如何解决在谷歌或工具中用两种车辆类型解决时间受限的 CVRP
我正在建模受时间约束的 CVRP。问题是在车辆（交付）容量和总花费时间（每辆车）的限制下，最小化总旅行时间（不包括包裹投递时间）。丢包时间是指在每个节点额外花费的时间，花费的总时间等于行程时间加上这个额外的时间。我有以下模型适用于单个车辆类型的情况。我想在那里引入两辆车类型的概念，这意味着我有一组V1类型的车辆和另一组V2类型的车辆。车辆类型的唯一区别是每次旅行的成本。让 x 表示 V1 的每时间单位旅行成本，y 表示 V2 的每时间单位旅行成本。我如何设计模型以使其包含此附加方面？
from ortools.constraint_solver import routing_enums_pb2
from ortools.constraint_solver import pywrapcp
def create_data_model(n_vehicles):
"""Stores the data for the problem."""
data = {}
data['time_matrix'] = TT #travel time
data['num_vehicles'] = n_vehicles
data['depot'] = 0
data['demands'] = demands
data['vehicle_capacities'] = vehicle_capacities
data['service_time'] = service_time
return data
def print_solution(data,manager,routing,solution):
"""Prints solution on console."""
print(f'Objective: {solution.ObjectiveValue()}')
max_route_time = 0; tour = {i:[] for i in range(data['num_vehicles'])}
for vehicle_id in range(data['num_vehicles']):
index = routing.Start(vehicle_id)
plan_output = 'Route for vehicle {}:\n'.format(vehicle_id)
route_time = 0
while not routing.IsEnd(index):
plan_output += ' {} -> '.format(manager.IndexToNode(index))
tour[vehicle_id].append(manager.IndexToNode(index))
prevIoUs_index = index
index = solution.Value(routing.Nextvar(index))
if prevIoUs_index != 0 and prevIoUs_index <= len(data['service_time'])-1:
service_time = data['service_time'][prevIoUs_index]
else:
service_time = 0
route_time += (routing.GetArcCostForVehicle(
prevIoUs_index,index,vehicle_id) + service_time)
plan_output += '{}\n'.format(manager.IndexToNode(index))
tour[vehicle_id].append(manager.IndexToNode(index))
plan_output += 'Travel time of the route: {} sec\n'.format(route_time)
print(plan_output)
max_route_time = max(route_time,max_route_time)
print('Maximum of the route time: {} sec'.format(max_route_time))
return(tour)
def main(n_vehicles):
number_of_veh = [n_vehicles][0]
solution_found = False
while solution_found == False:
"""Entry point of the program."""
# Instantiate the data problem.
data = create_data_model(number_of_veh)
# Create the routing index manager.
manager = pywrapcp.RoutingIndexManager(len(data['time_matrix']),data['num_vehicles'],data['depot'])
# Create Routing Model.
routing = pywrapcp.RoutingModel(manager)
# Create and register a transit callback.
def time_callback(from_index,to_index):
"""Returns the time between the two nodes."""
# Convert from routing variable Index to time matrix NodeIndex.
from_node = manager.IndexToNode(from_index)
to_node = manager.IndexToNode(to_index)
return data['time_matrix'][from_node][to_node]
transit_callback_index = routing.RegisterTransitCallback(time_callback)
# Define cost of each arc.
routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index)
# Create and register a transit callback.
def time_callback2(from_index,to_index):
"""Returns the time between the two nodes."""
