如何解决如何使用 OrTools 优化路线并组装 matrixDistance？
我正在尝试为 27 个地址创建距离数组，但返回的集合为空。我不明白。当我只放24个地址时，系统组装距离矩阵。
from __future__ import division
from __future__ import print_function
import requests
import json
import urllib.request
def create_data():
"""Creates the data."""
data = {}
data['API_key'] = 'API KEY'
data['addresses'] = ['R+Carlos+Camara+1454+Benfica+Fortaleza+CE',# depot
'AV+DEP+PAULINO+ROCHA+105+JABUTI+ITAITINGA+CE','R+CABO+VERDE+660+CJ+PALMEIRAS+FORTALEZA+CE','AV+Monsenhor+AMARILIO+RODRIGUES+604+JANGURUSSU+FORTALEZA+CE','R+PEDESTRE+IX+349+CANINDEZINHO+FORTALEZA+CE','RUA+MARECHAL+NAPION+733+BARRA+DO+CEara+FORTALEZA+CE','R+IRACEMA+880+CJ+PALMEIRAS+FORTALEZA+CE','R+JOSIAS+PAULA+DE+SOUZA+100+VICENTE+PINZON+FORTALEZA+CE','R+CJ+JOAO+PAULO+II+108+BARROSO+FORTALEZA+CE','AV+XXII+474+SENADOR+CARLOS+JEREISSATI+PACATUBA+CE','R+NUnes+FEIJO+1454+JANGURUSSU+FORTALEZA+CE','AV+A+CJ+JEREISSATI+III+600+SENADOR+CARLOS+JEREISSATI+PACATUBA+CE','AV+CENTRAL+5452+ICaraI+CAUCAIA+CE','R+CJ+JD+CASTELAO+4651+PASSARE+FORTALEZA+CE','R+FRIESIO+BARROSO+387+MONdubIM+FORTALEZA+CE','AV+C+CJ+SIT+SAO+JOAO+87+JANGURUSSU+FORTALEZA+CE','R+BOM+JESUS+200+BOM+JARDIM+FORTALEZA+CE','R+TENENTE+ROMA+206+ALTO+DA+BALANCA+FORTALEZA+CE','R+SHIRLEY+280+PAUPINA+FORTALEZA+CE','R+TEodoRO+DE+CASTRO+2509+GRAJA+LISBOA+FORTALEZA+CE','TV+SAO+FRANCISCO+332+MESSEJANA+FORTALEZA+CE','RUA+PERDIGAO+DE+OLIVEIRA+361+ParaNGABA+FORTALEZA+CE','R+ALM+SOARES+DUTRA+33+CUMBUCO+CAUCAIA+CE','R+CORDEIRO+DE+MIRANDA+1311+CJ+METROPOLITANO+CAUCAIA+CE','R+JOAQUIM+MACHADO+287+PAUPINA+FORTALEZA+CE','AV+ENG+LEAL+LIMA+VERDE+306+SAPIRANGA+FORTALEZA+CE',#Conjunto Vazio
'R+VERDE+180+JANGURUSSU+FORTALEZA+CE',#Conjunto vazio
]
return data
def create_distance_matrix(data):
addresses = data["addresses"]
API_key = data["API_key"]
# distance Matrix API only accepts 100 elements per request,so get rows in multiple
requests.
max_elements = 100
num_addresses = len(addresses) # 16 in this example.
# Maximum number of rows that can be computed per request (6 in this example).
max_rows = max_elements // num_addresses
# num_addresses = q * max_rows + r (q = 2 and r = 4 in this example).
q,r = divmod(num_addresses,max_rows)
dest_addresses = addresses
distance_matrix = []
# Send q requests,returning max_rows rows per request.
for i in range(q):
origin_addresses = addresses[i * max_rows: (i + 1) * max_rows]
response = send_request(origin_addresses,dest_addresses,API_key)
distance_matrix += build_distance_matrix(response)
# Get the remaining remaining r rows,if necessary.
if r > 0:
origin_addresses = addresses[q * max_rows: q * max_rows + r]
response = send_request(origin_addresses,API_key)
distance_matrix += build_distance_matrix(response)
return distance_matrix
def send_request(origin_addresses,API_key):
""" Build and send request for the given origin and destination addresses."""
