travelR
1 Exemplo
library(travelr)## travelr is SERIOUSLY in a 'pre-alpha' state... Lots of Luck!m<-matrix(c(5,50,100,200,
50,5,100,300,
50,100,5,100,
100,200,250,20),
nrow=4,ncol=4,byrow=TRUE)
dimnames(m)<-list(Rows=c("R1","R2","R3","R4"),Cols=c("C1","C2","C3","C4"))
df = as.data.frame(addmargins(m))
dff<-c(400,460,400,702)
mf.vector<-ipf(m,f,"absolute")
print(mf.vector)## Cols
## Rows C1 C2 C3 C4 Sum
## R1 9.655253 61.332644 89.958941 239.0532 400
## R2 80.573641 5.118244 75.071254 299.2369 460
## R3 112.518202 142.948899 5.241716 139.2912 400
## R4 197.252903 250.600212 229.728088 24.4188 702
## Sum 400.000000 460.000000 400.000000 702.0000 1962
## RMSE: 3.210344e-08
## Converged in 18 Iterationsf.1<-list(rows=c(400,460,400,702))
mf.list.1<-ipf(m,f.1,"absolute")## Warning in ipf(m, f.1, "absolute"): Not enough growth factor vectors for 2
## dimensions: recyclingprint(mf.list.1)## Cols
## Rows C1 C2 C3 C4 Sum
## R1 9.655253 61.332644 89.958941 239.0532 400
## R2 80.573641 5.118244 75.071254 299.2369 460
## R3 112.518202 142.948899 5.241716 139.2912 400
## R4 197.252903 250.600212 229.728088 24.4188 702
## Sum 400.000000 460.000000 400.000000 702.0000 1962
## RMSE: 3.210344e-08
## Converged in 18 Iterationsf.2<-list(rows=c(400,460,400,702),cols=c(260,400,500,802))
mf.list.2<-ipf(m,f.2,"absolute")
print(mf.list.2)## Cols
## Rows C1 C2 C3 C4 Sum
## R1 5.195016 43.599107 97.186482 254.01939 400
## R2 44.707064 3.752035 83.636365 327.90454 460
## R3 76.674278 128.697592 7.171974 187.45616 400
## R4 133.423642 223.951265 312.005179 32.61991 702
## Sum 260.000000 400.000000 500.000000 802.00000 1962
## RMSE: 5.744356e-08
## Converged in 20 Iterationsdf.1<-data.frame(rows=c(400,460,400,702),cols=c(260,400,500,802))
mf.df.1<-ipf(m,df.1,"absolute")
print(mf.df.1)## Cols
## Rows C1 C2 C3 C4 Sum
## R1 5.195016 43.599107 97.186482 254.01939 400
## R2 44.707064 3.752035 83.636365 327.90454 460
## R3 76.674278 128.697592 7.171974 187.45616 400
## R4 133.423642 223.951265 312.005179 32.61991 702
## Sum 260.000000 400.000000 500.000000 802.00000 1962
## RMSE: 5.744356e-08
## Converged in 20 Iterationsf.pct<-c(102,105,110,95)
mf.pct<-ipf(m,f.pct,"percent")
print(mf.pct)## Cols
## Rows C1 C2 C3 C4 Sum
## R1 5.34967 56.447730 118.765199 183.60735 364.1700
## R2 56.70229 5.983015 125.881758 291.91400 480.4811
## R3 57.13615 120.575886 6.342247 98.04920 282.1035
## R4 89.91189 189.743369 249.510796 15.42944 544.5955
## Sum 209.10000 372.750000 500.500000 589.00000 1671.3500
## RMSE: 2.477394
## All 50 Iterations Completed1.1 SiouxFalls
data(SiouxFalls)
#https://github.com/bstabler/TransportationNetworks/tree/master/SiouxFalls1.1.1 Matriz OD
SiouxFalls.od## X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15
## [1,] 0 100 100 500 200 300 500 800 500 1300 500 200 500 300 500
## [2,] 100 0 100 200 100 400 200 400 200 600 200 100 300 100 100
## [3,] 100 100 0 200 100 300 100 200 100 300 300 200 100 100 100
## [4,] 500 200 200 0 500 400 400 700 700 1200 1400 600 600 500 500
## [5,] 200 100 100 500 0 200 200 500 800 1000 500 200 200 100 200
## [6,] 300 400 300 400 200 0 400 800 400 800 400 200 200 100 200
## [7,] 500 200 100 400 200 400 0 1000 600 1900 500 700 400 200 500
## [8,] 800 400 200 700 500 800 1000 0 800 1600 800 600 600 400 600
## [9,] 500 200 100 700 800 400 600 800 0 2800 1400 600 600 600 900
## [10,] 1300 600 300 1200 1000 800 1900 1600 2800 0 4000 2000 1900 2100 4000
## [11,] 500 200 300 1500 500 400 500 800 1400 3900 0 1400 1000 1600 1400
## [12,] 200 100 200 600 200 200 700 600 600 2000 1400 0 1300 700 700
## [13,] 500 300 100 600 200 200 400 600 600 1900 1000 1300 0 600 700
## [14,] 300 100 100 500 100 100 200 400 600 2100 1600 700 600 0 1300
## [15,] 500 100 100 500 200 200 500 600 1000 4000 1400 700 700 1300 0
## [16,] 500 400 200 800 500 900 1400 2200 1400 4400 1400 700 600 700 1200
## [17,] 400 200 100 500 200 500 1000 1400 900 3900 1000 600 500 700 1500
## [18,] 100 0 0 100 0 100 200 300 200 700 200 200 100 100 200
## [19,] 300 100 0 200 100 200 400 700 400 1800 400 300 300 300 800
## [20,] 300 100 0 300 100 300 500 900 600 2500 600 500 600 500 1100
## [21,] 100 0 0 200 100 100 200 400 300 1200 400 300 600 400 800
## [22,] 400 100 100 400 200 200 500 500 700 2600 1100 700 1300 1200 2600
## [23,] 300 0 100 500 100 100 200 300 500 1800 1300 700 800 1100 1000
## [24,] 100 0 0 200 0 100 100 200 200 800 600 500 700 400 400
## X16 X17 X18 X19 X20 X21 X22 X23 X24
## [1,] 500 400 100 300 300 100 400 300 100
## [2,] 400 200 0 100 100 0 100 0 0
## [3,] 200 100 0 0 0 0 100 100 0
## [4,] 800 500 100 200 300 200 400 500 200
## [5,] 500 200 0 100 100 100 200 100 0
## [6,] 900 500 100 200 300 100 200 100 100
## [7,] 1400 1000 200 400 500 200 500 200 100
## [8,] 2200 1400 300 700 900 400 500 300 200
## [9,] 1400 900 200 400 600 300 700 500 200
## [10,] 4400 3900 700 1800 2500 1200 2600 1800 800
## [11,] 1400 1000 100 400 600 400 1100 1300 600
## [12,] 700 600 200 300 400 300 700 700 500
## [13,] 600 500 100 300 600 600 1300 800 800
## [14,] 700 700 100 300 500 400 1200 1100 400
## [15,] 1200 1500 200 800 1100 800 2600 1000 400
## [16,] 0 2800 500 1300 1600 600 1200 500 300
## [17,] 2800 0 600 1700 1700 600 1700 600 300
## [18,] 500 600 0 300 400 100 300 100 0
## [19,] 1300 1700 300 0 1200 400 1200 300 100
## [20,] 1600 1700 400 1200 0 1200 2400 700 400
## [21,] 600 600 100 400 1200 0 1800 700 500
## [22,] 1200 1700 300 1200 2400 1800 0 2100 1100
## [23,] 500 600 100 300 700 700 2100 0 700
## [24,] 300 300 0 100 400 500 1100 700 01.1.2 Número de Nós
SiouxFalls.net$numNodes## [1] 24Gráfico de Centróides
plot(SiouxFalls.net$nodes$X, SiouxFalls.net$nodes$Y)
1.1.3 Número de Conectores
SiouxFalls.net$numLinks## [1] 761.1.3.1 Número de Zonas
SiouxFalls.net$numZones## [1] 241.1.4 Custos
SiouxFalls.net$Penalty1.1.5 Atributos de Links
SiouxFalls.net$LinksSiouxFalls.net$nodes1.1.6 Geração de Viagens
A geração de viagens fornece o número de viagens entr pares OD na atualidade.
