40 | 13 | 4 | 3600.2 | 9528.6 | 5934.1 | 4340.7 | 8911.8 | 8911.8 | 37.7 | 33.4 | 6.5 | 51.3 | 0 | 8932
40 | 13 | 5 | 3600.2 | 11672.4 | 7244.4 | 5300.9 | 11636.1 | 11636.1 | 37.9 | 37.7 | 0.3 | 54.4 | 0 | 4768
40 | 20 | 1 | 3600.2 | 9473.3 | 6597.1 | 4913.9 | 9426.4 | 9426.4 | 30.4 | 30.0 | 0.5 | 47.9 | 0 | 18567
40 | 20 | 2 | 3600.1 | 6156.3 | 4538.2 | 3244.3 | 6156.3 | 6156.3 | 26.3 | 26.3 | 0.0 | 47.3 | 0 | 25300
40 | 20 | 3 | 3600.2 | 8245.3 | 5573.2 | 4057.7 | 8245.3 | 8245.3 | 32.4 | 32.4 | 0.0 | 50.8 | 0 | 22309
40 | 20 | 4 | 3600.4 | 8353.9 | 6369.4 | 4813.6 | 8315.2 | 8315.2 | 23.8 | 23.4 | 0.5 | 42.1 | 0 | 35245
40 | 20 | 5 | 3600.3 | 7336.8 | 5224.2 | 3912.2 | 6967.8 | 6967.8 | 28.8 | 25.0 | 5.0 | 43.9 | 1 | 1
50 | 12 | 1 | 3600.3 | 11783.0 | 6154.6 | 5373.6 | 11063.0 | 10584.5 | 47.8 | 44.4 | 10.2 | 51.4 | 0 | 100
50 | 12 | 2 | 3600.2 | 11186.2 | 5483.3 | 4343.6 | 10517.5 | 9871.9 | 51.0 | 47.9 | 11.8 | 58.7 | 0 | 316
50 | 12 | 3 | 3600.5 | 13175.2 | 6332.1 | 5432.0 | 10501.1 | 10501.1 | 51.9 | 39.7 | 20.3 | 48.3 | 0 | 136
50 | 12 | 4 | 3600.6 | 10388.0 | 4599.6 | 3856.7 | 8653.6 | 8653.6 | 55.7 | 46.9 | 16.7 | 55.4 | 0 | 240
50 | 12 | 5 | 3600.5 | 14439.5 | 5399.1 | 4455.9 | 9521.1 | 9186.5 | 62.6 | 43.3 | 36.4 | 53.2 | 0 | 244
50 | 16 | 1 | 3600.2 | 9181.5 | 5256.2 | 4584.7 | 8693.5 | 8693.5 | 42.8 | 39.5 | 5.3 | 47.3 | 0 | 382
50 | 16 | 2 | 3600.2 | 8638.9 | 3462.1 | 2923.1 | 5966.4 | 5966.4 | 59.9 | 42.0 | 30.9 | 51.0 | 0 | 1767
50 | 16 | 3 | 3600.3 | 13144.2 | 5453.2 | 4706.2 | 9239.6 | 9239.6 | 58.5 | 41.0 | 29.7 | 49.1 | 0 | 453
50 | 16 | 4 | 3600.2 | 7454.3 | 4331.1 | 3632.3 | 7453.7 | 7453.7 | 41.9 | 41.9 | 0.0 | 51.3 | 0 | 654
50 | 16 | 5 | 3600.2 | 7742.3 | 3703.0 | 3213.4 | 6924.8 | 6924.8 | 52.2 | 46.5 | 10.6 | 53.6 | 0 | 558
50 | 25 | 1 | 3600.2 | 5584.0 | 3415.8 | 3106.5 | 5561.8 | 5561.8 | 38.8 | 38.6 | 0.4 | 44.1 | 0 | 1952
50 | 25 | 2 | 3600.2 | 6954.6 | 4419.7 | 4073.8 | 6891.1 | 6891.1 | 36.5 | 35.9 | 0.9 | 40.9 | 0 | 3319
50 | 25 | 3 | 3600.2 | 5689.6 | 3749.4 | 3320.2 | 5582.7 | 5582.7 | 34.1 | 32.8 | 1.9 | 40.5 | 0 | 742
50 | 25 | 4 | 3600.3 | 5900.7 | 3562.3 | 3237.2 | 5900.7 | 5900.7 | 39.6 | 39.6 | 0.0 | 45.1 | 0 | 1026
