def _find_split_inequality(self: G, idx: int, **kwargs: Any):
assert idx in self._integer_indices, 'must lift and project on integer index'
x_idx = self.solution[idx]
assert self._is_fractional(
x_idx), "must lift and project on index with fractional value"
# build the CGLP model from ISE 418 Lecture 15 Slide 7 but for LP with >= constraints
lp = CyClpSimplex()
# declare variables
pi = lp.addVariable('pi', self.lp.nVariables)
pi0 = lp.addVariable('pi0', 1)
u1 = lp.addVariable('u1', self.lp.nConstraints)
u2 = lp.addVariable('u2', self.lp.nConstraints)
w1 = lp.addVariable('w1', self.lp.nVariables)
w2 = lp.addVariable('w2', self.lp.nVariables)
# set bounds
lp += u1 >= CyLPArray(np.zeros(self.lp.nConstraints))
lp += u2 >= CyLPArray(np.zeros(self.lp.nConstraints))
w_ub = CyLPArray(np.zeros(self.lp.nVariables))
w_ub[idx] = float('inf')
lp += w_ub >= w1 >= CyLPArray(np.zeros(self.lp.nVariables))
lp += w_ub >= w2 >= CyLPArray(np.zeros(self.lp.nVariables))
# set constraints
# (pi, pi0) must be valid for both parts of the disjunction
lp += 0 >= -pi + self.lp.coefMatrix.T * u1 - w1
lp += 0 >= -pi + self.lp.coefMatrix.T * u2 + w2
lp += 0 <= -pi0 + CyLPArray(
self.lp.constraintsLower) * u1 - floor(x_idx) * w1.sum()
lp += 0 <= -pi0 + CyLPArray(
self.lp.constraintsLower) * u2 + ceil(x_idx) * w2.sum()
# normalize variables
lp += u1.sum() + u2.sum() + w1.sum() + w2.sum() == 1
# set objective: find the deepest cut
# since pi * x >= pi0 for all x in disjunction, we want min pi * x_star - pi0
lp.objective = CyLPArray(self.solution) * pi - pi0
# solve
lp.primal(startFinishOptions='x')
assert lp.getStatusCode() == 0, 'we should get optimal solution'
assert lp.objectiveValue <= 0, 'pi * x >= pi -> pi * x - pi >= 0 -> ' \
'negative objective at x^* since it gets cut off'
# get solution
return lp.primalVariableSolution['pi'], lp.primalVariableSolution[
'pi0']
def solve_cylp(model, B_vectors, weights, ray, chunksize):
"""
Worker process for LP_solver_cylp_mp.
Parameters
----------
model : CyClpModel
Model of the LP Problem, see :py:func:`LP_solver_cylp_mp`
B_vectors : matrix
Matrix containing B vectors, see :py:func:`construct_B_vectors`
weights : array
Weights.
ray : int
Starting ray.
chunksize : int
Number of rays to process.
Returns
-------
soln : array
Solution to LP problem.
See Also
--------
LP_solver_cylp_mp : Parent function.
LP_solver_cylp : Single Process Solver.
"""
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([chunksize, n_gates])
# import LP model in solver
s = CyClpSimplex(model)
# disable logging in multiprocessing anyway
s.logLevel = 0
i = 0
for raynum in range(ray, ray + chunksize):
# 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[i, :] = s.primalVariableSolution['x'][n_gates:2 * n_gates]
i = i + 1
return soln
def solve_cylp(model, B_vectors, weights, ray, chunksize):
"""
Worker process for LP_solver_cylp_mp.
Parameters
----------
model : CyClpModel
Model of the LP Problem, see :py:func:`LP_solver_cylp_mp`
B_vectors : matrix
Matrix containing B vectors, see :py:func:`construct_B_vectors`
weights : array
Weights.
ray : int
Starting ray.
chunksize : int
Number of rays to process.
Returns
-------
soln : array
Solution to LP problem.
See Also
--------
LP_solver_cylp_mp : Parent function.
LP_solver_cylp : Single Process Solver.