1.1.6.1 Produção
productions<-rowSums(SiouxFalls.od)
productions## [1] 8800 4000 2800 11600 6100 7600 12100 16700 16200 45200 22300 13900
## [13] 14600 14100 21400 26100 23400 4800 12800 18500 11000 24400 14500 77001.1.6.2 Atração
attractions<-colSums(SiouxFalls.od)
attractions## X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13
## 8800 4000 2800 11700 6100 7600 12100 16700 16300 45100 22400 14000 14500
## X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24
## 14100 21300 26100 23400 4700 12800 18400 11000 24400 14500 78001.1.7 Parametros
cost.function<-with(SiouxFalls.net$Links,function(...)FFTime)
aclass <- make.assignment.class(SiouxFalls.net,"All",SiouxFalls.od)
aset <- new.assignment.set(SiouxFalls.net,list(All=aclass),cost.volume.type="vector",cost.function=cost.function)
paths <- build.paths(aset,aset$ff.cost)
travel.times <- skim.paths(paths,aset$ff.cost)[["All"]] # Popósito unico de viagem
travel.times## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0.000 5.973 4.199 8.199 10.341 10.914 15.749 12.780 15.370 18.465
## [2,] 6.181 0.000 10.380 10.680 8.789 4.941 9.776 6.807 13.818 15.657
## [3,] 4.131 10.104 0.000 4.000 6.142 10.054 14.889 11.920 11.171 14.266
## [4,] 8.061 11.051 3.930 0.000 2.142 6.054 10.889 7.920 7.171 10.266
## [5,] 9.952 8.909 5.821 1.891 0.000 3.912 8.747 5.778 5.029 8.124
## [6,] 11.178 4.997 9.669 5.739 3.848 0.000 4.835 1.866 8.877 10.716
## [7,] 16.379 10.198 14.870 10.940 9.049 5.201 0.000 3.048 11.838 8.889
## [8,] 13.331 7.150 11.822 7.892 6.001 2.153 2.969 0.000 9.929 8.850
## [9,] 14.764 13.721 10.633 6.703 4.812 8.724 12.081 9.818 0.000 3.095
## [10,] 17.713 16.204 13.582 9.652 7.761 11.207 8.986 9.054 2.949 0.000
## [11,] 14.112 17.205 9.981 6.154 8.296 12.208 14.176 14.074 8.139 5.190
## [12,] 8.298 14.271 4.167 8.167 10.309 14.221 19.056 16.087 14.005 11.056
## [13,] 11.340 17.313 7.209 11.209 13.351 17.263 19.550 19.129 17.047 14.098
## [14,] 18.264 21.357 14.133 10.306 12.448 16.360 16.888 16.956 12.291 9.342
## [15,] 23.406 19.167 19.275 15.466 13.787 14.170 11.949 12.017 8.975 6.026
## [16,] 18.459 12.278 16.950 13.020 11.129 7.281 5.060 5.128 6.964 4.015
## [17,] 20.611 14.430 19.102 15.172 13.281 9.433 7.212 7.280 9.116 6.167
## [18,] 18.576 12.395 17.067 13.137 11.246 7.398 2.197 5.245 9.910 6.961
## [19,] 22.502 16.321 20.993 17.063 15.172 11.324 9.103 9.171 11.007 8.058
## [20,] 22.447 16.266 19.978 17.008 15.117 11.269 6.068 9.116 13.781 10.832
## [21,] 18.227 22.454 14.096 18.096 18.736 17.457 12.256 15.304 13.924 10.975
## [22,] 20.299 21.074 16.168 18.238 16.875 16.077 10.876 13.924 12.063 9.114
## [23,] 17.320 23.293 13.189 14.159 16.301 20.213 15.020 18.068 16.144 13.195
## [24,] 15.273 21.246 11.142 15.142 17.284 20.643 15.442 18.490 17.110 14.161
## [,11] [,12] [,13] [,14] [,15] [,16] [,17] [,18] [,19] [,20]
## [1,] 13.997 8.131 11.219 18.130 23.069 17.615 19.778 17.677 21.917 21.522
## [2,] 16.820 14.312 17.400 20.953 18.744 11.642 13.805 11.704 15.944 15.549
## [3,] 9.798 3.932 7.020 13.931 18.870 16.755 18.918 16.817 21.057 20.502
## [4,] 6.140 7.862 10.950 10.273 15.212 12.755 14.918 12.817 17.057 16.662
## [5,] 8.031 9.753 12.841 12.164 14.148 10.613 12.776 10.675 14.915 14.520
## [6,] 11.879 13.601 16.689 16.012 13.803 6.701 8.864 6.763 11.003 10.608
## [7,] 13.873 18.802 18.542 17.136 11.976 4.874 7.037 1.928 9.176 5.773
## [8,] 13.834 15.754 18.842 17.097 11.937 4.835 6.998 4.897 9.137 8.742
## [9,] 8.079 13.893 16.981 12.212 9.119 7.021 9.184 9.884 11.323 13.729
## [10,] 4.984 10.798 13.886 9.117 6.024 3.926 6.089 6.789 8.228 10.634
## [11,] 0.000 5.814 8.902 4.133 9.072 9.116 11.279 11.979 11.918 15.824
## [12,] 5.866 0.000 3.088 9.999 14.938 14.982 17.145 17.845 17.784 16.570
## [13,] 8.908 3.042 0.000 9.911 12.243 18.024 16.980 17.353 15.089 13.482
## [14,] 4.152 9.966 9.968 0.000 4.939 11.828 9.676 14.691 7.785 11.713
## [15,] 9.312 15.108 12.066 5.160 0.000 6.889 4.737 9.752 2.846 6.774
## [16,] 8.999 14.813 17.901 12.262 7.102 0.000 2.163 2.863 4.302 6.708
## [17,] 11.151 16.965 17.005 10.099 4.939 2.152 0.000 5.015 2.139 6.067
## [18,] 11.945 17.759 16.614 15.208 10.048 2.946 5.109 0.000 7.248 3.845
## [19,] 12.112 17.908 14.866 7.960 2.800 4.043 1.891 6.906 0.000 3.928
## [20,] 15.816 15.811 12.769 11.859 6.699 6.817 5.790 3.871 3.899 0.000
## [21,] 12.909 9.929 6.887 8.757 4.949 11.838 9.686 10.059 7.795 6.188
## [22,] 12.084 12.001 8.959 7.932 3.088 9.977 7.825 8.679 5.934 4.808
## [23,] 8.005 9.022 5.980 3.853 7.232 14.121 11.969 12.823 10.078 8.952
## [24,] 9.955 6.975 3.933 5.803 8.135 15.024 12.872 13.245 10.981 9.374
## [,21] [,22] [,23] [,24]
## [1,] 18.513 20.374 17.277 15.327
## [2,] 21.431 20.461 23.458 21.508
## [3,] 14.314 16.175 13.078 11.128
## [4,] 18.244 18.319 14.261 15.058
## [5,] 19.327 17.255 16.152 16.949
## [6,] 16.490 15.520 19.599 19.444
## [7,] 11.655 10.685 14.764 14.609
## [8,] 14.624 13.654 17.733 17.578
## [9,] 14.298 12.226 16.200 17.252
## [10,] 11.203 9.131 13.105 14.157
## [11,] 13.354 12.179 8.121 10.168
## [12,] 10.382 12.243 9.146 7.196
## [13,] 7.294 9.155 6.058 4.108
## [14,] 9.221 8.046 3.988 6.035
## [15,] 5.179 3.107 7.186 8.133
## [16,] 12.281 10.209 14.288 15.235
## [17,] 10.118 8.046 12.125 13.072
## [18,] 9.727 8.757 12.836 12.681
## [19,] 7.979 5.907 9.986 10.933
## [20,] 5.882 4.912 8.991 8.836
## [21,] 0.000 1.861 4.904 2.954
## [22,] 2.072 0.000 4.079 5.026
## [23,] 5.233 4.144 0.000 2.047
## [24,] 3.186 5.047 1.950 0.0001.1.8 Distribuição de Viagens (Modelo Gravitacional e Função Gama)
A distribução de viagens compreende a etapa em que são estimados os valores futuros de viagens entre zonas dos pares OD. sempre considerando as potencialidades de atração e produção de viagens, bem como os custos associados aos trajetos entre os pares OD.