50 | 25 | 5 | 3600.1 | 6779.4 | 3848.2 | 3536.6 | 6372.0 | 6372.0 | 43.2 | 39.6 | 6.0 | 44.5 | 0 | 1053
Table 74: Summary results table for model $F2_{x^{\ell}}^{mtz}$ $|V|$ | p |  $|$#$|$ | cpu |  g$\overline{\text{U}}$R |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ | gUL | nod
---|---|---|---|---|---|---|---|---
20 | 5 | 5 | 1895.0 | 53.4 | 0.0 | 0.0 | 0.0 | 184894
20 | 6 | 1 | 3081.3 | 52.7 | 15.1 | 0.0 | 15.1 | 122908
20 | 10 | 4 | 1182.0 | 44.5 | 0.7 | 0.0 | 0.7 | 123582
30 | 7 | 0 | 3600.2 | 54.5 | 32.3 | 1.4 | 33.2 | 16083
30 | 10 | 0 | 3600.3 | 48.2 | 25.3 | 0.9 | 26.0 | 25108
30 | 15 | 0 | 3600.1 | 44.6 | 13.1 | 0.0 | 13.1 | 98659
40 | 10 | 0 | 3600.2 | 55.3 | 38.4 | 4.6 | 41.1 | 4715
40 | 13 | 0 | 3600.2 | 49.1 | 32.6 | 3.8 | 35.2 | 7085
40 | 20 | 1 | 3600.2 | 46.4 | 27.4 | 1.2 | 28.3 | 20284
50 | 12 | 0 | 3600.4 | 53.4 | 44.4 | 19.1 | 53.8 | 207
50 | 16 | 0 | 3600.2 | 50.5 | 42.2 | 15.3 | 51.1 | 763
50 | 25 | 0 | 3600.2 | 43.0 | 37.3 | 1.8 | 38.4 | 1618

Table 75: Instances results table for model $F2_{x^{\ell}}^{flow}$ $|V|$ | p | ins | cpu | objU | objL | objR |  obj$\overline{\text{U}}$ |  obj$\overline{\text{L}}$ | gUL |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ |  g$\overline{\text{U}}$R | opt | nod
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
20 | 5 | 1 | 3600.2 | 24444.4 | 23619.6 | 11628.1 | 24444.4 | 24444.4 | 3.4 | 3.4 | 0.0 | 52.4 | 0 | 388862
20 | 5 | 2 | 3600.1 | 26585.3 | 24759.4 | 13320.5 | 26585.3 | 26585.3 | 6.9 | 6.9 | 0.0 | 49.9 | 0 | 748964
20 | 5 | 3 | 3600.1 | 26159.6 | 23558.9 | 11682.6 | 26159.6 | 26159.6 | 9.9 | 9.9 | 0.0 | 55.3 | 0 | 371536
20 | 5 | 4 | 969.8 | 16558.9 | 16558.9 | 6951.0 | 16558.9 | 16558.9 | 0.0 | 0.0 | 0.0 | 58.0 | 1 | 141186
20 | 5 | 5 | 3600.2 | 29165.6 | 25177.3 | 14127.3 | 29165.6 | 29165.6 | 13.7 | 13.7 | 0.0 | 51.6 | 0 | 225653
20 | 6 | 1 | 3600.0 | 22562.4 | 18888.0 | 10139.9 | 22562.4 | 22562.4 | 16.3 | 16.3 | 0.0 | 55.1 | 0 | 165923
20 | 6 | 2 | 3600.1 | 20183.5 | 19982.2 | 10220.2 | 20183.5 | 20183.5 | 1.0 | 1.0 | 0.0 | 49.4 | 0 | 335477
20 | 6 | 3 | 3600.1 | 25238.2 | 21419.5 | 12124.6 | 25238.2 | 25238.2 | 15.1 | 15.1 | 0.0 | 52.0 | 0 | 196421