"""
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([chunksize, n_gates])
# import LP model in solver
s = CyClpSimplex(model)
# disable logging in multiprocessing anyway
s.logLevel = 0
i = 0
for raynum in range(ray, ray + chunksize):
# 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[i, :] = s.primalVariableSolution['x'][n_gates: 2 * n_gates]
i = i + 1
return soln
def __init__(self: T,
lp: CyClpSimplex,
integer_indices: List[int],
idx: int = None,
lower_bound: Union[float, int] = -float('inf'),
b_idx: int = None,
b_dir: str = None,
b_val: float = None,
depth: int = 0,
ancestors: tuple = None):
"""
:param lp: model object simplex is run against. Assumed Ax >= b
:param idx: index of this node (e.g. in the branch and bound tree)
:param integer_indices: 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
:param ancestors: tuple of nodes that preceded this node (e.g. were branched
on to create this node)
"""
assert isinstance(lp, CyClpSimplex), 'lp must be CyClpSimplex instance'
assert all(0 <= idx < lp.nVariables and isinstance(idx, int)
for idx in integer_indices), 'indices must match variables'
assert idx is None or isinstance(
idx, int), 'node idx must be integer if provided'
assert len(set(integer_indices)) == len(integer_indices), \
'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 integer_indices or b_idx is None, \
'branch index corresponds to integer variable if it exists'
assert b_dir in ['right', 'left'] or b_dir is None, \
'we can only branch right or left'
if b_val is not None:
good_left = 0 < b_val - lp.variablesUpper[b_idx] < 1
good_right = 0 < lp.variablesLower[b_idx] - b_val < 1
assert (b_dir == 'left' and good_left) or \
(b_dir == 'right' and good_right), 'branch val should be within 1 of both bounds'
assert isinstance(depth,
int) and depth >= 0, 'depth is a positive integer'
if ancestors is not None:
assert isinstance(ancestors,
tuple), 'ancestors must be a tuple if provided'
assert idx not in ancestors, 'idx cannot be an ancestor of itself'
lp.logLevel = 0
self.lp = lp
self._integer_indices = integer_indices
self.idx = idx
self._var_indices = list(range(lp.nVariables))
self._row_indices = list(range(lp.nConstraints))
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'
self.is_leaf = True
ancestors = ancestors or tuple()
idx_tuple = (idx, ) if idx is not None else tuple()
self.lineage = ancestors + idx_tuple or None # test all 4 ways this can pan out
def _base_branch(self: T,
branch_idx: int,
next_node_idx: int = None,
**kwargs: Any) -> Dict[str, T]:
""" Creates two new copies of the node with new bounds placed on the variable
with index <idx>, one with the variable's lower bound set to the ceiling
of its current value and another with the variable's upper bound set to
the floor of its current value.
:param branch_idx: index of variable to branch on
:param next_node_idx: index that should be assigned to the next node created.
If left None, assign no indices to both child nodes.