base.distribution <- hwy.gamma.function(travel.times,-0.02,-0.123) # HBW coefficients from NCHRP 365
trip.table <- ipf(base.distribution,list(rows=productions, cols=attractions),method="absolute")
aset <- hwy.update.demand(aset,"All",trip.table)
aset## $network
## Highway Network:
## Nodes: 24 Links: 76 Zones: 24
## First Through Node: 1
##
## $penalties
## [1] -1
##
## $cost.function
## function (volume, aset)
## {
## as.data.frame(cost.function(cost.volume(volume), aset))
## }
## <bytecode: 0x564acbf4e6f0>
## <environment: 0x564acbf4cfc0>
##
## $classes
## $classes$All
## $name
## [1] "All"
##
## $network.set
## $edges
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
## A 0 0 1 1 2 2 2 3 3 3 4 4 4 5
## B 1 2 0 5 0 3 11 2 4 10 3 5 8 1
## Link 0 1 2 3 4 5 6 7 8 9 10 11 12 13
## [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
## A 5 5 6 6 7 7 7 7 8 8 8 9
## B 4 7 7 17 5 6 8 15 4 7 9 8
## Link 14 15 16 17 18 19 20 21 22 23 24 25
## [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
## A 9 9 9 9 10 10 10 10 11 11 11 12
## B 10 14 15 16 3 9 11 13 2 10 12 11
## Link 26 27 28 29 30 31 32 33 34 35 36 37
## [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
## A 12 13 13 13 14 14 14 14 15 15 15 15
## B 23 10 14 22 9 13 18 21 7 9 16 17
## Link 38 39 40 41 42 43 44 45 46 47 48 49
## [,51] [,52] [,53] [,54] [,55] [,56] [,57] [,58] [,59] [,60] [,61] [,62]
## A 16 16 16 17 17 17 18 18 18 19 19 19
## B 9 15 18 6 15 19 14 16 19 17 18 20
## Link 50 51 52 53 54 55 56 57 58 59 60 61
## [,63] [,64] [,65] [,66] [,67] [,68] [,69] [,70] [,71] [,72] [,73] [,74]
## A 19 20 20 20 21 21 21 21 22 22 22 23
## B 21 19 21 23 14 19 20 22 13 21 23 12
## Link 62 63 64 65 66 67 68 69 70 71 72 73
## [,75] [,76]
## A 23 23
## B 20 22
## Link 74 75
## attr(,"numNodes")
## [1] 24
## attr(,"numZones")
## [1] 24
## attr(,"numLinks")
## [1] 76
## attr(,"firstThruNode")
## [1] 0
##
## $turns
## [,1]
## Node -1
## Parent -1
## Child -1
## Turn -1
##
## $offsets
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
## NODE 0 1 2 3 4 5 6 7 8 9 10 11 12
## Start 0 2 4 7 10 13 16 18 22 25 30 34 37
## End 2 4 7 10 13 16 18 22 25 30 34 37 39
## TurnOn 0 0 0 0 0 0 0 0 0 0 0 0 0
## TurnOff 0 0 0 0 0 0 0 0 0 0 0 0 0
## [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24]
## NODE 13 14 15 16 17 18 19 20 21 22 23
## Start 39 42 46 50 53 56 59 63 66 70 73
## End 42 46 50 53 56 59 63 66 70 73 76
## TurnOn 0 0 0 0 0 0 0 0 0 0 0
## TurnOff 0 0 0 0 0 0 0 0 0 0 0
##
## attr(,"class")
## [1] "highway.network.set"
##
## $demand
##
## 0.00000 507.55977 324.83890 767.30831 276.09426 336.39498
## 481.47700 0.00000 55.30066 208.56643 124.30146 264.18079
## 332.87530 59.71046 0.00000 257.81426 92.40287 74.01197
## 788.77789 206.58493 258.71759 0.00000 601.06520 476.20531
## 288.20157 125.01952 94.18590 611.60733 0.00000 289.46418
## 314.05180 259.88251 73.76149 473.23977 283.19948 0.00000
## 259.27245 213.13486 60.83656 388.64327 231.60007 492.00720
## 535.56929 441.58007 125.72679 804.74550 480.37127 1030.15629
## 412.18597 178.66908 134.14530 859.61475 513.71462 410.63053
## 769.58817 353.38207 250.14755 1599.13025 953.49194 810.80346
## 611.22807 158.43971 198.99533 1259.68453 452.65892 363.33955
## 958.21796 173.09810 314.10771 741.90447 266.94907 214.55135
## 735.46078 133.17476 239.95266 569.38485 205.11172 165.06520
## 235.92023 61.20521 76.66969 483.71013 174.20014 140.14317
## 159.13724 102.45939 51.65231 324.53323 188.13598 234.77069
## 357.01722 293.09840 83.75267 534.57728 318.35581 674.56001
## 257.43384 211.12757 60.38023 385.13779 229.25118 484.95975
## 65.47779 53.75153 15.36026 98.03757 58.38237 123.69208
## 106.20778 87.04192 24.90738 158.79946 94.49492 199.69713
## 186.30341 152.68664 49.21338 278.56099 165.76134 350.31389
## 174.68553 39.37777 56.77022 135.22751 58.76258 90.13762
## 298.77171 103.32836 97.03918 293.84077 163.72730 236.61311
## 283.72042 51.50562 92.23348 320.06898 115.37812 92.92921
## 188.41857 34.18175 61.30476 145.86262 52.58941 45.37254
## Sum 8800.00000 4000.00000 2800.00000 11700.00000 6100.00000 7600.00000
##
## 280.66070 576.4649 379.5857 697.3755 607.6058 950.04033
## 219.02404 451.2453 170.7029 366.4369 158.6090 162.83741
## 61.71758 126.7995 126.5274 232.1724 202.6856 319.26820
## 395.56040 814.2446 813.0571 1488.5210 1249.3943 756.16593
## 239.39943 493.7437 493.4132 901.1463 455.9734 276.25939
## 497.79349 1037.7571 385.9460 827.4367 357.9240 217.11001
## 0.00000 1401.5062 420.4909 1640.0428 440.3812 179.44887
## 1410.31820 0.0000 754.5908 2330.3908 625.7323 370.46551
## 411.23787 774.3873 0.0000 4443.1293 1180.8505 429.50050
## 1630.31117 2294.8309 4519.6548 0.0000 4698.9106 1701.21576
## 433.19358 622.8328 1187.5683 4647.0436 0.0000 1614.30281
## 179.26962 367.9211 433.1798 1687.8429 1618.6540 0.00000
## 189.32242 283.1772 333.2491 1297.2654 1239.7476 1959.15156
## 199.93360 281.4470 456.9622 1781.8590 1714.8805 619.59245
## 471.58620 663.8309 882.2343 3448.6898 1141.3475 416.53708
## 1360.24725 1914.4657 1379.7695 5410.0349 1442.2143 525.02302
## 976.05441 1373.8464 991.7493 3876.2036 1037.7714 378.38543
## 366.02463 351.0034 177.4524 693.0426 185.7418 67.75517
## 401.51760 565.1785 408.3361 1593.4434 480.0823 175.53275
## 1024.37012 991.4735 503.4874 1961.9598 527.5240 396.79222
## 262.18101 254.7015 274.8289 1070.8774 420.8191 458.78853
## 688.74153 668.7592 766.3378 2988.5825 1031.4292 783.40088
## 269.72851 262.2294 302.6419 1178.3958 1127.0652 745.82157
## 131.80662 128.1539 