenerator(cut_gen, name=cut_name)
# solve
status = cbcModel.branchAndBound()
else:
if not verbose:
model.logLevel = 0
status = model.primal() # solve
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)
x = lp.addVariable('x', LP.numVars)
if LP.sense[0] == '>=':
lp += A * x >= b
else:
lp += A * x <= b
#lp += x >= 0
c = CyLPArray(LP.c)
# We are maximizing, so negate objective
if LP.sense[1] == 'Min':
lp.objective = c * x
else:
lp.objective = -c * x
lp.logLevel = 0
lp.primal(startFinishOptions = 'x')
np.set_printoptions(precision = 2, linewidth = 200)
print('Basic variables: ', lp.basicVariables)
print("Current tableaux and reduced costs:")
print(lp.reducedCosts)
print(np.around(lp.tableau, decimals = 3))
print('Right-hand side of optimal tableaux:')
#There is a bug in CyLP and this is wrong
#print lp.rhs
if LP.sense[0] == '<=':
print(np.dot(lp.basisInverse, lp.constraintsUpper))
else:
print(np.dot(lp.basisInverse, lp.constraintsLower))
print('Inverse of optimal basis:')
print(np.around(lp.basisInverse, 3))
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 []
x = lp.addVariable('x', LP.numVars)
if LP.sense[0] == '>=':
lp += A * x >= b
else:
lp += A * x <= b
#lp += x >= 0
c = CyLPArray(LP.c)
# We are maximizing, so negate objective
if LP.sense[1] == 'Min':
lp.objective = c * x
else:
lp.objective = -c * x
lp.logLevel = 0
lp.primal(startFinishOptions='x')
np.set_printoptions(precision=2, linewidth=200)
print 'Basic variables: ', lp.basicVariables
print "Current tableaux and reduced costs:"
print lp.reducedCosts
print np.around(lp.tableau, decimals=3)
print 'Right-hand side of optimal tableaux:'
#There is a bug in CyLP and this is wrong
#print lp.rhs
if LP.sense[0] == '<=':
print np.dot(lp.basisInverse, lp.constraintsUpper)
else:
print np.dot(lp.basisInverse, lp.constraintsLower)
print 'Inverse of optimal basis:'
print np.around(lp.basisInverse, 3)
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 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 computePriceSweep(thisSlice):
###### BEGINNING OF MULTIPROCESSING FUNCTION ###########
myLength = thisSlice.shape[1]
# Simulation parameters - set these!
storagePriceSet = np.arange(1.0,20.1,0.25)
# storagePriceSet = np.arange(1.0,3.1,1)
eff_round = 0.9 # Round-trip efficiency
E_min = 0
E_max = 1
# Endogenous parameters; calculated automatically
(eff_in, eff_out) = [np.sqrt(eff_round)] *2 # Properly account for the round trip efficiency of storage
P_max = E_max/eff_in # Max discharge power at grid intertie, e.g max limit for C_i
P_min = -1*E_max/eff_out # Max charge power at grid intertie, e.g. min D_i
# Create a set of zero-filled dataframes for storing results
resultIndex = pd.MultiIndex.from_product([thisSlice.index,['size','kwhPassed','profit']])
results = pd.DataFrame(index = resultIndex, columns=storagePriceSet)
# Create clean problem matrices - needs efficiency and length!
(A, b, A_eq, b_eq) = createABMatrices(myLength, delta_T, eff_in, eff_out, P_min, P_max, E_min, E_max)
# Define model:
coolStart = CyClpSimplex()
coolStart.logLevel = 0
x_var = coolStart.addVariable('x',myLength*3+2)
# Add constraints to model:
coolStart += A * x_var <= b.toarray()
coolStart += A_eq * x_var == b_eq.toarray()
# print("Finished with problem setup")
# sys.stdout.flush()
# everythingStarts = time.time()
# startTime = time.time()
for myNodeName in thisSlice.index:
## Set up prices
# myNodeName = thisSlice.index[i]
energyPrice = thisSlice.loc[myNodeName,:] / 1000.0 # Price $/kWh as array
c = np.concatenate([[0.0],[0.0]*(myLength+1),energyPrice,energyPrice],axis=0) #placeholder; No cost for storage state; charged for what we consume, get paid for what we discharge
#[[storagePricePlaceholder],[0]*(myLength+1),myPrice,myPrice],axis=1)
c_clp = CyLPArray(c)
sweepStartTime = time.time()
for myStoragePrice in storagePriceSet:
c_clp[0] = myStoragePrice * simulationYears
coolStart.objective = c_clp * x_var
# Run the model
coolStart.primal()
# Results- Rows are Nodes, indexed by name. Columns are Storage price, indexed by price
x_out = coolStart.primalVariableSolution['x']
results.loc[(myNodeName,'size'), myStoragePrice] = x_out[0]
results.loc[(myNodeName,'profit'), myStoragePrice] = np.dot(-c, x_out)
results.loc[(myNodeName,'kwhPassed'),myStoragePrice] = sum(x_out[2+myLength : 2+myLength*2]) * eff_in # Note: this is the net power pulled from the grid, not the number of cycles when the system is unconstrained
storagePriceSet = storagePriceSet[::-1] # Reverse the price set so that we start from the same price for the next node to make warm-start more effective
# if ((i+1) % reportFrequency == 0): # Save our progress along the way
# elapsedTime = time.time()-startTime
# print("Finished node %s; \t%s computations in \t%.4f s \t(%.4f s/solve)"
# % (i, scenariosPerReport,elapsedTime,elapsedTime/scenariosPerReport))
# sys.stdout.flush()
# sizeDf.to_csv('Data/VaryingPrices_StorageSizing_v2.csv')
# profitDf.to_csv('Data/VaryingPrices_StorageProfits_v2.csv')
# cycleDf.to_csv('Data/VaryingPrices_StorageCycles_v2.csv')
# print("Done in %.3f s"%(time.time()-everythingStarts))
return results
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
# 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]
n = c.shape[0]
# Problem
model = CyClpSimplex()
# Variables
x = model.addVariable('x', n)
if self.is_mip(data):
for i in data[s.BOOL_IDX]:
model.setInteger(x[i])
for i in data[s.INT_IDX]:
model.setInteger(x[i])
# Constraints
# eq
model += A[0:dims[s.EQ_DIM], :] * x == 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 <= b[leq_start:leq_end]
# no boolean vars available in cbc -> model as int + restrict to [0,1]
if self.is_mip(data):
for i in data[s.BOOL_IDX]:
model += 0 <= x[i] <= 1
# Objective
model.objective = c
# Build model & solve
status = None
if self.is_mip(data):
cbcModel = model.getCbcModel() # need to convert model
if not verbose:
cbcModel.logLevel = 0
# Add cut-generators (optional)
for cut_name, cut_func in six.iteritems(
self.SUPPORTED_CUT_GENERATORS):
if cut_name in solver_opts and solver_opts[cut_name]:
module = importlib.import_module("cylp.cy.CyCgl")
funcToCall = getattr(module, cut_func)
cut_gen = funcToCall()
cbcModel.addCutGenerator(cut_gen, name=cut_name)
# solve
status = cbcModel.branchAndBound()
else:
if not verbose:
model.logLevel = 0
status = model.primal() # solve
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 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 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 []
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 []