# Convert from routing variable Index to time matrix NodeIndex.
from_node = manager.IndexToNode(from_index)
to_node = manager.IndexToNode(to_index)
if from_node != 0:
return data['time_matrix'][from_node][to_node] + data['service_time'][from_node]
else:
return data['time_matrix'][from_node][to_node]
transit_callback_index2 = routing.RegisterTransitCallback(time_callback2)
# Add Time constraint.
dimension_name = 'Time'
routing.AddDimension(
transit_callback_index2,# no slack
Operational_hours*3600,# vehicle maximum travel time
True,# start cumul to zero
dimension_name)
time_dimension = routing.GetDimensionorDie(dimension_name)
def demand_callback(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'][from_node]
demand_callback_index = routing.RegisterUnaryTransitCallback(
demand_callback)
routing.AddDimensionWithVehicleCapacity(
demand_callback_index,# null capacity slack
data['vehicle_capacities'],# vehicle maximum capacities
True,# start cumul to zero
'Capacity')
# 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(VRP_time_limit)
# Solve the problem.
solution = routing.solveWithParameters(search_parameters)
# Print solution on console.
if solution:
tour = print_solution(data,solution)
solution_found = True
else:
print('No solution found! Increasing the vehicle numbers by one and resolving.\n')
solution_found = False
number_of_veh += 1
return(tour,number_of_veh)
编辑
根据@Mizux 的回答，我写了以下内容，结果出现了以下错误。
from ortools.constraint_solver import routing_enums_pb2
from ortools.constraint_solver import pywrapcp
def create_data_model(n_vehicles):
"""Stores the data for the problem."""
data = {}
TT = np.array(df.values)
data['time_matrix'] = TT
data['num_vehicles'] = n_vehicles
data['depot'] = 0
data['demands'] = demands
if len(vehicle_capacities) < n_vehicles:
data['vehicle_capacities'] = [vehicle_capacities[0]]*n_vehicles
else:
data['vehicle_capacities'] = vehicle_capacities
data['service_time'] = service_time
return data
def print_solution(data,max_route_time)
print('Maximum of the route time: {} sec'.format(max_route_time))
return(tour)
def main(n_vehicles,cost1,cost2):
number_of_veh = [n_vehicles][0]
solution_found = False
while solution_found == False:
Num_of_Class6 = int(n_vehicles*Percent_of_Class6)
Num_of_Hybrid = n_vehicles - Num_of_Class6
V = list(range(n_vehicles))
V2 = list(set(np.random.choice(V,size=Num_of_Class6,replace=False)))
V1 = list(set(V)-set(V2))
"""Entry point of the program."""
# Instantiate the data problem.
data = create_data_model(number_of_veh)
# Create the routing index manager.
manager = pywrapcp.RoutingIndexManager(len(data['time_matrix']),data['depot'])
# Create Routing Model.
routing = pywrapcp.RoutingModel(manager)
'''Major Diff Starts Here'''
# Create and register a transit callback.
def time_callback(from_index,to_index,cost):
"""Returns the time between the two nodes."""
# Convert from routing variable Index to time matrix NodeIndex.
from_node = manager.IndexToNode(from_index)
to_node = manager.IndexToNode(to_index)
return data['time_matrix'][from_node][to_node]*cost
range_extender_callback = partial(time_callback,cost=cost1)
class6_callback = partial(time_callback,cost=cost2)
transit_callback_index_V1 = routing.RegisterTransitCallback(range_extender_callback)
transit_callback_index_V2 = routing.RegisterTransitCallback(class6_callback)
'''Major Diff Ends Here'''
# Define cost of each arc.
for v in V1:
routing.SetArcCostEvaluatorOfVehicle(transit_callback_index_V1,v)
for v in V2:
routing.SetArcCostEvaluatorOfVehicle(transit_callback_index_V2,v)
# Create and register a transit callback.
def time_callback2(from_index,solution)
solution_found = True
else:
print('No solution found! Increasing the vehicle numbers by one and resolving.\n')
solution_found = False
number_of_veh += 1
return(tour,number_of_veh,V1,V2)
main(n_vehicles,cost2)
输出为：
Beginning the Googe OR-tools to solve the problem.
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-15-0447402a4e3d> in <module>
166 return(tour,V2)
167
--> 168 final_tour,V2 = main(n_vehicles,cost2)
<ipython-input-15-0447402a4e3d> in main(n_vehicles,cost2)
104 routing.SetArcCostEvaluatorOfVehicle(transit_callback_index_V1,v)
105 for v in V2:
--> 106 routing.SetArcCostEvaluatorOfVehicle(transit_callback_index_V2,v)
107
108 # Create and register a transit callback.