138.2343 538.1075 454.6565 496.60461
## Sum 12100.00000 16700.0000 16300.0000 45100.0000 22400.0000 14000.00000
##
## 717.0495 236.18043 162.74522 385.40505 276.45600 69.54798
## 123.2141 61.70049 103.14465 300.38819 215.23717 54.20438
## 239.7312 78.63850 54.11983 84.74064 60.77875 15.29175
## 570.6145 483.16807 331.92915 542.68441 388.95678 97.92709
## 208.7042 176.68622 175.42768 328.21009 235.10150 59.22417
## 164.2502 139.01663 232.56620 680.64827 486.63971 122.81188
## 205.8302 190.69403 460.54983 1352.64747 965.40421 360.01437
## 280.4119 270.95194 654.39555 1922.16108 1371.80643 346.79812
## 324.9553 457.58905 855.90294 1341.18960 959.11818 170.33061
## 1285.8136 1813.93194 3401.20208 5347.43878 3811.08391 676.33506
## 1215.8725 1727.19335 1177.25125 1409.93794 1009.40459 179.30849
## 1926.3401 625.73582 429.79490 514.76448 369.10661 65.59381
## 0.0000 710.35402 674.92838 396.10557 423.01528 78.28772
## 687.9491 0.00000 1280.92127 649.62410 797.29799 82.70895
## 675.5594 1250.21590 0.00000 1538.25238 1894.50118 195.33589
## 397.3168 623.28345 1510.97326 0.00000 3209.20409 567.57156
## 418.1537 768.78545 1870.01682 3225.97721 0.00000 405.58876
## 86.7449 80.38129 194.34904 574.56452 408.57459 0.00000
## 284.4672 524.08415 1283.22762 1316.54952 1633.99857 166.55587
## 643.3928 560.74566 1360.04804 1613.69888 1723.29458 426.40034
## 746.1859 459.09805 942.90587 478.20956 586.91494 108.58587
## 1272.2727 1125.99180 2646.52955 1334.18309 1638.85289 285.41214
## 1214.1266 1238.05385 1025.55682 522.24312 640.50586 111.62376
## 811.0435 497.51992 471.51404 240.37606 294.74621 54.54142
## Sum 14500.0000 14100.00000 21300.00000 26100.00000 23400.00000 4700.00000
##
## 113.49491 204.52344 170.08579 293.46680 280.65706 186.45879
## 88.28937 159.12376 43.91609 107.64055 48.35516 32.10431
## 24.94960 45.86182 56.62463 97.64874 93.47544 62.15366
## 159.58052 287.60213 135.32500 291.38706 314.17023 148.36092
## 96.41691 173.77810 54.77862 153.96177 114.98880 54.30803
## 199.32982 359.33420 98.93324 242.55975 95.20233 50.60547
## 395.04469 1039.82917 284.79687 698.61818 273.70767 145.49886
## 561.33045 1012.07146 278.23868 682.28141 267.63861 142.26759
## 392.91254 499.58182 266.52646 749.75082 297.80838 136.26854
## 1558.38911 1978.93778 1055.51844 2972.06935 1178.65079 539.16245
## 498.83430 526.44257 409.87319 1031.21723 1115.29548 450.08181
## 182.47513 364.06259 450.47453 776.17748 744.18172 495.59677
## 286.35146 600.10759 744.72898 1281.58475 1231.73914 822.73389
## 540.78820 567.75473 443.85200 1117.69367 1216.01526 488.87139
## 1292.52229 1344.58291 941.89619 2668.44298 1034.73867 479.03748
## 1302.16920 1647.37795 469.59352 1321.73350 517.70196 239.95868
## 1622.44698 1681.88772 579.21364 1631.72086 638.17458 295.73340
## 166.90758 440.83212 120.19517 294.95067 115.42067 61.35784
## 0.00000 1151.06968 394.84830 1113.93203 434.66420 201.36361
## 1173.03729 0.00000 895.78128 2201.49259 857.67333 455.98853
## 398.08840 836.25060 0.00000 1815.21809 797.46141 533.92364
## 1112.91116 2202.65055 1795.93559 0.00000 1959.20528 905.48373
## 434.04481 857.47426 784.20255 1957.76947 0.00000 872.68063
## 199.68530 418.86304 524.66125 898.68226 873.07383 0.00000
## Sum 12800.00000 18400.00000 11000.00000 24400.00000 14500.00000 7800.00000
## Sum
## 8800
## 4000
## 2800
## 11600
## 6100
## 7600
## 12100
## 16700
## 16200
## 45200
## 22300
## 13900
## 14600
## 14100
## 21400
## 26100
## 23400
## 4800
## 12800
## 18500
## 11000
## 24400
## 14500
## 7700
## Sum 360600
## RMSE: 6.67032e-09
## Converged in 11 Iterations
##
## attr(,"class")
## [1] "highway.assignment.class"
##
##
## $ff.vol
## All
## 1 0
## 2 0
## 3 0
## 4 0
## 5 0
## 6 0
## 7 0
## 8 0
## 9 0
## 10 0
## 11 0
## 12 0
## 13 0
## 14 0
## 15 0
## 16 0
## 17 0
## 18 0
## 19 0
## 20 0
## 21 0
## 22 0
## 23 0
## 24 0
## 25 0
## 26 0
## 27 0
## 28 0
## 29 0
## 30 0
## 31 0
## 32 0
## 33 0
## 34 0
## 35 0
## 36 0
## 37 0
## 38 0
## 39 0
## 40 0
## 41 0
## 42 0
## 43 0
## 44 0
## 45 0
## 46 0
## 47 0
## 48 0
## 49 0
## 50 0
## 51 0
## 52 0
## 53 0
## 54 0
## 55 0
## 56 0
## 57 0
## 58 0
## 59 0
## 60 0
## 61 0
## 62 0
## 63 0
## 64 0
## 65 0
## 66 0
## 67 0
## 68 0
## 69 0
## 70 0
## 71 0
## 72 0
## 73 0
## 74 0
## 75 0
## 76 0
##
## $ff.cost
## cost.function(cost.volume(volume), aset)
## 1 5.973
## 2 4.199
## 3 6.181
## 4 4.941
## 5 4.131
## 6 4.000
## 7 3.932
## 8 3.930
## 9 2.142
## 10 6.140
## 11 1.891
## 12 3.912
## 13 5.029
## 14 4.997
## 15 3.848
## 16 1.866
## 17 3.048
## 18 1.928
## 19 2.153
## 20 2.969
## 21 9.929
## 22 4.835
## 23 4.812
## 24 9.818
## 25 3.095
## 26 2.949
## 27 4.984
## 28 6.024
## 29 3.926
## 30 7.931
## 31 6.154
## 32 5.190
## 33 5.814
## 34 4.133
## 35 4.167
## 36 5.866
## 37 3.088
## 38 3.042
## 39 4.108
## 40 4.152
## 41 4.939
## 42 3.988
## 43 6.026
## 44 5.160
## 45 2.846
## 46 3.107
## 47 5.128
## 48 4.015
## 49 2.163
## 50 2.863
## 51 7.913
## 52 2.152
## 53 2.139
## 54 2.197
## 55 2.946
## 56 3.845
## 57 2.800
## 58 1.891
## 59 3.928
## 60 3.871
## 61 3.899
## 62 5.882
## 63 4.912
## 64 6.188
## 65 1.861
## 66 2.954
## 67 3.088
## 68 4.808
## 69 2.072
## 70 4.079
## 71 3.853
## 72 4.144
## 73 2.047
## 74 3.933
## 75 3.186
## 76 1.950
##
## $objective.function
## function (volume)
## cost.integrator(cf, ff.vol, ff.cost, volume, cf(volume), tol,
## max.depth)
## <bytecode: 0x564acbf86aa8>
## <environment: 0x564acbf86178>
##
## attr(,"class")
## [1] "highway.assignment.set"1.1.9 Distribuição
#method = c("AON", "MSA", "Frank.Wolfe", "ParTan" )
