Google OR-Tools：具有多种货物类型和容量的 CVRP
Google OR-Tools: CVRP with multiple cargo types and capacities
我正在尝试解决具有多种货物类型和容量的 CVRP。假设我有四辆车和两种货物（橘子和苹果）。每个 Vehicle 确实对苹果和橙子有不同的容量，每个节点都有不同的需求。两辆车只能运苹果，两辆车只能运橙子。所以我定义了以下数据：
data['demands_oranges'] = [0, 1, 1, 2, 4, 2, 4, 1, 8, 1, 2, 1, 2, 4, 4, 8, 8]
data['demands_apples'] = [0, 1, 1, 2, 4, 2, 4, 1, 8, 1, 2, 1, 2, 4, 4, 8, 8]
data['vehicle_capacities_oranges'] = [0, 0, 40, 40]
data['vehicle_capacities_apples'] = [40, 40, 0, 0]
此外，我为每个容量定义了两个维度：
# Add Capacity constraint.
def demand_callback_apples(from_index):
"""Returns the demand of the node."""
# Convert from routing variable Index to demands NodeIndex.
from_node = manager.IndexToNode(from_index)
return data['demands_apples'][from_node]
demand_callback_index_apples = routing.RegisterUnaryTransitCallback(
demand_callback_apples)
routing.AddDimensionWithVehicleCapacity(
demand_callback_index_apples,
0, # null capacity slack
data['vehicle_capacities_apples'], # vehicle maximum capacities
True, # start cumul to zero
'Capacity_apples')
def demand_callback_oranges(from_index):
"""Returns the demand of the node."""
# Convert from routing variable Index to demands NodeIndex.
from_node = manager.IndexToNode(from_index)
return data['demands_oranges'][from_node]
demand_callback_index_oranges = routing.RegisterUnaryTransitCallback(
demand_callback_oranges)
routing.AddDimensionWithVehicleCapacity(
demand_callback_index_oranges,
0, # null capacity slack
data['vehicle_capacities_oranges'], # vehicle maximum capacities
True, # start cumul to zero
'Capacity_oranges')
问题是，此输入数据没有返回解。尽管事实上车辆容量还远未超过。
当我使用时，模型出于某种原因工作：
data['vehicle_capacities_oranges'] = [0, 0, 40, 40]
data['vehicle_capacities_apples'] = [0, 0, 40, 40]
但这不是我需要的。这是什么原因？
代码：
"""Capacited Vehicles Routing Problem (CVRP)."""
from ortools.constraint_solver import routing_enums_pb2
from ortools.constraint_solver import pywrapcp
def create_data_model():
"""Stores the data for the problem."""
data = {}
data['distance_matrix'] = [
[
0, 548, 776, 696, 582, 274, 502, 194, 308, 194, 536, 502, 388, 354,
468, 776, 662
],
[
548, 0, 684, 308, 194, 502, 730, 354, 696, 742, 1084, 594, 480, 674,
1016, 868, 1210
],
[
776, 684, 0, 992, 878, 502, 274, 810, 468, 742, 400, 1278, 1164,
1130, 788, 1552, 754
],
[
696, 308, 992, 0, 114, 650, 878, 502, 844, 890, 1232, 514, 628, 822,
1164, 560, 1358
],
[
582, 194, 878, 114, 0, 536, 764, 388, 730, 776, 1118, 400, 514, 708,
1050, 674, 1244
],
[
274, 502, 502, 650, 536, 0, 228, 308, 194, 240, 582, 776, 662, 628,
514, 1050, 708
],
[
502, 730, 274, 878, 764, 228, 0, 536, 194, 468, 354, 1004, 890, 856,
514, 1278, 480
],
[
194, 354, 810, 502, 388, 308, 536, 0, 342, 388, 730, 468, 354, 320,
662, 742, 856
],
[
308, 696, 468, 844, 730, 194, 194, 342, 0, 274, 388, 810, 696, 662,
320, 1084, 514
],
[
194, 742, 742, 890, 776, 240, 468, 388, 274, 0, 342, 536, 422, 388,
274, 810, 468
],
[
536, 1084, 400, 1232, 1118, 582, 354, 730, 388, 342, 0, 878, 764,
730, 388, 1152, 354
],
[
502, 594, 1278, 514, 400, 776, 1004, 468, 810, 536, 878, 0, 114,
308, 650, 274, 844
],
[