20 | 6 | 4 | 3600.1 | 20161.1 | 18279.0 | 9580.3 | 20161.1 | 20161.1 | 9.3 | 9.3 | 0.0 | 52.5 | 0 | 225022
20 | 6 | 5 | 3600.1 | 27296.4 | 21800.5 | 12384.4 | 27296.4 | 27296.4 | 20.1 | 20.1 | 0.0 | 54.6 | 0 | 163036
20 | 10 | 1 | 3384.3 | 15074.8 | 15074.8 | 8445.0 | 15074.8 | 15074.8 | 0.0 | 0.0 | 0.0 | 44.0 | 1 | 833011
20 | 10 | 2 | 3600.1 | 18393.0 | 14385.5 | 9917.5 | 18092.9 | 18092.9 | 21.8 | 20.5 | 1.6 | 45.2 | 0 | 348294
20 | 10 | 3 | 1981.2 | 14169.6 | 14169.6 | 7261.8 | 14169.6 | 14169.6 | 0.0 | 0.0 | 0.0 | 48.8 | 1 | 293849
20 | 10 | 4 | 2654.0 | 19027.0 | 19027.0 | 10680.8 | 19027.0 | 19027.0 | 0.0 | 0.0 | 0.0 | 43.9 | 1 | 653172
20 | 10 | 5 | 60.4 | 9742.5 | 9742.5 | 5785.7 | 9742.5 | 9742.5 | 0.0 | 0.0 | 0.0 | 40.6 | 1 | 9557
30 | 7 | 1 | 3600.1 | 15759.0 | 10812.2 | 7366.4 | 15759.0 | 15759.0 | 31.4 | 31.4 | 0.0 | 53.3 | 0 | 17111
30 | 7 | 2 | 3600.1 | 18192.6 | 11200.1 | 7335.1 | 17867.0 | 17867.0 | 38.4 | 37.3 | 1.8 | 59.0 | 0 | 12509
30 | 7 | 3 | 3600.1 | 15619.6 | 10576.1 | 7474.4 | 15619.6 | 15619.6 | 32.3 | 32.3 | 0.0 | 52.1 | 0 | 19543
30 | 7 | 4 | 3600.2 | 18356.9 | 12923.3 | 9136.9 | 18356.9 | 18356.9 | 29.6 | 29.6 | 0.0 | 50.2 | 0 | 21006
30 | 7 | 5 | 3601.1 | 15687.1 | 9883.4 | 6495.7 | 15460.6 | 15460.6 | 37.0 | 36.1 | 1.4 | 58.0 | 0 | 21129
30 | 10 | 1 | 3600.9 | 12598.8 | 9018.2 | 6404.5 | 12598.8 | 12598.8 | 28.4 | 28.4 | 0.0 | 49.2 | 0 | 31186
30 | 10 | 2 | 3600.3 | 9788.8 | 7148.7 | 5334.9 | 9620.6 | 9620.6 | 27.0 | 25.7 | 1.7 | 44.5 | 0 | 20870
30 | 10 | 3 | 3600.5 | 9334.3 | 7037.7 | 5107.6 | 9329.9 | 9329.9 | 24.6 | 24.6 | 0.0 | 45.3 | 0 | 20789
30 | 10 | 4 | 3600.1 | 15579.8 | 11004.8 | 7446.2 | 15224.5 | 15224.5 | 29.4 | 27.7 | 2.3 | 51.1 | 0 | 24320
30 | 10 | 5 | 3600.1 | 15060.9 | 10352.5 | 7183.9 | 14665.7 | 14665.7 | 31.3 | 29.4 | 2.6 | 51.0 | 0 | 27056
30 | 15 | 1 | 3600.1 | 10085.3 | 7536.9 | 4987.7 | 10085.3 | 10085.3 | 25.3 | 25.3 | 0.0 | 50.5 | 0 | 72506
30 | 15 | 2 | 3600.2 | 10658.1 | 8586.4 | 6108.2 | 10658.1 | 10658.1 | 19.4 | 19.4 | 0.0 | 42.7 | 0 | 83497
30 | 15 | 3 | 3600.2 | 8466.4 | 7613.4 | 4447.6 | 8466.4 | 8466.4 | 10.1 | 10.1 | 0.0 | 47.5 | 0 | 201941
