def populate_dual_subproblem(data, upper_cost=None, flow_cost=None):
"""
Function that populates the Benders Dual Subproblem, as suggested by the
paper "Minimal Infeasible Subsystems and Bender's cuts" by Fischetti,
Salvagnin and Zanette.
:param data: Problem data structure
:param upper_cost: Link setup decisions fixed in the master
:param flow_cost: This is the cost of the continuous variables of the
master problem, as explained in the paper
:return: Numpy array of Gurobi model objects
"""
# Gurobi model objects
subproblems = np.empty(shape=(data.periods, data.commodities),
dtype=object)
# Construct model for period/commodity 0.
# Then, copy this and change the coefficients
dual_subproblem = Model('dual_subproblem_(0,0)')
# Ranges we are going to need
arcs, periods, commodities = xrange(data.arcs.size), xrange(
data.periods), xrange(data.commodities)
# Origins and destinations of commodities
origins, destinations = data.origins, data.destinations
# We use arrays to store variable indexes and variable objects. Why use
# both? Gurobi wont let us get the values of individual variables
# within a callback.. We just get the values of a large array of
# variables, in the order they were initially defined. To separate them
# in variable categories, we will have to use index arrays
flow_index = np.zeros(shape=data.nodes, dtype=int)
flow_duals = np.empty_like(flow_index, dtype=object)
ubounds_index = np.zeros(shape=len(arcs), dtype=int)
ubounds_duals = np.empty_like(ubounds_index, dtype=object)
# Makes sure we don't add variables more than once
flow_duals_names = set()
if upper_cost is None:
upper_cost = np.zeros(shape=(len(periods), len(arcs)), dtype=float)
if flow_cost is None:
flow_cost = np.zeros(shape=(len(periods), len(commodities)),
dtype=float)
# Populate all variables in one loop, keep track of their indexes
# Data for period = 0, com = 0
count = 0
for arc in arcs:
ubounds_duals[arc] = dual_subproblem.addVar(
obj=-upper_cost[0, arc], lb=0., name='ubound_dual_a{}'.format(arc))
ubounds_index[arc] = count
count += 1
start_node, end_node = get_2d_index(data.arcs[arc], data.nodes)
start_node, end_node = start_node - 1, end_node - 1
for node in (start_node, end_node):
var_name = 'flow_dual_n{}'.format(node)
if var_name not in flow_duals_names:
flow_duals_names.add(var_name)
obj, ub = 0., GRB.INFINITY
if data.origins[0] == node:
obj = 1.
if data.destinations[0] == node:
obj = -1.
ub = 0.
flow_duals[node] = \
dual_subproblem.addVar(
obj=obj, lb=0., name=var_name)
flow_index[node] = count
count += 1
opt_var = dual_subproblem.addVar(obj=-flow_cost[0, 0],
lb=0.,
name='optimality_var')
dual_subproblem.params.threads = 2
dual_subproblem.params.LogFile = ""
dual_subproblem.update()
# Add constraints
demand = data.demand[0, 0]
for arc in arcs:
start_node, end_node = get_2d_index(data.arcs[arc], data.nodes)
start_node, end_node = start_node - 1, end_node - 1
lhs = flow_duals[start_node] - flow_duals[end_node] \
- ubounds_duals[arc] - \
opt_var * data.variable_cost[arc] * demand
dual_subproblem.addConstr(lhs <= 0., name='flow_a{}'.format(arc))
# Original Fischetti model
lhs = quicksum(ubounds_duals) + opt_var
dual_subproblem.addConstr(lhs == 1, name='normalization_constraint')
# Store variable indices
dual_subproblem._ubounds_index = ubounds_index
dual_subproblem._flow_index = flow_index
dual_subproblem._all_variables = np.array(dual_subproblem.getVars())
dual_subproblem._flow_duals = np.take(dual_subproblem._all_variables,
flow_index)
dual_subproblem._ubound_duals = np.take(dual_subproblem._all_variables,
ubounds_index)
dual_subproblem.setParam('OutputFlag', 0)
dual_subproblem.modelSense = GRB.MAXIMIZE
dual_subproblem.update()
subproblems[0, 0] = dual_subproblem
for period, com in product(periods, commodities):
if (period, com) != (0, 0):
model = dual_subproblem.copy()
optimality_var = model.getVarByName('optimality_var')
optimality_var.Obj = -flow_cost[period, com]
demand = data.demand[period, com]
for node in xrange(data.nodes):
variable = model.getVarByName('flow_dual_n{}'.format(node))
if origins[com] == node:
obj = 1.