assignment.results <- highway.assign(aset,method="Frank.Wolfe")## Frank-Wolfe highway assignmentassignment.results## $aset
## $network
## Highway Network:
## Nodes: 24 Links: 76 Zones: 24
## First Through Node: 1
##
## $penalties
## [1] -1
##
## $cost.function
## function (volume, aset)
## {
## as.data.frame(cost.function(cost.volume(volume), aset))
## }
## <bytecode: 0x564acbf4e6f0>
## <environment: 0x564acbf4cfc0>
##
## $classes
## $classes$All
## $name
## [1] "All"
##
## $network.set
## $edges
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
## A 0 0 1 1 2 2 2 3 3 3 4 4 4 5
## B 1 2 0 5 0 3 11 2 4 10 3 5 8 1
## Link 0 1 2 3 4 5 6 7 8 9 10 11 12 13
## [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
## A 5 5 6 6 7 7 7 7 8 8 8 9
## B 4 7 7 17 5 6 8 15 4 7 9 8
## Link 14 15 16 17 18 19 20 21 22 23 24 25
## [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
## A 9 9 9 9 10 10 10 10 11 11 11 12
## B 10 14 15 16 3 9 11 13 2 10 12 11
## Link 26 27 28 29 30 31 32 33 34 35 36 37
## [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
## A 12 13 13 13 14 14 14 14 15 15 15 15
## B 23 10 14 22 9 13 18 21 7 9 16 17
## Link 38 39 40 41 42 43 44 45 46 47 48 49
## [,51] [,52] [,53] [,54] [,55] [,56] [,57] [,58] [,59] [,60] [,61] [,62]
## A 16 16 16 17 17 17 18 18 18 19 19 19
## B 9 15 18 6 15 19 14 16 19 17 18 20
## Link 50 51 52 53 54 55 56 57 58 59 60 61
## [,63] [,64] [,65] [,66] [,67] [,68] [,69] [,70] [,71] [,72] [,73] [,74]
## A 19 20 20 20 21 21 21 21 22 22 22 23
## B 21 19 21 23 14 19 20 22 13 21 23 12
## Link 62 63 64 65 66 67 68 69 70 71 72 73
## [,75] [,76]
## A 23 23
## B 20 22
## Link 74 75
## attr(,"numNodes")
## [1] 24
## attr(,"numZones")
## [1] 24
## attr(,"numLinks")
## [1] 76
## attr(,"firstThruNode")
## [1] 0
##
## $turns
## [,1]
## Node -1
## Parent -1
## Child -1
## Turn -1
##
## $offsets
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
## NODE 0 1 2 3 4 5 6 7 8 9 10 11 12
## Start 0 2 4 7 10 13 16 18 22 25 30 34 37
## End 2 4 7 10 13 16 18 22 25 30 34 37 39
## TurnOn 0 0 0 0 0 0 0 0 0 0 0 0 0
## TurnOff 0 0 0 0 0 0 0 0 0 0 0 0 0
## [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24]
## NODE 13 14 15 16 17 18 19 20 21 22 23
## Start 39 42 46 50 53 56 59 63 66 70 73
## End 42 46 50 53 56 59 63 66 70 73 76
## TurnOn 0 0 0 0 0 0 0 0 0 0 0
## TurnOff 0 0 0 0 0 0 0 0 0 0 0
##
## attr(,"class")
## [1] "highway.network.set"
##
## $demand
##
## 0.00000 507.55977 324.83890 767.30831 276.09426 336.39498
## 481.47700 0.00000 55.30066 208.56643 124.30146 264.18079
## 332.87530 59.71046 0.00000 257.81426 92.40287 74.01197
## 788.77789 206.58493 258.71759 0.00000 601.06520 476.20531
## 288.20157 125.01952 94.18590 611.60733 0.00000 289.46418
## 314.05180 259.88251 73.76149 473.23977 283.19948 0.00000
## 259.27245 213.13486 60.83656 388.64327 231.60007 492.00720
## 535.56929 441.58007 125.72679 804.74550 480.37127 1030.15629
## 412.18597 178.66908 134.14530 859.61475 513.71462 410.63053
## 769.58817 353.38207 250.14755 1599.13025 953.49194 810.80346
## 611.22807 158.43971 198.99533 1259.68453 452.65892 363.33955
## 958.21796 173.09810 314.10771 741.90447 266.94907 214.55135
## 735.46078 133.17476 239.95266 569.38485 205.11172 165.06520
## 235.92023 61.20521 76.66969 483.71013 174.20014 140.14317
## 159.13724 102.45939 51.65231 324.53323 188.13598 234.77069
## 357.01722 293.09840 83.75267 534.57728 318.35581 674.56001
## 257.43384 211.12757 60.38023 385.13779 229.25118 484.95975
## 65.47779 53.75153 15.36026 98.03757 58.38237 123.69208
## 106.20778 87.04192 24.90738 158.79946 94.49492 199.69713
## 186.30341 152.68664 49.21338 278.56099 165.76134 350.31389
## 174.68553 39.37777 56.77022 135.22751 58.76258 90.13762
## 298.77171 103.32836 97.03918 293.84077 163.72730 236.61311
## 283.72042 51.50562 92.23348 320.06898 115.37812 92.92921
## 188.41857 34.18175 61.30476 145.86262 52.58941 45.37254
## Sum 8800.00000 4000.00000 2800.00000 11700.00000 6100.00000 7600.00000
##
## 280.66070 576.4649 379.5857 697.3755 607.6058 950.04033
## 219.02404 451.2453 170.7029 366.4369 158.6090 162.83741
## 61.71758 126.7995 126.5274 232.1724 202.6856 319.26820
## 395.56040 814.2446 813.0571 1488.5210 1249.3943 756.16593
## 239.39943 493.7437 493.4132 901.1463 455.9734 276.25939
## 497.79349 1037.7571 385.9460 827.4367 357.9240 217.11001
## 0.00000 1401.5062 420.4909 1640.0428 440.3812 179.44887
## 1410.31820 0.0000 754.5908 2330.3908 625.7323 370.46551
## 411.23787 774.3873 0.0000 4443.1293 1180.8505 429.50050
## 1630.31117 2294.8309 4519.6548 0.0000 4698.9106 1701.21576
## 433.19358 622.8328 1187.5683 4647.0436 0.0000 1614.30281
## 179.26962 367.9211 433.1798 1687.8429 1618.6540 0.00000
## 189.32242 283.1772 333.2491 1297.2654 1239.7476 1959.15156
## 199.93360 281.4470 456.9622 1781.8590 1714.8805 619.59245
## 471.58620 663.8309 882.2343 3448.6898 1141.3475 416.53708
## 1360.24725 1914.4657 1379.7695 5410.0349 1442.2143 525.02302
## 976.05441 1373.8464 991.7493 3876.2036 1037.7714 378.38543
## 366.02463 351.0034 177.4524 693.0426 185.7418 67.75517
## 401.51760 565.1785 408.3361 1593.4434 480.0823 175.53275
## 1024.37012 991.4735 503.4874 1961.9598 527.5240 396.79222
## 262.18101 254.7015 274.8289 1070.8774 420.8191 458.78853
## 688.74153 668.7592 766.3378 2988.5825 1031.4292 783.40088
## 269.72851 262.2294 302.6419 1178.3958 1127.0652 745.82157
## 131.80662 128.1539 138.2343 538.1075 454.6565 496.60461
## Sum 12100.00000 16700.0000 16300.0000 45100.0000 22400.0000 