388, 480, 1164, 628, 514, 662, 890, 354, 696, 422, 764, 114, 0, 194,
536, 388, 730
],
[
354, 674, 1130, 822, 708, 628, 856, 320, 662, 388, 730, 308, 194, 0,
342, 422, 536
],
[
468, 1016, 788, 1164, 1050, 514, 514, 662, 320, 274, 388, 650, 536,
342, 0, 764, 194
],
[
776, 868, 1552, 560, 674, 1050, 1278, 742, 1084, 810, 1152, 274,
388, 422, 764, 0, 798
],
[
662, 1210, 754, 1358, 1244, 708, 480, 856, 514, 468, 354, 844, 730,
536, 194, 798, 0
],
]
data['demands_oranges'] = [0, 1, 1, 2, 4, 2, 4, 1, 8, 1, 2, 1, 2, 4, 4, 8, 8]
data['demands_apples'] = [0, 1, 1, 2, 4, 2, 4, 1, 8, 1, 2, 1, 2, 4, 4, 8, 8]
data['vehicle_capacities_oranges'] = [0, 0, 40, 40]
data['vehicle_capacities_apples'] = [0, 0, 40, 40]
data['price_per_km'] = [1, 1, 1, 1]
data["price_per_stop"] = [1, 1, 1, 1]
data['num_vehicles'] = 4
data['depot'] = 0
return data
def print_solution(data, manager, routing, solution):
"""Prints solution on console."""
for capacity_ID in ['demands_oranges','demands_apples']:
print("____Capacity_{}_____".format(capacity_ID))
total_distance = 0
total_load = 0
for vehicle_id in range(data['num_vehicles']):
index = routing.Start(vehicle_id)
plan_output = 'Route for vehicle {}:\n'.format(vehicle_id)
route_distance = 0
route_load = 0
while not routing.IsEnd(index):
node_index = manager.IndexToNode(index)
route_load += data[str(capacity_ID)][node_index]
plan_output += ' {0} Load({1}) -> '.format(node_index, route_load)
previous_index = index
index = solution.Value(routing.NextVar(index))
route_distance += routing.GetArcCostForVehicle(
previous_index, index, vehicle_id)
plan_output += ' {0} Load({1})\n'.format(manager.IndexToNode(index),
route_load)
plan_output += 'Distance of the route: {}m\n'.format(route_distance)
plan_output += 'Load of the route: {}\n'.format(route_load)
print(plan_output)
total_distance += route_distance
total_load += route_load
print('Total distance of all routes: {}m'.format(total_distance))
print('Total load of all routes: {}'.format(total_load))
def main():
"""Solve the CVRP problem."""
# Instantiate the data problem.
data = create_data_model()
# Create the routing index manager.
manager = pywrapcp.RoutingIndexManager(len(data['distance_matrix']),
data['num_vehicles'], data['depot'])
# Create Routing Model.
routing = pywrapcp.RoutingModel(manager)
### Kosten festlegen ###
def create_cost_callback(dist_matrix, km_costs, stop_costs):
# Create a callback to calculate distances between cities.
def distance_callback(from_index, to_index):
from_node = manager.IndexToNode(from_index)
to_node = manager.IndexToNode(to_index)
return int(dist_matrix[from_node][to_node]) * (km_costs) + (stop_costs)
return distance_callback
for i in range(data['num_vehicles']):
cost_callback = create_cost_callback(data['distance_matrix'], data["price_per_km"][i],
data["price_per_stop"][i]) # Callbackfunktion erstellen
cost_callback_index = routing.RegisterTransitCallback(cost_callback) # registrieren
routing.SetArcCostEvaluatorOfVehicle(cost_callback_index, i) # Vehicle zuordnen
# Add Capacity constraint.
def demand_callback_apples(from_index):
"""Returns the demand of the node."""
