def is_solution_feasible(prob, sol, tol):
assign_vars = prob.assign_vars
assign_vals = dict([((i, j, k), sol[assign_vars[i, j, k]])
for (i, j, k) in assign_vars.keys()])
if "Tours" in prob.options:
threshold = prob.options["Tours"]
else:
threshold = 1.0 - prob.tol # Default is only consider integer arcs
# Get the graphs for each vehicle
vehNodes, vehArcs = get_graphs(prob.vrp, assign_vals, threshold)
# Loop over the vehicles that are used
for k in prob.vrp.VEHS:
# Extract the nodes and arcs for each vehicle to pass into get_subtour()
if (sol[prob.use_vars[k]] > prob.tol):
kNodes = vehNodes[k]
kArcs = vehArcs[k]
if len(kNodes) > 0:
# Look for subtour in each vehicles graph from the first nod
nodes, arcs = get_subtour(kNodes, kArcs, kNodes[0])
# If a subtour is found then the solution is not feasible, so will generate cuts
if (len(nodes) == len(arcs)) and (len(nodes) < len(kNodes)):
return False
# Else no subtours
return True
def is_solution_feasible(prob, sol, tol):
assign_vars = prob.assign_vars
assign_vals = dict([((i, j, k), sol[assign_vars[i, j, k]])
for (i, j, k) in assign_vars.keys()])
if "Tours" in prob.options:
threshold = prob.options["Tours"]
else:
threshold = 1.0 - prob.tol # Default is only consider integer arcs
# Get the graphs for each vehicle
nodes = prob.vrp.EXTLOCS[:]
arcs = [(i, j, k) for (i, j, k) in assign_vars.keys()
if sol[assign_vars[i, j, k]] > threshold]
# Loop over the vehicles that are used
for k in prob.vrp.VEHS:
# Extract the arcs for each vehicle to pass into get_subtour()
vehArcs = [x[:2] for x in arcs if x[2] == k]
# Look for subtour in each vehicles graph from the first node
tNodes, tArcs = get_subtour(nodes, vehArcs, nodes[1])
# If a subtour is found then the solution is not feasible, so will generate cuts
if (len(tNodes) == len(tArcs)) and (len(tNodes) < len(nodes)):
# print("Solution has subtours!")
return False
# No subtours
# print("Solution has no subtours!")
return True
def generate_cuts(prob, sol):
# No constraints added initially
cons = []
cons_added = 0
# Get the assignment variables
assign_vars = prob.assign_vars
assign_vals = dict([((i, j, k), sol[assign_vars[i, j, k]])
for (i, j, k) in assign_vars.keys()])
# Get the threshold for whether an arc should be considered
# as part of the solution (almost = 1 by default)
if "Tours" in prob.options:
threshold = prob.options["Tours"]
else:
threshold = 1.0 - prob.tol # Default is only consider integer arcs
# Get the graph structure for each vehicle
vehNodes, vehArcs = get_graphs(prob.vrp, assign_vals, threshold)
# Loop over the vehicles that are used
for k in prob.vrp.VEHS:
# Extract the nodes and arcs for each vehicle
if (sol[prob.use_vars[k]] > prob.tol):
kNodes = vehNodes[k]
kArcs = vehArcs[k]
# Define the set of nodes that have not been put in a connected component
not_connected = set(kNodes)
# While any nodes are not in a connected component
while not_connected:
# Get an unconnected node
start = not_connected.pop()
# Find a subtour from that node
nodes, arcs = get_subtour(kNodes, kArcs, start)
# If it is a subtour (and not a complete tour), add a subtour elimination constraint
if (len(nodes) == len(arcs)) and (len(nodes) < len(kNodes)):
cons_added += 1
# Option 1
cons.append(
lpSum(assign_vars[i, j, k]
for (i, j) in kArcs) <= len(kArcs) - 1)
# Remove the subtour nodes as they are now connected
not_connected -= set(nodes)
if len(cons) > 0:
return cons
else:
return None
def is_solution_feasible(prob, sol, tol):
# User callback for checking feasibility
# Display feasibility checks if desired
# assignments = get_assignments(prob, sol, tol)
# prob.vrp.setSolution(assignments, tol)
# prob.vrp.displaySolution(title="Feasibility Check", showProb=None)
# Get the threshold for whether an arc should be considered
# as part of the solution (almost = 1 by default)
if "Tours" in prob.options:
threshold = prob.options["Tours"]
else:
threshold = 1.0 - prob.tol # Default is only consider integer arcs
# Get the assignment variables
assign_vars = prob.assign_vars
assign_vals = dict([((i, j, k), sol[assign_vars[i, j, k]])
for (i, j, k) in assign_vars.keys()])
# Get the graphs for each vehicle
nodes = prob.vrp.EXTLOCS[:]
arcs = [(i, j, k) for (i, j, k) in assign_vars.keys()
if sol[assign_vars[i, j, k]] > threshold]
# Loop over the vehicles that are used
for k in prob.vrp.VEHS:
# Extract the arcs for each vehicle to pass into get_subtour()
vehArcs = [x[:2] for x in arcs if x[2] == k]
# Define the set of nodes that have not been put in a connected component
not_connected = set(nodes[:])
# While any nodes are not in a connected component
while not_connected:
# Get an unconnected node
start = not_connected.pop()
# Find a subtour from that node
tNodes, tArcs = get_subtour(nodes, vehArcs, start)
# tNodes, tArcs = get_subtour(nodes, vehArcs, nodes[0])
# If a subtour is found then the solution is not feasible, so will declare it as such
if (len(tNodes) == len(tArcs)) and (len(tNodes) < len(nodes)) and (
'O' not in tNodes):
# print("Solution has subtours!")
return False
# Remove the subtour nodes as they are now connected
not_connected -= set(tNodes)
# Otherwise it is feasible
# print("Solution has no subtours!")
return True
def generate_cuts(prob, sol):
'''
obj_val = 0.0
for v in prob.objective:
obj_val += prob.objective[v] * sol[v]
print("In generate_cuts...")