14000.00000
##
## 717.0495 236.18043 162.74522 385.40505 276.45600 69.54798
## 123.2141 61.70049 103.14465 300.38819 215.23717 54.20438
## 239.7312 78.63850 54.11983 84.74064 60.77875 15.29175
## 570.6145 483.16807 331.92915 542.68441 388.95678 97.92709
## 208.7042 176.68622 175.42768 328.21009 235.10150 59.22417
## 164.2502 139.01663 232.56620 680.64827 486.63971 122.81188
## 205.8302 190.69403 460.54983 1352.64747 965.40421 360.01437
## 280.4119 270.95194 654.39555 1922.16108 1371.80643 346.79812
## 324.9553 457.58905 855.90294 1341.18960 959.11818 170.33061
## 1285.8136 1813.93194 3401.20208 5347.43878 3811.08391 676.33506
## 1215.8725 1727.19335 1177.25125 1409.93794 1009.40459 179.30849
## 1926.3401 625.73582 429.79490 514.76448 369.10661 65.59381
## 0.0000 710.35402 674.92838 396.10557 423.01528 78.28772
## 687.9491 0.00000 1280.92127 649.62410 797.29799 82.70895
## 675.5594 1250.21590 0.00000 1538.25238 1894.50118 195.33589
## 397.3168 623.28345 1510.97326 0.00000 3209.20409 567.57156
## 418.1537 768.78545 1870.01682 3225.97721 0.00000 405.58876
## 86.7449 80.38129 194.34904 574.56452 408.57459 0.00000
## 284.4672 524.08415 1283.22762 1316.54952 1633.99857 166.55587
## 643.3928 560.74566 1360.04804 1613.69888 1723.29458 426.40034
## 746.1859 459.09805 942.90587 478.20956 586.91494 108.58587
## 1272.2727 1125.99180 2646.52955 1334.18309 1638.85289 285.41214
## 1214.1266 1238.05385 1025.55682 522.24312 640.50586 111.62376
## 811.0435 497.51992 471.51404 240.37606 294.74621 54.54142
## Sum 14500.0000 14100.00000 21300.00000 26100.00000 23400.00000 4700.00000
##
## 113.49491 204.52344 170.08579 293.46680 280.65706 186.45879
## 88.28937 159.12376 43.91609 107.64055 48.35516 32.10431
## 24.94960 45.86182 56.62463 97.64874 93.47544 62.15366
## 159.58052 287.60213 135.32500 291.38706 314.17023 148.36092
## 96.41691 173.77810 54.77862 153.96177 114.98880 54.30803
## 199.32982 359.33420 98.93324 242.55975 95.20233 50.60547
## 395.04469 1039.82917 284.79687 698.61818 273.70767 145.49886
## 561.33045 1012.07146 278.23868 682.28141 267.63861 142.26759
## 392.91254 499.58182 266.52646 749.75082 297.80838 136.26854
## 1558.38911 1978.93778 1055.51844 2972.06935 1178.65079 539.16245
## 498.83430 526.44257 409.87319 1031.21723 1115.29548 450.08181
## 182.47513 364.06259 450.47453 776.17748 744.18172 495.59677
## 286.35146 600.10759 744.72898 1281.58475 1231.73914 822.73389
## 540.78820 567.75473 443.85200 1117.69367 1216.01526 488.87139
## 1292.52229 1344.58291 941.89619 2668.44298 1034.73867 479.03748
## 1302.16920 1647.37795 469.59352 1321.73350 517.70196 239.95868
## 1622.44698 1681.88772 579.21364 1631.72086 638.17458 295.73340
## 166.90758 440.83212 120.19517 294.95067 115.42067 61.35784
## 0.00000 1151.06968 394.84830 1113.93203 434.66420 201.36361
## 1173.03729 0.00000 895.78128 2201.49259 857.67333 455.98853
## 398.08840 836.25060 0.00000 1815.21809 797.46141 533.92364
## 1112.91116 2202.65055 1795.93559 0.00000 1959.20528 905.48373
## 434.04481 857.47426 784.20255 1957.76947 0.00000 872.68063
## 199.68530 418.86304 524.66125 898.68226 873.07383 0.00000
## Sum 12800.00000 18400.00000 11000.00000 24400.00000 14500.00000 7800.00000
## Sum
## 8800
## 4000
## 2800
## 11600
## 6100
## 7600
## 12100
## 16700
## 16200
## 45200
## 22300
## 13900
## 14600
## 14100
## 21400
## 26100
## 23400
## 4800
## 12800
## 18500
## 11000
## 24400
## 14500
## 7700
## Sum 360600
## RMSE: 6.67032e-09
## Converged in 11 Iterations
##
## attr(,"class")
## [1] "highway.assignment.class"
##
##
## $ff.vol
## All
## 1 0
## 2 0
## 3 0
## 4 0
## 5 0
## 6 0
## 7 0
## 8 0
## 9 0
## 10 0
## 11 0
## 12 0
## 13 0
## 14 0
## 15 0
## 16 0
## 17 0
## 18 0
## 19 0
## 20 0
## 21 0
## 22 0
## 23 0
## 24 0
## 25 0
## 26 0
## 27 0
## 28 0
## 29 0
## 30 0
## 31 0
## 32 0
## 33 0
## 34 0
## 35 0
## 36 0
## 37 0
## 38 0
## 39 0
## 40 0
## 41 0
## 42 0
## 43 0
## 44 0
## 45 0
## 46 0
## 47 0
## 48 0
## 49 0
## 50 0
## 51 0
## 52 0
## 53 0
## 54 0
## 55 0
## 56 0
## 57 0
## 58 0
## 59 0
## 60 0
## 61 0
## 62 0
## 63 0
## 64 0
## 65 0
## 66 0
## 67 0
## 68 0
## 69 0
## 70 0
## 71 0
## 72 0
## 73 0
## 74 0
## 75 0
## 76 0
##
## $ff.cost
## cost.function(cost.volume(volume), aset)
## 1 5.973
## 2 4.199
## 3 6.181
## 4 4.941
## 5 4.131
## 6 4.000
## 7 3.932
## 8 3.930
## 9 2.142
## 10 6.140
## 11 1.891
## 12 3.912
## 13 5.029
## 14 4.997
## 15 3.848
## 16 1.866
## 17 3.048
## 18 1.928
## 19 2.153
## 20 2.969
## 21 9.929
## 22 4.835
## 23 4.812
## 24 9.818
## 25 3.095
## 26 2.949
## 27 4.984
## 28 6.024
## 29 3.926
## 30 7.931
## 31 6.154
## 32 5.190
## 33 5.814
## 34 4.133
## 35 4.167
## 36 5.866
## 37 3.088
## 38 3.042
## 39 4.108
## 40 4.152
## 41 4.939
## 42 3.988
## 43 6.026
## 44 5.160
## 45 2.846
## 46 3.107
## 47 5.128
## 48 4.015
## 49 2.163
## 50 2.863
## 51 7.913
## 52 2.152
## 53 2.139
## 54 2.197
## 55 2.946
## 56 3.845
## 57 2.800
## 58 1.891
## 59 3.928
## 60 3.871
## 61 3.899
## 62 5.882
## 63 4.912
## 64 6.188
## 65 1.861
## 66 2.954
## 67 3.088
## 68 4.808
## 69 2.072
## 70 4.079
## 71 3.853
## 72 4.144
## 73 2.047
## 74 3.933
## 75 3.186
## 76 1.950
##
## $objective.function
## function (volume)
## cost.integrator(cf, ff.vol, ff.cost, volume, cf(volume), tol,
## max.depth)
## <bytecode: 0x564acbf86aa8>
## <environment: 0x564acbf86178>
##
## attr(,"class")
## [1] "highway.assignment.set"
##
## $costs
## cost.function(cost.volume(volume), aset)
## 1 5.973
## 2 4.199
## 3 6.181
## 4 4.941
## 5 4.131
## 6 4.000
## 7 3.932
## 8 3.930
## 9 2.142
## 10 6.140
## 11 1.891
## 12 3.912
## 13 5.029
## 14 4.997
## 15 3.848
## 16 1.866
## 17 3.048
## 18 1.928
## 19 2.153
## 20 2.969
## 21 9.929
## 22 4.835
## 23 4.812
## 24 9.818
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## 26 2.949