# Convert from routing variable Index to demands NodeIndex.
from_node = manager.IndexToNode(from_index)
return data['demands_apples'][from_node]
demand_callback_index_apples = routing.RegisterUnaryTransitCallback(
demand_callback_apples)
routing.AddDimensionWithVehicleCapacity(
demand_callback_index_apples,
0, # null capacity slack
data['vehicle_capacities_apples'], # vehicle maximum capacities
True, # start cumul to zero
'Capacity_apples')
def demand_callback_oranges(from_index):
"""Returns the demand of the node."""
# Convert from routing variable Index to demands NodeIndex.
from_node = manager.IndexToNode(from_index)
return data['demands_oranges'][from_node]
demand_callback_index_oranges = routing.RegisterUnaryTransitCallback(
demand_callback_oranges)
routing.AddDimensionWithVehicleCapacity(
demand_callback_index_oranges,
0, # null capacity slack
data['vehicle_capacities_oranges'], # vehicle maximum capacities
True, # start cumul to zero
'Capacity_oranges')
# Setting first solution heuristic.
search_parameters = pywrapcp.DefaultRoutingSearchParameters()
search_parameters.first_solution_strategy = (
routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC)
search_parameters.local_search_metaheuristic = (
routing_enums_pb2.LocalSearchMetaheuristic.GUIDED_LOCAL_SEARCH)
search_parameters.time_limit.FromSeconds(10)
# Solve the problem.
solution = routing.SolveWithParameters(search_parameters)
# Print solution on console.
if solution:
print_solution(data, manager, routing, solution)
print(solution)
if __name__ == '__main__':
main()
所有位置只能访问一次
因此，如果您有 apples 和 oranges，您应该复制该位置，这样一辆车将访问一个，另一辆车将访问一个车辆...
注意：当您更改容量以使车辆可以携带两种类型时，它就可以工作
我正在尝试解决具有多种货物类型和容量的 CVRP。假设我有四辆车和两种货物（橘子和苹果）。每个 Vehicle 确实对苹果和橙子有不同的容量，每个节点都有不同的需求。两辆车只能运苹果，两辆车只能运橙子。所以我定义了以下数据：
data['demands_oranges'] = [0, 1, 1, 2, 4, 2, 4, 1, 8, 1, 2, 1, 2, 4, 4, 8, 8]
data['demands_apples'] = [0, 1, 1, 2, 4, 2, 4, 1, 8, 1, 2, 1, 2, 4, 4, 8, 8]
data['vehicle_capacities_oranges'] = [0, 0, 40, 40]
data['vehicle_capacities_apples'] = [40, 40, 0, 0]
此外，我为每个容量定义了两个维度：
# Add Capacity constraint.
def demand_callback_apples(from_index):
"""Returns the demand of the node."""
# Convert from routing variable Index to demands NodeIndex.
from_node = manager.IndexToNode(from_index)
return data['demands_apples'][from_node]
demand_callback_index_apples = routing.RegisterUnaryTransitCallback(
demand_callback_apples)
routing.AddDimensionWithVehicleCapacity(
demand_callback_index_apples,
0, # null capacity slack
data['vehicle_capacities_apples'], # vehicle maximum capacities
True, # start cumul to zero
'Capacity_apples')
def demand_callback_oranges(from_index):
"""Returns the demand of the node."""