:return: dict of Nodes with the new bounds keyed by direction they branched
"""
assert next_node_idx is None or isinstance(next_node_idx, int), \
'next node index should be integer if provided'
assert self.lp_feasible, 'must solve before branching'
assert branch_idx in self._integer_indices, 'must branch on integer index'
b_val = self.solution[branch_idx]
assert self._is_fractional(
b_val), "index branched on must be fractional"
self.is_leaf = False
# get end basis to warm start the children
# appears to be tuple (variable statuses, slack statuses)
basis = self.lp.getBasisStatus()
# create new lp's for each direction
children = {'right': CyClpSimplex(), 'left': CyClpSimplex()}
for direction, lp in children.items():
x = lp.addVariable('x', self.lp.nCols)
l = CyLPArray(self.lp.variablesLower.copy())
u = CyLPArray(self.lp.variablesUpper.copy())
if direction == 'left':
u[branch_idx] = floor(b_val)
else:
l[branch_idx] = ceil(b_val)
lp += l <= x <= u
lp += CyLPArray(self.lp.constraintsLower.copy()) <= self.lp.coefMatrix * x \
<= CyLPArray(self.lp.constraintsUpper.copy())
lp.objective = self.lp.objective
lp.setBasisStatus(*basis) # warm start
# return instances of the subclass that calls this function
return {
'left':
type(self)(lp=children['left'],
integer_indices=self._integer_indices,
idx=next_node_idx,
lower_bound=self.objective_value,
b_idx=branch_idx,
b_dir='left',
b_val=b_val,
depth=self.depth + 1,
ancestors=self.lineage),
'right':
type(self)(lp=children['right'],
integer_indices=self._integer_indices,
idx=next_node_idx +
1 if next_node_idx is not None else next_node_idx,
lower_bound=self.objective_value,
b_idx=branch_idx,
b_dir='right',
b_val=b_val,
depth=self.depth + 1,
ancestors=self.lineage),
'next_node_idx':
next_node_idx + 2 if next_node_idx is not None else next_node_idx
}
def find_strong_disjunctive_cut(self, root_id: int) -> Tuple[CyLPArray, float]:
""" Generate a strong cut valid for the disjunction encoded in the subtree
rooted at node <root_id>. This cut is optimized to maximize the violation
of the LP relaxation solution at node <root_id>
see ISE 418 Lecture 13 slide 3, Lecture 14 slide 9, and Lecture 15 slides
6-7 for derivation
:param root_id: id of the node off which we will base the disjunction
:return: a valid inequality (pi, pi0), i.e. pi^T x >= pi0 for all x in
the convex hull of the disjunctive terms' LP relaxations
"""
# sanity checks
assert root_id in self.tree, 'parent must already exist in tree'
root = self.tree.get_node_instances(root_id)
# get each disjunctive term
terminal_nodes = self.tree.get_leaves(root_id)
# terminal nodes pruned for infeasibility do not expand disjunction, so remove them
disjunctive_nodes = {n.idx: n for n in terminal_nodes if n.lp_feasible is not False}
var_dicts = [{v.name: v.dim for v in n.lp.variables} for n in disjunctive_nodes.values()]
assert all(var_dicts[0] == d for d in var_dicts), \
'Each disjunctive term should have the same variables. The feature allowing' \
' otherwise remains to be developed.'
# useful constants
num_vars = sum(var_dim for var_dim in var_dicts[0].values())
inf = root.lp.getCoinInfinity()
# set infinite lower/upper bounds to 0 so they don't create numerical issues in constraints
lb = {idx: CyLPArray([val if val > -inf else 0 for val in n.lp.variablesLower])
for idx, n in disjunctive_nodes.items()} # adjusted lower bound
ub = {idx: CyLPArray([val if val < inf else 0 for val in n.lp.variablesUpper])
for idx, n in disjunctive_nodes.items()} # adjusted upper bound
# set corresponding variables in cglp to 0 to reflect there is no bound
# i.e. this variable should not exist in cglp
wb = {idx: CyLPArray([inf if val > -inf else 0 for val in n.lp.variablesLower])
for idx, n in disjunctive_nodes.items()} # w bounds - variable on lb constraints
vb = {idx: CyLPArray([inf if val < inf else 0 for val in n.lp.variablesUpper])
for idx, n in disjunctive_nodes.items()} # v bounds - variable on ub constraints
# instantiate LP
cglp = CyClpSimplex()
cglp.logLevel = 0 # quiet output when resolving
# declare variables (what to do with case when we have degenerate constraint)
pi = cglp.addVariable('pi', num_vars)
pi0 = cglp.addVariable('pi0', 1)