## 27 4.984
## 28 6.024
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## 30 7.931
## 31 6.154
## 32 5.190
## 33 5.814
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## 38 3.042
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## 42 3.988
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## 46 3.107
## 47 5.128
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## 50 2.863
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## 56 3.845
## 57 2.800
## 58 1.891
## 59 3.928
## 60 3.871
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## 62 5.882
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## 64 6.188
## 65 1.861
## 66 2.954
## 67 3.088
## 68 4.808
## 69 2.072
## 70 4.079
## 71 3.853
## 72 4.144
## 73 2.047
## 74 3.933
## 75 3.186
## 76 1.950
##
## $paths
## $paths$All
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## [1,] 13 9 15 15 14 20 23 20 23 12
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##
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## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
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## , , 15
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## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
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## [1,] 18 15 15 15 16 17 21 14 21 20
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## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
## [1,] 1 5 3 4 5 7 17 15 9 15 9 10 23 14
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## [1,] 18 16 16 15 16 18 21 14 21 20
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## [1,] 1 5 3 4 5 7 17 6 9 15 9 10 23 14
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## [1,] 18 17 15 17 16 17 19 19 21 20
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## , , 19
##
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
## [1,] 1 5 3 4 5 7 17 15 9 15 13 12 23 14
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## [1,] 18 16 18 15 18 18 21 14 21 20
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## , , 20
##
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
## [1,] 1 5 11 4 5 7 17 6 9 15 9 12 23 14
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## [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24]
## [1,] 18 17 18 19 19 19 19 19 21 20
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##
## , , 21
##
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
## [1,] 2 5 11 2 8 7 17 6 9 14 13 12 23 22
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## [1,] 21 16 18 19 14 20 20 20 23 20
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## , , 22
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## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
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##
## attr(,"numNodes")
## [1] 24
## attr(,"numLinks")
## [1] 76
## attr(,"numZones")
## [1] 24
## attr(,"firstThruNode")
## [1] 0
##
##
## $volumes
## All
## 1 3202.1784
## 2 6471.3040
## 3 2984.6223
## 4 5339.6593
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## 7 8582.4326
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## 10 4134.9473
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## 12 9096.1673
## 13 6072.6154
## 14 5122.1031
## 15 8246.3366
## 16 15086.7298
## 17 7945.9277
## 18 13845.0727
## 19 14019.3430
## 20 8255.2656
## 21 754.5908
## 22 13933.6607
## 23 6491.9440
## 24 774.3873
## 25 16620.0357
## 26 17159.1608
## 27 18997.0718
## 28 10360.5691
## 29 27139.7405
## 30 0.0000
## 31 4862.9645
## 32 18209.8657
## 33 9682.5467
## 34 13840.4632
## 35 8602.4736
## 36 10535.4904
## 37 11989.6531
## 38 12962.6377
## 39 11578.5329
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## 42 6717.5564
## 43 10518.5184
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## 46 23512.1277
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## 59 4745.2950
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## 61 4817.1256
## 62 3959.5531
## 63 5837.1857
## 64 3647.6141
## 65 12240.3243
## 66 13450.1838
## 67 20351.0211
## 68 5686.5608
## 69 12987.8429
## 70 8645.3891
## 71 9368.2425
## 72 6081.1760
## 73 6524.9184
## 74 12451.5175
## 75 12390.7262
## 76 6611.3914
##
## $iset
## NULL
##
## $intercept
## NULL
##
## $results
## $results$iter
## [1] 1
##
## $results$elapsed
## [1] 0.558
##
## $results$objective
## [1] 2970021
##
## $results$gap
## [1] 0
##
## $results$relative.gap
## [1] 0
##
## $results$lower.bound
## [1] 2970021
##
## $results$best.lower.bound
## [1] 2970021
##
## $results$avg.excess.cost
## [1] 0
##
## $results$lambda
## [1] 1
##
##
## $log
## [1] FALSE
##
## $method
## [1] ".highway.assignment.Frank.Wolfe"loaded.links <- assignment.results$volumes
loaded.links2 Documentação
Details
The highway.assign function performs a traffic assignment using the network and demand data specified in its first argument, which is an assignment.set. The assignment method is chosen using the method argument, which may refer to user-defined methods as described below. The control argument is a list of values that set values for convergence criteria and adjust the behavior of the algorithm in various ways. Valid control elements for the built-in algorithms are described below.
