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Frank-Wolfe Algorithm : Find User Equilibrium in Traffic Assignment

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Traffic Assignment by Frank-Wolfe Algorithm

Introduction

  • Find traffic assignment value at User Equilibrium, by FWA.
  • Network & OD File : Sioux-Falls Network

Sioux-Falls Network

(image created by Changhyun Kwon)

Shortest Path Algorithm

  • SPA_Dijkstra_ver1.ipynb : Dijkstra Method, ver.1
  • SPA_Dijkstra_ver2.ipynb : Dijkstra Method, ver.2
  • SPA_Moore_ver1.ipynb : Moore Method, ver.1

Frank-Wolfe Algorithm

  • UE_Frank_Wolfe_Algorithm_Tutorial.ipynb : Frank-Wolfe Algorithm, Step by Step Tutorial
  • UE_Frank_wolfe_Algorithm_RUN.ipynb : RUN Frank-Wolfe Algorithm(with SPA : Dijkstra ver.2)

Result

Link Travel Volume at UE

Link_num O D x_n Cost
1 1 2 4004.328254 6.00051422
2 1 3 6973.989 4.004731023
3 2 1 3980.266057 6.000501971
4 2 6 5739.247095 6.346453854
5 3 1 6998.051197 4.004796655
6 3 4 12937.87987 4.196132921
7 3 12 8756.519521 4.011758612
8 4 3 12999.86912 4.199918949
9 4 5 16434.39247 2.218844618
10 4 11 5391.820399 7.310006251
11 5 4 16555.1137 2.225346037
12 5 6 8458.701638 9.124469389
13 5 9 14538.12276 8.350384034
14 6 2 5715.184898 6.324015053
15 6 5 8483.750272 9.185439621
16 6 8 11735.13663 11.88075941
17 7 8 10638.79404 4.524461869
18 7 18 14733.4668 2.099800771
19 8 6 11736.12307 11.88408207
20 8 7 10747.89645 4.587964746
21 8 9 5760.221791 12.53872773
22 8 16 7827.593875 8.73326592
23 9 5 14633.79536 8.439451367
24 9 8 5726.378296 12.47958753
25 9 10 21386.32473 5.51030143
26 10 9 21548.15383 5.587149439
27 10 11 16475.4057 9.472067532
28 10 15 22185.71471 11.31180911
29 10 16 12017.50016 16.13351902
30 10 17 7535.465401 13.49834859
31 11 4 5433.088429 7.350575269
32 11 10 16476.64108 9.473073597
33 11 12 8357.286284 11.92166692
34 11 14 10269.31703 11.47115543
35 12 3 8718.592461 4.011556212
36 12 11 8562.386639 12.36843385
37 12 13 13574.23054 3.086374894
38 13 12 13841.40384 3.09157613
39 13 24 13076.92821 10.59722936
40 14 11 10206.72008 11.33536453
41 14 15 8542.05203 9.623416231
42 14 23 7747.349587 6.474746777
43 15 10 22174.39696 11.303684
44 15 14 8442.256618 9.463258119
45 15 19 20739.90418 4.520787372
46 15 22 20551.88685 6.437924555
47 16 8 7971.526224 8.943015724
48 16 10 12040.81333 16.20427083
49 16 17 11700.2239 4.502475927
50 16 18 13068.60855 3.330730565
51 17 10 7584.063702 13.60541726
52 17 16 11746.8099 4.522443483
53 17 19 11936.87864 5.061581438
54 18 7 14624.36438 2.097600052
55 18 16 13189.26807 3.33686588
56 18 20 17006.53316 4.528045022
57 19 15 20661.72733 4.50934409
58 19 17 12032.06294 5.110602018
59 19 20 9254.187016 7.4220289
60 20 18 16918.09026 4.522567081
61 20 19 9271.194473 7.43461855
62 20 21 6241.379074 8.282266702
63 20 22 7082.26767 7.433678897
64 21 20 6085.158251 8.169446912
65 21 22 10153.77612 3.88467613
66 21 24 12616.08859 8.001704292
67 22 15 20418.95053 6.393593156
68 22 20 7067.053053 7.423233735
69 22 21 10865.32456 4.158077171
70 22 23 11214.48373 9.030585813
71 23 14 7784.548052 6.498568545
72 23 22 11777.88123 9.548739453
73 23 24 7715.470367 3.154044254
74 24 13 13244.1015 10.76698331
75 24 21 11748.31933 7.337305741
76 24 23 8316.066335 3.340705953

Z(x)

Z(x)

Convergence Score

Convergence Score

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