def build_address_str(addresses):
# Build a pipe-separated string of addresses
address_str = ''
for i in range(len(addresses) - 1):
address_str += addresses[i] + '|'
address_str += addresses[-1]
return address_str
request = 'https://maps.googleapis.com/maps/api/distancematrix/json?units=imperial'
origin_address_str = build_address_str(origin_addresses)
dest_address_str = build_address_str(dest_addresses)
request = request + '&origins=' + origin_address_str + '&destinations=' + \
dest_address_str + '&key=' + API_key
jsonResult = urllib.request.urlopen(request).read()
response = json.loads(jsonResult)
return response
def build_distance_matrix(response):
distance_matrix = []
for row in response['rows']:
row_list = [row['elements'][j]['distance']['value'] for j in range(len(row['elements']))]
distance_matrix.append(row_list)
return distance_matrix
########
# Main #
########
def main():
"""Entry point of the program"""
# Create the data.
data = create_data()
addresses = data['addresses']
API_key = data['API_key']
distance_matrix = create_distance_matrix(data)
print(distance_matrix)
if __name__ == '__main__':
main()
使用下面的算法我可以优化最小距离的路线，但我也需要优化权重之和，没有路线可以超过100，有趣的是保持在60和90之间。它意味着它将使用 60% 到 90% 的时间供应超市，超过 100 意味着服务不会很好。但我不知道如何实现这个限制。在这个例子中，车辆 1 有 100 多个，我可以将商店扔给车辆 3，这太低了。
from ortools.constraint_solver import routing_enums_pb2
from ortools.constraint_solver import pywrapcp
import pandas as pd
def create_data_model():
"""Stores the data for the problem."""
data = {}
data['distance_matrix'] = [[0,22972,15918,14739,12260,7874,16321,12618,12136,20286,14582,20989,19583,12544,9415,14593,8701,5595,18205,10380,11606,5471,28244,15180,19088],[29448,18885,19844,28925,36734,19138,32722,20508,27405,19013,27135,48981,22834,25845,16567,33286,25147,13481,35607,19994,32821,57642,38376,14362],[17133,10750,2432,14259,26384,1212,18107,3544,16138,2754,16841,34315,5275,8433,2767,18620,12832,5699,20941,7679,12922,42976,23710,6582],[16900,14836,2916,17169,24186,1749,17227,2664,19047,4152,19750,37225,4395,8067,4165,13139,10225,8608,16334,7446,12042,45886,26620,9491],[12150,22554,16449,12233,16331,16702,24381,11976,12050,17359,12753,25224,11029,7254,17372,4735,17379,17503,8396,16769,7900,33884,14618,18387],[7851,31385,24331,23152,15926,24734,13912,20549,25582,22996,26285,12218,20957,17180,23006,12639,16703,26618,12502,20020,10883,20879,14277,27501],[17332,11944,1217,2742,15454,22085,17972,3409,17332,2953,18035,35510,5140,7273,2965,12344,13031,6893,15539,7877,13876,44170,24904,7776],[11522,26596,19542,16377,24422,13517,18156,15374,30601,18206,31304,24449,15783,17965,18217,21085,8510,21829,22975,15228,17840,33110,24893,22712],[12495,13389,3614,1654,17867,19781,3433,15191,19745,5000,20448,30635,2359,7887,5011,12958,8189,8622,16153,6915,10007,39295,27318,9505],[20521,24318,18212,19171,13669,25953,18465,31235,18829,19122,500,33725,17883,14108,19135,16212,24232,19267,19407,25783,17744,42385,23119,20150],[16702,10424,2545,3654,16657,23987,2948,19976,4052,18535,19239,36713,6378,9654,971,14726,12401,5657,17921,7247,14025,45374,26108,6540],[20143,23940,17834,18793,13291,25575,18087,30857,18452,18744,33347,17505,13730,18757,15834,23854,18889,19029,25405,17366,42007,22741,19772],[24121,42972,36866,37825,27254,12622,37120,25838,32475,33763,37776,34466,32594,28819,37789,24278,28629,37921,19467,31946,22522,8661,11823,38804],[13864,14342,4478,2518,10725,19678,4298,16560,1516,17105,5953,17808,31393,4866,5963,9937,9558,9575,13132,6952,11469,40054,23900,10458],[9744,18478,8018,6553,7048,16000,6851,17780,6295,13427,10089,14130,27716,5349,10099,6260,10777,13711,9454,11088,7792,36377,21641,14594],[16204,9926,2568,3676,16679,23490,2970,19478,4787,18557,19261,36735,6518,9677,14748,11903,5159,17943,6750,19577,45396,26130,6042],[8518,26325,11952,5182,12699,12157,21028,11695,15488,16077,25786,10748,6973,15499,21274,3922,17490,4269,34446,22157],[4705,20812,13759,9495,17540,11990,11275,8803,8493,23720,12423,24423,23986,8901,11084,12434,14203,16045,16094,9447,10959,32646,19889,16928],[16517,7670,6754,8533,16794,23802,7007,19791,7577,18672,6082,19375,36850,9903,13714,4436,21155,12216,23476,7062,19890,45511,26245,1429],[10174,26621,16655,14695,8462,12121,14900,22764,14438,18117,18231,18821,20668,13491,9716,18242,3919,15762,25091,19227,5239,29329,6994,25974],[11406,15283,8229,5816,25666,18692,8632,14680,4860,27545,6894,28248,30687,6866,11195,6904,16266,7105,10513,19914,14779,39348,35117,5617],[5409,25829,12996,11036,7348,10232,13028,17999,10033,16523,17440,17226,21949,10442,7538,17450,10996,21062,5333,14461,30610,13561,21945],[32109,50960,44854,45813,35241,20609,45107,33826,40463,41750,45764,42454,10043,40582,36807,45777,32266,36617,45909,27455,39933,30510,19810,46792],[15615,31200,25094,26053,15482,13846,25347,23418,27165,21990,26004,22694,12069,24933,21158,26017,9839,22142,26149,6158,32665,11230,20730,27032],[15780,11894,8827,7797,23066,9576,19054,6841,21461,5345,22164,35061,9166,17318,4847,23944,11479,1605,24288,6326,19153,43722,29034,0]]
data['addresses'] = ['R+Carlos+Camara+1454+Benfica+Fortaleza+CE',# depot
'AV+DEP+PAULINO+ROCHA+105+JABUTI+ITAITINGA+CE',]
data['weights'] = [0,12,15,13,7,23,10,11,9,8,6,5,12]
data['num_vehicles'] = 4
data['depot'] = 0
return data
def print_solution(data,manager,routing,solution):
"""Prints solution on console."""