~/.local/lib/python3.7/site-packages/ortools/constraint_solver/pywrapcp.py in SetArcCostEvaluatorOfVehicle(self,evaluator_index,vehicle)
5224 def SetArcCostEvaluatorOfVehicle(self,evaluator_index: "int",vehicle: "int") -> "void":
5225 r""" Sets the cost function for a given vehicle route."""
-> 5226 return _pywrapcp.RoutingModel_SetArcCostEvaluatorOfVehicle(self,vehicle)
5227
5228 def SetFixedcostOfAllVehicles(self,cost: "int64_t") -> "void":
TypeError: in method 'RoutingModel_SetArcCostEvaluatorOfVehicle',argument 3 of type 'int'
解决方法
为了解决这个问题，我跟着Mizux的回答。我有以下 MWE 供将来考虑。我希望它对某人有所帮助！
from ortools.constraint_solver import routing_enums_pb2
from ortools.constraint_solver import pywrapcp
import numpy as np
from functools import partial
n_vehicles = 4 #Number of vehicles
max_vehicle_tt = 3600 #Maximum travel time for each vehicle (excludes service times)
data = {}
data['time_matrix'] = np.array([[ 0,1187,1200,1110,1134,892,1526,903,1482,1544],[1232,13,90,67,426,537,419,493,555],[1218,57,82,73,412,523,405,479,541],[1177,23,370,481,364,438,500],[1187,80,380,491,374,448,509],[ 870,390,403,314,337,729,17,686,747],[1539,557,543,485,495,733,726,53,68],[ 882,384,397,307,331,723,679,741],[1496,514,500,442,451,689,683,122],[1584,602,588,530,539,777,68,771,122,0]])
data['num_vehicles'] = n_vehicles
data['depot'] = 0
data['demands'] = [0,4,3,1,12,24,20]
data['vehicle_capacities'] = [30]*data['num_vehicles']
data['service_time'] = [0,18,27,25,11,92,6,239,143]
def print_solution(data,manager,routing,solution):
"""Prints solution on console."""
print(f'Objective: {solution.ObjectiveValue()}')
max_route_time = 0; tour = {i:[] for i in range(data['num_vehicles'])}
for vehicle_id in range(data['num_vehicles']):
index = routing.Start(vehicle_id)
plan_output = 'Route for vehicle {}:\n'.format(vehicle_id)
route_time = 0
while not routing.IsEnd(index):
plan_output += ' {} -> '.format(manager.IndexToNode(index))
tour[vehicle_id].append(manager.IndexToNode(index))
previous_index = index
index = solution.Value(routing.NextVar(index))
if previous_index != 0 and previous_index <= len(data['service_time'])-1:
service_time = data['service_time'][previous_index]
else:
service_time = 0
route_time += (routing.GetArcCostForVehicle(
previous_index,index,vehicle_id) + service_time)
plan_output += '{}\n'.format(manager.IndexToNode(index))
tour[vehicle_id].append(manager.IndexToNode(index))
plan_output += 'Travel time of the route: {} sec\n'.format(route_time)
print(plan_output)
max_route_time = max(route_time,max_route_time)
print('Maximum of the route time: {} sec'.format(max_route_time))
return(tour)
def main(n_vehicles,cost1,cost2):
np.random.seed(0)
Num_of_Class6 = int(n_vehicles*0.6)
Num_of_Hybrid = n_vehicles - Num_of_Class6
V = list(range(n_vehicles))
V2 = list(set(np.random.choice(V,size=Num_of_Class6,replace=False)))
V1 = list(set(V)-set(V2))
print('V1:%s'%V1); print('V2:%s'%V2)
# Create the routing index manager.
manager = pywrapcp.RoutingIndexManager(len(data['time_matrix']),data['num_vehicles'],data['depot'])
# Create Routing Model.
routing = pywrapcp.RoutingModel(manager)
# Create and register a transit callback.
def time_callback(from_index,to_index,cost):
"""Returns the time between the two nodes."""