print("Solution value =", obj_val)
sys.stdout.flush()
for var in prob.variables():
if abs(sol[var]) > prob.tol:
print(var.name, "=", sol[var])
'''
cons = []
cons_added = 0
assign_vars = prob.assign_vars
assign_vals = dict([((i, j, k), sol[assign_vars[i, j, k]]) for (i, j, k) in assign_vars.keys()])
if "Tours" in prob.options:
threshold = prob.options["Tours"]
else:
threshold = 1.0 - prob.tol # Default is only consider integer arcs
vehNodes, vehArcs = get_graphs(prob.vrp, assign_vals, threshold)
for k in prob.vrp.VEHS:
if (sol[prob.use_vars[k]] > prob.tol):
kNodes = vehNodes[k]
kArcs = vehArcs[k]
# print(k, kNodes, kArcs)
not_connected = set(kNodes)
while not_connected:
start = not_connected.pop()
nodes, arcs = get_subtour(kNodes, kArcs, start)
# print(nodes, arcs)
# print(len(nodes), len(arcs), len(kNodes))
if (len(nodes) == len(arcs)) and (len(nodes) < len(kNodes)):
cons_added += 1
# prob.vrp.setSolution(assign_vals, prob.tol)
# prob.vrp.displaySolution(title="Subtour example", showProb=False)
cons.append(lpSum(assign_vars[i, j, k]
for (i, j) in kArcs) \
<= len(kArcs) - 1)
# print("Subtour elimination!", cons[-1])
# return cons
not_connected -= set(nodes)
if len(cons) > 0:
return cons
else:
return None
def is_solution_feasible(prob, sol, tol):
'''
obj_val = 0.0
for v in prob.objective:
obj_val += prob.objective[v] * sol[v]
print("In is_solution_feasible...")
print("Solution value =", obj_val)
sys.stdout.flush()
for var in prob.variables():
if abs(sol[var]) > prob.tol:
print(var.name, "=", sol[var])
'''
assign_vars = prob.assign_vars
'''
# Display the current node solution
prob.vrp.setSolution(assign_vars, sol, prob.tol)
prob.vrp.displaySolution()
'''
assign_vals = dict([((i, j, k), sol[assign_vars[i, j, k]])
for (i, j, k) in assign_vars.keys()])
if "Tours" in prob.options:
threshold = prob.options["Tours"]
else:
threshold = 1.0 - prob.tol # Default is only consider integer arcs
vehNodes, vehArcs = get_graphs(prob.vrp, assign_vals, threshold)
for k in prob.vrp.VEHS:
if (sol[prob.use_vars[k]] > prob.tol):
kNodes = vehNodes[k]
kArcs = vehArcs[k]
# print(k, kNodes, kArcs)
if len(kNodes) > 0:
nodes, arcs = get_subtour(kNodes, kArcs, kNodes[0])
# print(nodes, arcs)
if (len(nodes) == len(arcs)) and (len(nodes) < len(kNodes)):
# print("Solution has subtours!")
return False
# print("Solution has no subtours!")
return True
def generate_cuts(prob, sol):
# No constraints added
cons = []
cons_added = 0
# Get the assignment variables and values
assign_vars = prob.assign_vars
assign_vals = dict([((i, j, k), sol[assign_vars[i, j, k]])
for (i, j, k) in assign_vars.keys()])
# Get the threshold for whether an arc should be considered
# as part of the solution (almost = 1 by default)
if "Tours" in prob.options:
threshold = prob.options["Tours"]
else:
threshold = 1.0 - prob.tol # Default is only consider integer arcs
# Get the graphs for each vehicle
nodes = prob.vrp.EXTLOCS[:]
arcs = [(i, j, k) for (i, j, k) in assign_vars.keys()
if sol[assign_vars[i, j, k]] > threshold]
# Loop over the vehicles that are used
for k in prob.vrp.VEHS:
# Extract the arcs for each vehicle
vehArcs = [x[:2] for x in arcs if x[2] == k]
# Define the set of nodes that have not been put in a connected component
not_connected = set(nodes[:])
# While any nodes are not in a connected component
while not_connected:
# Get an unconnected node
start = not_connected.pop()
# Find a subtour from that starting node
tNodes, tArcs = get_subtour(nodes, vehArcs, start)
# If it is a subtour (and not a complete tour), add a subtour elimination constraint provided that
# the depot is not included in the subtour,
if len(tNodes) == len(tArcs) and len(tNodes) < len(nodes) and (
'O' not in tNodes):
cons_added += 1
# If a subtour is found then that graph must be banned
# Option 1
cons.append(
lpSum(assign_vars[i, j, k]
for (i, j) in tArcs) <= len(tArcs) - 1)
# Option 2
# cons.append(lpSum(assign_vars[i, j, k]
# for i in tNodes
# for j in set(nodes).difference(tNodes)) +
# lpSum(assign_vars[j, i, k]
# for i in tNodes
# for j in set(nodes).difference(tNodes))
# >= 2)
# print("Subtour elimination!", cons[-1])
# Return one subtour elimination constraint at a time
if cons_added == 1:
return cons
# Remove the subtour nodes as they are now connected
not_connected -= set(tNodes)
if len(cons) > 0:
return cons
else:
return None