print(f'Objective: {solution.ObjectiveValue()}')
max_route_distance = 0
matrix_route = []
matrix_car = []
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
while not routing.IsEnd(index):
plan_output += ' {} -> '.format(manager.IndexToNode(index))
prevIoUs_index = index
index = solution.Value(routing.Nextvar(index))
route_distance += routing.GetArcCostForVehicle(
prevIoUs_index,index,vehicle_id)
matrix_route.append(manager.IndexToNode(index)) #Criando a matrix de indices
matrix_car.append(f"Veículo {vehicle_id}") #Craindo a matriz com o nome das rotas
plan_output += '{}\n'.format(manager.IndexToNode(index))
plan_output += 'distance of the route: {}m\n'.format(route_distance)
print(plan_output)
max_route_distance = max(route_distance,max_route_distance)
#DataFrame with Routes
df = pd.DataFrame(zip(matrix_route,matrix_car),columns = ['Routes','Car'])
zero_value = df[df['Routes']<=0]
df = df.drop(zero_value.index)
print(df)
#DataFrame with adresses
df_info = pd.DataFrame(zip(data['addresses'],data['weights']),columns=
["addresses","weights"])
#df_remove_depot = df_info.loc[df_info['addresses']=='3610+Hacks+Cross+Rd+Memphis+TN']
df_remove_depot =
df_info.loc[df_info['addresses']=='R+Carlos+Camara+1454+Benfica+Fortaleza+CE']
df_info = df_info.drop(df_remove_depot.index)
print(df_info)
## Merge
tabela = pd.merge(df_info,df,left_index=True,right_on="Routes",how="left")
## Save excel
print(tabela)
tabela.to_excel('C:/Users/mateuscarvalho/Documents/Mateus Carvalho - 2021/Otimização de rotas.xlsx',index = False)
#Menor distância
print('Maximum of the route distances: {}m'.format(max_route_distance))
def main():
"""Entry point of the program."""
# 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)
# Create and register a transit callback.
def distance_callback(from_index,to_index):
"""Returns the distance between the two nodes."""
# Convert from routing variable Index to distance matrix NodeIndex.
from_node = manager.IndexToNode(from_index)
to_node = manager.IndexToNode(to_index)
return data['distance_matrix'][from_node][to_node]
transit_callback_index = routing.RegisterTransitCallback(distance_callback)
# Define cost of each arc.
routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index)
# Add distance constraint.
dimension_name = 'distance'
routing.AddDimension(
transit_callback_index,# no slack
70000,# vehicle maximum travel distance
True,# start cumul to zero
dimension_name)
distance_dimension = routing.GetDimensionorDie(dimension_name)
distance_dimension.SetGlobalSpanCostCoefficient(100)
# Setting first solution heuristic.
search_parameters = pywrapcp.DefaultRoutingSearchParameters()
search_parameters.first_solution_strategy = (
routing_enums_pb2.FirstSolutionStrategy.PATH_CHEApest_ARC)
# Solve the problem.
solution = routing.solveWithParameters(search_parameters)
# Print solution on console.
if solution:
print_solution(data,solution)
else:
print('No solution found !')
if __name__ == '__main__':
main()
解决方法
创建一个负载/权重维度，在每个节点上添加一个 cumulVarSoftUpperBound 为 90 以激励求解器不超重？
先验证
assert len(data['distance_matrix']) == data['weights']
然后我们可以创建一个额外的重量维度来将负载限制为 100。
# Add Capacity constraint.
def load_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['weights'][from_node]
load_callback_index = routing.RegisterUnaryTransitCallback(load_callback)
routing.AddDimension(
load_callback_index,# null capacity slack
100,# vehicle maximum capacity
True,# start cumul to zero
'Load')
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