elif destinations[com] == node:
obj = -1.
else:
obj = 0.
variable.obj = obj
for arc in arcs:
variable = model.getVarByName('ubound_dual_a{}'.format(arc))
variable.Obj = -np.sum(upper_cost[:period + 1, arc])
constraint = model.getConstrByName('flow_a{}'.format(arc))
model.chgCoeff(constraint, optimality_var,
-demand * data.variable_cost[arc])
model._all_variables = np.array(model.getVars())
model.update()
subproblems[period, com] = model
return subproblems
def populate_dual_subproblem(data):
"""
Function that populates the Benders Dual Subproblem, as suggested by the
paper "Minimal Infeasible Subsystems and Bender's cuts" by Fischetti,
Salvagnin and Zanette.
:param data: Problem data structure
:param upper_cost: Link setup decisions fixed in the master
:param flow_cost: This is the cost of the continuous variables of the
master problem, as explained in the paper
:return: Numpy array of Gurobi model objects
"""
# Gurobi model objects
subproblems = np.empty(shape=(data.periods, data.commodities),
dtype=object)
# Construct model for period/commodity 0.
# Then, copy this and change the coefficients
subproblem = Model('subproblem_(0,0)')
# Ranges we are going to need
arcs, periods, commodities, nodes = xrange(data.arcs.size), xrange(
data.periods), xrange(data.commodities), xrange(data.nodes)
# Other data
demand, var_cost = data.demand, data.variable_cost
# Origins and destinations of commodities
origins, destinations = data.origins, data.destinations
# We use arrays to store variable indexes and variable objects. Why use
# both? Gurobi wont let us get the values of individual variables
# within a callback.. We just get the values of a large array of
# variables, in the order they were initially defined. To separate them
# in variable categories, we will have to use index arrays
flow_vars = np.empty_like(arcs, dtype=object)
# Populate all variables in one loop, keep track of their indexes
# Data for period = 0, com = 0
for arc in arcs:
flow_vars[arc] = subproblem.addVar(obj=demand[0, 0] * var_cost[arc],
lb=0.,
ub=1.,
name='flow_a{}'.format(arc))
subproblem.update()
# Add constraints
for node in nodes:
out_arcs = get_2d_index(data.arcs, data.nodes)[0] == node + 1
in_arcs = get_2d_index(data.arcs, data.nodes)[1] == node + 1
lhs = quicksum(flow_vars[out_arcs]) - quicksum(flow_vars[in_arcs])
subproblem.addConstr(lhs == 0., name='flow_bal{}'.format(node))
subproblem.update()
# Store variables
subproblem._all_variables = flow_vars.tolist()
# Set parameters
subproblem.setParam('OutputFlag', 0)
subproblem.modelSense = GRB.MINIMIZE
subproblem.params.threads = 2
subproblem.params.LogFile = ""
subproblem.update()
subproblems[0, 0] = subproblem
for period, com in product(periods, commodities):
if (period, com) != (0, 0):
model = subproblem.copy()
model.ModelName = 'subproblem_({},{})'.format(period, com)
flow_cost = data.demand[period, com] * var_cost
model.setObjective(LinExpr(flow_cost.tolist(), model.getVars()))
model.setAttr('rhs', model.getConstrs(), [0.0] * data.nodes)
model._all_variables = model.getVars()
model.update()
subproblems[period, com] = model
return subproblems