# Convert from routing variable Index to demands NodeIndex.
from_node = manager.IndexToNode(from_index)
return data['demands_oranges'][from_node]
demand_callback_index_oranges = routing.RegisterUnaryTransitCallback(
demand_callback_oranges)
routing.AddDimensionWithVehicleCapacity(
demand_callback_index_oranges,
0, # null capacity slack
data['vehicle_capacities_oranges'], # vehicle maximum capacities
True, # start cumul to zero
'Capacity_oranges')
问题是，此输入数据没有返回解。尽管事实上车辆容量还远未超过。 当我使用时，模型出于某种原因工作：
data['vehicle_capacities_oranges'] = [0, 0, 40, 40]
data['vehicle_capacities_apples'] = [0, 0, 40, 40]
但这不是我需要的。这是什么原因？
代码：
"""Capacited Vehicles Routing Problem (CVRP)."""
from ortools.constraint_solver import routing_enums_pb2
from ortools.constraint_solver import pywrapcp
def create_data_model():
"""Stores the data for the problem."""
data = {}
data['distance_matrix'] = [
[
0, 548, 776, 696, 582, 274, 502, 194, 308, 194, 536, 502, 388, 354,
468, 776, 662
],
[
548, 0, 684, 308, 194, 502, 730, 354, 696, 742, 1084, 594, 480, 674,
1016, 868, 1210
],
[
776, 684, 0, 992, 878, 502, 274, 810, 468, 742, 400, 1278, 1164,
1130, 788, 1552, 754
],
[
696, 308, 992, 0, 114, 650, 878, 502, 844, 890, 1232, 514, 628, 822,
1164, 560, 1358
],
[
582, 194, 878, 114, 0, 536, 764, 388, 730, 776, 1118, 400, 514, 708,
1050, 674, 1244
],
[
274, 502, 502, 650, 536, 0, 228, 308, 194, 240, 582, 776, 662, 628,
514, 1050, 708
],
[
502, 730, 274, 878, 764, 228, 0, 536, 194, 468, 354, 1004, 890, 856,
514, 1278, 480
],
[
194, 354, 810, 502, 388, 308, 536, 0, 342, 388, 730, 468, 354, 320,
662, 742, 856
],
[
308, 696, 468, 844, 730, 194, 194, 342, 0, 274, 388, 810, 696, 662,
320, 1084, 514
],
[
194, 742, 742, 890, 776, 240, 468, 388, 274, 0, 342, 536, 422, 388,
274, 810, 468
],
[
536, 1084, 400, 1232, 1118, 582, 354, 730, 388, 342, 0, 878, 764,
730, 388, 1152, 354
],
[
502, 594, 1278, 514, 400, 776, 1004, 468, 810, 536, 878, 0, 114,
308, 650, 274, 844
],
[
388, 480, 1164, 628, 514, 662, 890, 354, 696, 422, 764, 114, 0, 194,
536, 388, 730
],
[
354, 674, 1130, 822, 708, 628, 856, 320, 662, 388, 730, 308, 194, 0,
342, 422, 536
],
[
468, 1016, 788, 1164, 1050, 514, 514, 662, 320, 274, 388, 650, 536,
342, 0, 764, 194
],
[
776, 868, 1552, 560, 674, 1050, 1278, 742, 1084, 810, 1152, 274,
388, 422, 764, 0, 798
],
[
662, 1210, 754, 1358, 1244, 708, 480, 856, 514, 468, 354, 844, 730,
536, 194, 798, 0
],
]
data['demands_oranges'] = [0, 1, 1, 2, 4, 2, 4, 1, 8, 1, 2, 1, 2, 4, 4, 8, 8]
data['demands_apples'] = [0, 1, 1, 2, 4, 2, 4, 1, 8, 1, 2, 1, 2, 4, 4, 8, 8]
data['vehicle_capacities_oranges'] = [0, 0, 40, 40]
data['vehicle_capacities_apples'] = [0, 0, 40, 40]
data['price_per_km'] = [1, 1, 1, 1]
data["price_per_stop"] = [1, 1, 1, 1]
data['num_vehicles'] = 4
data['depot'] = 0
return data
def print_solution(data, manager, routing, solution):
"""Prints solution on console."""