u = {idx: cglp.addVariable(f'u_{idx}', n.lp.nConstraints) for idx, n in
disjunctive_nodes.items()}
w = {idx: cglp.addVariable(f'w_{idx}', n.lp.nVariables) for idx, n in
disjunctive_nodes.items()}
v = {idx: cglp.addVariable(f'v_{idx}', n.lp.nVariables) for idx, n in
disjunctive_nodes.items()}
# bound them
for idx in disjunctive_nodes:
cglp += u[idx] >= 0
cglp += 0 <= w[idx] <= wb[idx]
cglp += 0 <= v[idx] <= vb[idx]
# add constraints
for i, n in disjunctive_nodes.items():
# (pi, pi0) must be valid for each disjunctive term's LP relaxation
cglp += 0 >= -pi + n.lp.coefMatrix.T * u[i] + \
np.matrix(np.eye(num_vars)) * w[i] - np.matrix(np.eye(num_vars)) * v[i]
cglp += 0 <= -pi0 + CyLPArray(n.lp.constraintsLower) * u[i] + \
lb[i] * w[i] - ub[i] * v[i]
# normalize variables so they don't grow arbitrarily
cglp += sum(var.sum() for var_dict in [u, w, v] for var in var_dict.values()) == 1
# set objective: find the deepest cut
# since pi * x >= pi0 for all x in disjunction, we want min pi * x_star - pi0
cglp.objective = CyLPArray(root.solution) * pi - pi0
# solve
cglp.primal(startFinishOptions='x')
assert cglp.getStatusCode() == 0, 'we should get optimal solution'
assert cglp.objectiveValue <= 0, 'pi * x >= pi0 -> pi * x - pi0 >= 0 -> ' \
'negative objective at x^* since it gets cut off'
# get solution
return cglp.primalVariableSolution['pi'], cglp.primalVariableSolution['pi0']
def _bound_dual(self, cur_lp: CyClpSimplex) -> CyClpSimplex:
""" Place a bound on each index of the dual variable associated with the
constraints of this node's LP relaxation and resolve. We do this by adding
to each constraint i the slack variable 's_i' in the node's LP relaxation,
and we give each new variable a large, positive coefficient in the objective.
By duality, we get the desired dual LP constraints. Therefore, for nodes
with infeasible primal LP relaxations and unbounded dual LP relaxations,
resolving gives us a finite (albeit very large) dual solution, which can
be used to parametrically lower bound the objective value of this node as
we change its right hand side.
:param cur_lp: the CyClpSimplex instance for which we want to bound its
dual solution and resolve
:return: A CyClpSimplex instance representing the same model as input,
with the additions prescribed in the method description
"""
# we add slack at end so user does not have to worry about adding to each node they create
# and so we don't have to go back and update needlessly
assert isinstance(cur_lp, CyClpSimplex), 'must give CyClpSimplex instance'
for i, constr in enumerate(cur_lp.constraints):
assert f's_{i}' not in [v.name for v in cur_lp.variables], \
f"variable 's_{i}' is a reserved name. please name your variable something else"
# cylp lacks (a documented) way to add a column, so rebuild the LP :[
new_lp = CyClpSimplex()
new_lp.logLevel = 0 # quiet output when resolving
# recreate variables
var_map = {v: new_lp.addVariable(v.name, v.dim) for v in cur_lp.variables}
# bound them
for orig_v, new_v in var_map.items():
new_lp += CyLPArray(orig_v.lower) <= new_v <= CyLPArray(orig_v.upper)
# re-add constraints, with slacks this time
s = {}
for i, constr in enumerate(cur_lp.constraints):
s[i] = new_lp.addVariable(f's_{i}', constr.nRows)
new_lp += s[i] >= CyLPArray(np.zeros(constr.nRows))
new_lp += CyLPArray(constr.lower) <= \
sum(constr.varCoefs[v] * var_map[v] for v in constr.variables) \
+ np.matrix(np.identity(constr.nRows))*s[i] <= CyLPArray(constr.upper)
# set objective
new_lp.objective = sum(
CyLPArray(cur_lp.objectiveCoefficients[orig_v.indices]) * new_v for
orig_v, new_v in var_map.items()
) + sum(self._M * v.sum() for v in s.values())
# warm start
orig_var_status, orig_slack_status = cur_lp.getBasisStatus()
# each s_i at lower bound of 0 when added - status 3
np.concatenate((orig_var_status, np.ones(sum(v.dim for v in s.values()))*3))
new_lp.setBasisStatus(orig_var_status, orig_slack_status)
# rerun and reassign
new_lp.dual(startFinishOptions='x')
return new_lp
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(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 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 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
