def get_first_dest_qubo(self, start_step, dests, costs, source):
fir_qubo = Qubo()
for dest in dests:
in_index = ((start_step, dest), (start_step, dest))
in_cost = costs[source][dest]
fir_qubo.add(in_index, in_cost)
return fir_qubo
def get_last_dest_qubo(self, final_step, dests, costs, source):
las_qubo = Qubo()
for dest in dests:
out_index = ((final_step, dest), (final_step, dest))
out_cost = costs[dest][source]
las_qubo.add(out_index, out_cost)
return las_qubo
def get_capacity_qubo(self, capacity, start_step, final_step):
dests = self.dests
weights = self.weights
cap_qubo = Qubo()
for (d1, d2) in combinations(dests, 2):
for (s1, s2) in combinations(range(start_step, final_step + 1), 2):
index = ((s1, d1), (s2, d2))
cost = weights[d1] * weights[d2] / capacity**2
cap_qubo.add(index, cost)
return cap_qubo
def get_order_qubo(self, start_step, final_step, dests, costs):
source = self.source
ord_qubo = Qubo()
# Order constraint
for step in range(start_step, final_step):
for dest1 in dests:
for dest2 in dests:
cost = costs[dest1][dest2]
index = ((step, dest1), (step + 1, dest2))
ord_qubo.add(index, cost)
return ord_qubo
def get_time_qubo(self, start_step, final_step):
dests = self.dests
time_windows = self.time_windows
tim_qubo = Qubo()
for (d1, d2) in product(dests, dests):
for (s1, s2) in combinations(range(start_step, final_step + 1), 2):
index = ((s1, d1), (s2, d2))
time_diff = time_windows[d1] - time_windows[d2] + 1
step_diff = s2 - s1
cost = float(time_diff) * float(step_diff)
if time_diff < 0:
cost = 0.
tim_qubo.add(index, cost)
return tim_qubo
def get_qubo(self, only_one_const, order_const):
tsp_qubo = Qubo()
steps_num = len(self.dests)
source = self.source
# Only one vertex for one step.
for step in range(steps_num):
tsp_qubo.add_only_one_constraint([(step, i) for i in self.dests], only_one_const)
# Only one step for one vertex
for dest in self.dests:
tsp_qubo.add_only_one_constraint([(step, dest) for step in range(steps_num)], only_one_const)
# Constraints for first and last destination.
for dest in self.dests:
in_index = ((0, dest), (0, dest))
out_index = (steps_num - 1, dest), (steps_num - 1, dest)
in_cost = self.costs[source][dest]
out_cost = self.costs[dest][source]
tsp_qubo.add(in_index, in_cost * order_const)
tsp_qubo.add(out_index, out_cost * order_const)
# Constraints for next steps.
for step in range(steps_num - 1):
for i in self.dests:
for j in self.dests:
cost = self.costs[i][j]
index = ((step, i), (step + 1, j))
tsp_qubo.add(index, cost * order_const)
return tsp_qubo
def get_qubo_with_time(self, vehicle_limits, only_one_const, order_const,
capacity_const, time_const):
# Steps counting.
steps = 0
for (_, r) in vehicle_limits:
steps += r
dests = self.dests
costs = self.costs
source = self.source
time_windows = self.time_windows
dests_with_times = list()
vrp_qubo = Qubo()
# Time blocks counting.
time_blocks_num = int(
max([time_windows[i] for i in time_windows]) / self.TIME_BLOCK)
for dest in dests:
first = int((time_windows[dest] - self.TIME_WINDOW_RADIUS) /
self.TIME_BLOCK)
last = int((time_windows[dest] + self.TIME_WINDOW_RADIUS) /
self.TIME_BLOCK)
dests_with_times += [(time, dest) for time in range(first, last)]
vrp_qubo.add_only_one_constraint(
[(step, (time, dest))
for step, time in product(range(steps), range(first, last))],
only_one_const)
# Adding qubits for source.
dests_with_source = dests_with_times.copy()
dests_with_source += [(time, source)
for time in range(time_blocks_num)]
# Costs for dests_with_times.
costs_with_times = dict()
for (t1, d1), (t2, d2) in product(dests_with_source,
dests_with_source):
cost = only_one_const
if t1 <= t2:
cost = costs[d1][d2]
if not (t1, d1) in costs_with_times:
costs_with_times[(t1, d1)] = dict()
costs_with_times[(t1, d1)][(t2, d2)] = cost
start = 0
for vehicle in range(len(vehicle_limits)):
min_size = vehicle_limits[vehicle][0]
max_size = vehicle_limits[vehicle][1]