for capacity_ID in ['demands_oranges','demands_apples']:
print("____Capacity_{}_____".format(capacity_ID))
total_distance = 0
total_load = 0
for vehicle_id in range(data['num_vehicles']):
index = routing.Start(vehicle_id)
plan_output = 'Route for vehicle {}:\n'.format(vehicle_id)
route_distance = 0
route_load = 0
while not routing.IsEnd(index):
node_index = manager.IndexToNode(index)
route_load += data[str(capacity_ID)][node_index]
plan_output += ' {0} Load({1}) -> '.format(node_index, route_load)
previous_index = index
index = solution.Value(routing.NextVar(index))
route_distance += routing.GetArcCostForVehicle(
previous_index, index, vehicle_id)
plan_output += ' {0} Load({1})\n'.format(manager.IndexToNode(index),
route_load)
plan_output += 'Distance of the route: {}m\n'.format(route_distance)
plan_output += 'Load of the route: {}\n'.format(route_load)
print(plan_output)
total_distance += route_distance
total_load += route_load
print('Total distance of all routes: {}m'.format(total_distance))
print('Total load of all routes: {}'.format(total_load))
def main():
"""Solve the CVRP problem."""
# Instantiate the data problem.
data = create_data_model()
# Create the routing index manager.
manager = pywrapcp.RoutingIndexManager(len(data['distance_matrix']),
data['num_vehicles'], data['depot'])
# Create Routing Model.
routing = pywrapcp.RoutingModel(manager)
### Kosten festlegen ###
def create_cost_callback(dist_matrix, km_costs, stop_costs):
# Create a callback to calculate distances between cities.
def distance_callback(from_index, to_index):
from_node = manager.IndexToNode(from_index)
to_node = manager.IndexToNode(to_index)
return int(dist_matrix[from_node][to_node]) * (km_costs) + (stop_costs)
return distance_callback
for i in range(data['num_vehicles']):
cost_callback = create_cost_callback(data['distance_matrix'], data["price_per_km"][i],
data["price_per_stop"][i]) # Callbackfunktion erstellen
cost_callback_index = routing.RegisterTransitCallback(cost_callback) # registrieren
routing.SetArcCostEvaluatorOfVehicle(cost_callback_index, i) # Vehicle zuordnen
# Add Capacity constraint.
def demand_callback_apples(from_index):
"""Returns the demand of the node."""
# Convert from routing variable Index to demands NodeIndex.
from_node = manager.IndexToNode(from_index)
return data['demands_apples'][from_node]
demand_callback_index_apples = routing.RegisterUnaryTransitCallback(
demand_callback_apples)
routing.AddDimensionWithVehicleCapacity(
demand_callback_index_apples,
0, # null capacity slack
data['vehicle_capacities_apples'], # vehicle maximum capacities
True, # start cumul to zero
'Capacity_apples')
def demand_callback_oranges(from_index):
"""Returns the demand of the node."""
# Convert from routing variable Index to demands NodeIndex.
from_node = manager.IndexToNode(from_index)
return data['demands_oranges'][from_node]
demand_callback_index_oranges = routing.RegisterUnaryTransitCallback(
demand_callback_oranges)
routing.AddDimensionWithVehicleCapacity(
demand_callback_index_oranges,
0, # null capacity slack
data['vehicle_capacities_oranges'], # vehicle maximum capacities
True, # start cumul to zero
'Capacity_oranges')
# Setting first solution heuristic.
search_parameters = pywrapcp.DefaultRoutingSearchParameters()
search_parameters.first_solution_strategy = (
routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC)
search_parameters.local_search_metaheuristic = (
routing_enums_pb2.LocalSearchMetaheuristic.GUIDED_LOCAL_SEARCH)
search_parameters.time_limit.FromSeconds(10)
# Solve the problem.
solution = routing.SolveWithParameters(search_parameters)
# Print solution on console.
if solution:
print_solution(data, manager, routing, solution)
print(solution)
if __name__ == '__main__':
main()
所有位置只能访问一次
因此，如果您有 apples 和 oranges，您应该复制该位置，这样一辆车将访问一个，另一辆车将访问一个车辆...
注意：当您更改容量以使车辆可以携带两种类型时，它就可以工作