# Convert from routing variable Index to time matrix NodeIndex.
from_node = manager.IndexToNode(from_index)
to_node = manager.IndexToNode(to_index)
return data['time_matrix'][from_node][to_node]*cost
range_extender_callback = partial(time_callback,cost=cost1)
class6_callback = partial(time_callback,cost=cost2)
transit_callback_index_V1 = routing.RegisterTransitCallback(range_extender_callback)
transit_callback_index_V2 = routing.RegisterTransitCallback(class6_callback)
# Define cost of each arc.
for v in V1:
routing.SetArcCostEvaluatorOfVehicle(transit_callback_index_V1,int(v))
for v in V2:
routing.SetArcCostEvaluatorOfVehicle(transit_callback_index_V2,int(v))
# Create and register a transit callback to limit the total travel+service time
def time_callback2(from_index,to_index):
"""Returns the time between the two nodes."""
# Convert from routing variable Index to time matrix NodeIndex.
from_node = manager.IndexToNode(from_index)
to_node = manager.IndexToNode(to_index)
if from_node != 0:
return data['time_matrix'][from_node][to_node] + data['service_time'][from_node]
else:
return data['time_matrix'][from_node][to_node]
transit_callback_index2 = routing.RegisterTransitCallback(time_callback2)
# Add Time constraint.
dimension_name = 'Time'
routing.AddDimensionWithVehicleCapacity(
transit_callback_index2,# no slack
[max_vehicle_tt]*data['num_vehicles'],# vehicle maximum travel time
True,# start cumul to zero
dimension_name)
time_dimension = routing.GetDimensionOrDie(dimension_name)
def demand_callback(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'][from_node]
demand_callback_index = routing.RegisterUnaryTransitCallback(
demand_callback)
routing.AddDimensionWithVehicleCapacity(
demand_callback_index,# null capacity slack
data['vehicle_capacities'],# vehicle maximum capacities
True,# start cumul to zero
'Capacity')
# 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(1)
# Solve the problem.
solution = routing.SolveWithParameters(search_parameters)
# Print solution on console.
if solution:
tour = print_solution(data,solution)
return(tour,V1,V2)
else:
print('No solution found!\n')
tour,V2 = main(n_vehicles,0.5,0.7)
奖励：使用以下功能检查关键解决方案指标。
pairs = {}; serv_time = {}; tt ={}; cont_to_obj = {}
for i,j in tour.items():
if len(j) > 2:
serv_time[i] = sum([data['service_time'][k] for k in j])
print('Service time for vehicle %s: %s.'%(i,serv_time[i]))
num_deliveries = sum([data['demands'][k] for k in j])
print('Number of deliveries for vehicle %s: %s.'%(i,num_deliveries))
pairs[i] = list(zip(j,j[1:]))
tt[i] = sum([data['time_matrix'][k] for k in pairs[i]])
print('Travel time for vehicle %s: %s.'%(i,tt))
print('Total time for vehicle %s: %s'%(i,serv_time[i]+tt[i]))
if i in V1:
cont_to_obj[i] = sum([int(data['time_matrix'][k]*0.002244) for k in pairs[i]])
else:
cont_to_obj[i] = sum([int(data['time_matrix'][k]*0.0080517) for k in pairs[i]])
print('Contribution to the obj. fun. for vehicle %s: %s\n'%(i,cont_to_obj[i]))
只需注册两个公交回调（即每个车辆类型一个）
然后使用 AddDimension() 的重载来传递已注册的公交回调索引数组。
版权声明：本文内容由互联网用户自发贡献，该文观点与技术仅代表作者本人。本站仅提供信息存储空间服务，不拥有所有权，不承担相关法律责任。如发现本站有涉嫌侵权/违法违规的内容， 请发送邮件至 dio@foxmail.com 举报，一经查实，本站将立刻删除。