min_final = start + min_size - 1
max_final = start + max_size - 1
# First steps should have normal destinations.
if min_size != 0:
for step in range(start, min_final + 1):
vrp_qubo.add_only_one_constraint(
[(step, dest) for dest in dests_with_times],
only_one_const)
ord_min_qubo = self.get_order_qubo(start, min_final,
dests_with_times)
vrp_qubo.merge_with(ord_min_qubo, 1., order_const)
# In other steps vehicles can wait in source.
if max_size != min_size:
for step in range(min_final + 1, max_final + 1):
vrp_qubo.add_only_one_constraint(
[(step, dest) for dest in dests_with_source],
only_one_const)
ord_max_qubo = self.get_order_qubo(min_final + 1, max_final,
dests_with_source,
costs_with_times)
vrp_qubo.merge_with(ord_max_qubo, 1., order_const)
# From min_final step to min_final + 1 step.
if min_size != 0 and min_size != max_size:
for dest1 in dests_with_times:
for dest2 in dests_with_source:
cost = costs[dest1][dest2]
index = ((min_final, dest1), (min_final + 1, dest2))
vrp_qubo.add(index, cost * order_const)
# First and last destinations.
fir_qubo = self.get_first_dest_qubo(start, dests_with_times,
costs_with_times, (0, source))
las_qubo = self.get_last_dest_qubo(max_final, dests_with_source,
costs_with_times,
(time_blocks_num - 1, source))
vrp_qubo.merge_with(fir_qubo, 1., order_const)
vrp_qubo.merge_with(las_qubo, 1., order_const)
# Capacity constraints.
if capacity_const != 0:
capacity = capacities[vehicle]
cap_qubo = self.get_capacity_qubo(capacity, start, max_final)
vrp_qubo.merge_with(cap_qubo, 1., capacity_const)
# Time constraints.
if time_const != 0:
time_costs = self.time_costs
new_time_costs = dict()
for ((t1, d1), (t2, d2)) in product(dests_with_source,
dests_with_source):
new_time_costs[(t1, d1)][(t2, d2)] = time_costs[d1][d2]
tim_qubo = self.get_time_qubo2(start, max_final)
vrp_qubo.merge_with(tim_qubo, 1., time_const)
start = max_final + 1
return vrp_qubo
def get_qubo_with_both_limits(self, vehicle_limits, only_one_const,
order_const, capacity_const, time_const):
steps = 0
for (_, r) in vehicle_limits:
steps += r
capacities = self.capacities
dests = self.dests
source = self.source
dests_with_source = dests.copy()
dests_with_source.append(source)
costs = self.costs
vrp_qubo = Qubo()
# Only one step for one destination.
for dest in self.dests:
vrp_qubo.add_only_one_constraint([(step, dest)
for step in range(steps)],
only_one_const)
start = 0
for vehicle in range(len(vehicle_limits)):
min_size = vehicle_limits[vehicle][0]
max_size = vehicle_limits[vehicle][1]
min_final = start + min_size - 1
max_final = start + max_size - 1
# First steps should have normal destinations.
if min_size != 0:
for step in range(start, min_final + 1):
vrp_qubo.add_only_one_constraint([(step, dest)
for dest in dests],
only_one_const)
ord_min_qubo = self.get_order_qubo(start, min_final, dests,
costs)
vrp_qubo.merge_with(ord_min_qubo, 1., order_const)
# In other steps vehicles can wait in source.
if max_size != min_size:
for step in range(min_final + 1, max_final + 1):
vrp_qubo.add_only_one_constraint(
[(step, dest) for dest in dests_with_source],
only_one_const)
ord_max_qubo = self.get_order_qubo(min_final + 1, max_final,
dests_with_source, costs)
vrp_qubo.merge_with(ord_max_qubo, 1., order_const)
# From min_final step to min_final + 1 step.
if min_size != 0 and min_size != max_size:
for dest1 in dests:
for dest2 in dests_with_source:
cost = costs[dest1][dest2]
index = ((min_final, dest1), (min_final + 1, dest2))
vrp_qubo.add(index, cost * order_const)
# First and last destinations.
fir_qubo = self.get_first_dest_qubo(start, dests, costs, source)
las_qubo = self.get_last_dest_qubo(max_final, dests_with_source,
costs, source)
vrp_qubo.merge_with(fir_qubo, 1., order_const)
vrp_qubo.merge_with(las_qubo, 1., order_const)
# Capacity constraints.
if capacity_const != 0:
capacity = capacities[vehicle]
cap_qubo = self.get_capacity_qubo(capacity, start, max_final)
vrp_qubo.merge_with(cap_qubo, 1., capacity_const)
# Time constraints.
if time_const != 0:
tim_qubo = self.get_time_qubo(start, max_final)
vrp_qubo.merge_with(tim_qubo, 1., time_const)
start = max_final + 1
return vrp_qubo