Most of the highway assignment algorithms reflect descriptions provided in Sheffi (1985). ParTan is described in Lee and Nie, 2001.
Overview of Built-In Algorithms
The method specifies the algorithm to be used for the traffic assignment. Four common assignment algorithms are built in:
AON
“All-or-Nothing” assignment. The algorithm builds shortest paths fromthe free-flow speeds defined for the assignment set, and loads all the demand onto those paths without considering capacity limits. The steps are these:
Build paths
Load Traffic
StopMSA
“Multiple Successive Averages” does a simple form of capacity restraint by averaging the volumes from successive AON assignments where the next assignment uses the costs from the average volumes from all the previous assignment volumes. The steps are these:
Build paths using costs from average link volumes (initially free-flow)
Load Traffic
Compute the new average volume and the associated link costs
If maximum number of iterations is reached, stop, otherwise return to step 1.Frank.Wolfe
Computes an equilibrium assignment using the simple, low-resource, but slowly converging Frank-Wolfe algorithm. This is a widely used method in travel demand modeling, but it is gradually becomign obsolete due to advances in computing capacity and the desire to achieve faster convergence to a narrower tolerance. (The TravelR project exists in part to help explore practical implementations of alternative algorithms.) The steps are these:
Build paths using costs from current equilibrium link volumes (initially free-flow)
Load Traffic
Compute the combination of equilibrium volume and shortest path volume that minimizes the objective function
Update the equilibrium volume to the combined value
Recompute link costs from equilibrium flow
If convergence target is met, stop, otherwise return to step 1.ParTan
The “Parallel-Tangent” algorithm extends the Frank-Wolfe approach by rectifying the search direction using a previous search direction. This algorithm converges somewhat faster than the basic Frank-Wolfe method. There is an additional line search for the second and subsequent iterations that finds the lowest cost combination of the previous equilibrium volumes and the current combined volume from a standard Frank-Wolfe step. The steps are these:
Build paths using costs from current equilibrium link volumes (initially free-flow)
Load Traffic
Compute the combination of equilibrium volume and shortest path volume that minimizes the objective function
Compute the combination of the new combined value and the equilibrium result at the start of the previous iteration that minimizes the objective function
Save the current equilibrium volume for a later iteration
Update the equlibrium volume with the final combined volume
Recompute link costs from the new equilibrium flow
If convergence target is met, stop, otherwise return to step 1.Additional algorithms can be implemented in specially named functions provided by the user, through a mechanism similar to (but less sophisticated than) R’s S3 methods. The supplied method name is prefixed by “highway.assignment.” and a function by that name is sought in the calling environment of the function. The internal methods are named differently and are sought only when the search for user-defined functions fails. It is thus possible to supply an alternate implementation for one of the internal methods by providing a function with a suitable name (e.g. highway.assignment.Frank.Wolfe)
The function that implements an assignment algorithm will be passed the aset and control parameters, and should return a list of values, with elements comparable to those returned by the standard algorithms. An element called method will be concatenated to the list returned from the algorithm function.
Control Parameters
The control argument is a list of optional parameters that alter the behavior of the assignment algorithms in various ways. The sets of elements relevant to each built-in algorithm are described first, and a description of each follows.
All Methods
intercept (see below), log, verboseAON
No additional parametersMSA
max.iterFrank.Wolfe
max.iter, min.relative.gap, max.elapsed, opt.tolParTan
max.iter, min.relative.gap, max.elapsed, opt.tolintercept If this value is an intercept.set, then do select link processing (not set by default); see below verbose If greater than 0, add additional messages (higher numbers imply more, but all the functions are currently quite terse; default is 1 log If TRUE, return results of each iteration in a data.frame; defaults to FALSE max.iter Maximum number of iterations before stopping (defaults to 4 for MSA, and 100 for other algorithms min.relative.gap Equilibrium algorithms will stop if relative.gap statistic drops below this value (default 1e-4) max.elapsed Maximum allowable run-time in seconds (default 3600) opt.tol Tolerance for line search optimization (default .Machine$double.eps^0.5)
Select Link Processing
Travel modelers often seek information on which specific links are assigned demand for particular zone pairs. The select link results are reported either as a matrix of demand from origin to destination that passes through one of the selected links, or as a vector of volumes tha results when the selected demand matrix is assigned.
Internally, select link processing identifies links of interest, constructs a subset of the matrix of the demand matrix that only includes origins and destinations, and assigns that demand to the network. Currently, select link processing applies to all assignment classes, and the selected demand and link volumes for each class are maintained separately. Naturally, one is rarely interested in flows that follow a single path (say the shortest path). Consequently, within the assignment algorithms when an intercept is specified, the intercepts and demands are computed at each iteration, and the results are combined using the same factors used for the total equilibrium flow. Thus, the intercepts will include a portion of traffic due to rarely used alternate paths that may intercept a link of interest.
Needless to say, processing select link intercepts on a large network, or through many iterations, will be substantially slower than simply computing a total equilibrium assignment.
See intercept.set for details about setting up a select link analysis. Value
Returns a list with various elements. The possible elements are enumerated in the following table, which shows the element name and description. Certain elements are only returned if suitable control values are provided, and they are so indicated. aset the assignment set which was assigned (identical to the aset argument costs a data.frame with one column per assignment class and one row per link paths the shortest path tree for the final assignment iteration resulting from the final costs volumes a data.frame of volumes, with one column per assignment class and one row per link iset the control argument describing the intercept (only present if it was supplied) intercept A list of two elements: od a list of intercepted demand matrices, one for each class, and volumes a data frame with one column per class of intercepted volumes (only present if an intercept set was supplied in the control argument) results data.frame of one row with the assignment statistics from the final iteration log data.frame with assignment statistics from all iterations method the method selected either as an argument or by default Author(s)
Jeremy Raw References
Lee, D.-H., and Nie, Y. “Accelerating Strategies and Computational Studies of the Frank-Wolfe Algorithm for the Traffic Assignment Problem”, 2001, Transportation Resarch Record, 1771:97-105. Sheffi, Y., 1985, Urban Transportation Networks, Prentice-Hall; available online as a PDF at http://web.mit.edu/sheffi/www/urbanTransportation.html See Also