30 | 15 | 4 | 3600.2 | 9980.5 | 8232.0 | 6027.4 | 9980.5 | 9980.5 | 17.5 | 17.5 | 0.0 | 39.6 | 0 | 121065
30 | 15 | 5 | 3600.2 | 9687.3 | 8948.5 | 5553.1 | 9687.3 | 9687.3 | 7.6 | 7.6 | 0.0 | 42.7 | 0 | 156793
40 | 10 | 1 | 3600.2 | 16413.8 | 8195.2 | 6302.4 | 14500.9 | 14500.9 | 50.1 | 43.5 | 11.7 | 56.5 | 0 | 4659
40 | 10 | 2 | 3600.2 | 12551.9 | 7094.4 | 5155.4 | 12213.5 | 12213.5 | 43.5 | 41.9 | 2.7 | 57.8 | 0 | 7051
40 | 10 | 3 | 3600.2 | 11101.8 | 7712.1 | 5381.9 | 11071.1 | 11071.1 | 30.5 | 30.3 | 0.3 | 51.4 | 0 | 13715
40 | 10 | 4 | 3600.3 | 9676.5 | 6210.5 | 4294.9 | 9502.0 | 9502.1 | 35.8 | 34.6 | 1.8 | 54.8 | 0 | 13074
40 | 10 | 5 | 3600.2 | 13047.0 | 6297.4 | 4805.2 | 10972.0 | 10972.1 | 51.7 | 42.6 | 15.9 | 56.2 | 0 | 4405
40 | 13 | 1 | 3600.2 | 9885.2 | 6866.7 | 5384.9 | 9885.2 | 9885.2 | 30.5 | 30.5 | 0.0 | 45.5 | 0 | 19684
40 | 13 | 2 | 3615.9 | 9010.9 | 6514.3 | 5015.9 | 9010.9 | 9010.9 | 27.7 | 27.7 | 0.0 | 44.3 | 0 | 17953
40 | 13 | 3 | 3600.2 | 11654.6 | 6711.0 | 5340.0 | 10645.3 | 10645.3 | 42.4 | 37.0 | 8.7 | 49.8 | 0 | 7251
40 | 13 | 4 | 3600.2 | 10119.1 | 5866.1 | 4340.7 | 8911.8 | 8911.8 | 42.0 | 34.2 | 11.9 | 51.3 | 0 | 12789
40 | 13 | 5 | 3600.3 | 11793.4 | 6730.8 | 5300.9 | 11636.1 | 11636.1 | 42.9 | 42.2 | 1.3 | 54.4 | 0 | 12655
40 | 20 | 1 | 3600.5 | 9459.2 | 6458.1 | 4913.9 | 9426.4 | 9426.4 | 31.7 | 31.5 | 0.3 | 47.9 | 0 | 36085
40 | 20 | 2 | 3600.5 | 6156.3 | 4582.3 | 3244.3 | 6156.3 | 6156.3 | 25.6 | 25.6 | 0.0 | 47.3 | 0 | 35807
40 | 20 | 3 | 3600.2 | 8245.3 | 5152.3 | 4057.7 | 8245.3 | 8245.3 | 37.5 | 37.5 | 0.0 | 50.8 | 0 | 22014
40 | 20 | 4 | 3600.2 | 8394.1 | 6078.2 | 4813.6 | 8315.2 | 8315.2 | 27.6 | 26.9 | 0.9 | 42.1 | 0 | 35781
40 | 20 | 5 | 3600.3 | 6967.8 | 5224.2 | 3912.2 | 6967.8 | 6967.8 | 25.0 | 25.0 | 0.0 | 43.9 | 0 | 37866
50 | 12 | 1 | 3600.2 | 15615.4 | 6089.2 | 5373.6 | 11063.0 | 10584.5 | 61.0 | 45.0 | 32.2 | 51.4 | 0 | 1363
50 | 12 | 2 | 3600.3 | 14920.5 | 5493.5 | 4343.6 | 10517.5 | 9871.9 | 63.2 | 47.8 | 33.8 | 58.7 | 0 | 231
50 | 12 | 3 | 3600.3 | 12731.7 | 6286.9 | 5432.0 | 10501.1 | 10501.1 | 50.6 | 40.1 | 17.5 | 48.3 | 0 | 189
50 | 12 | 4 | 3600.2 | 10388.0 | 4442.6 | 3856.7 | 8653.6 | 8653.6 | 57.2 | 48.7 | 16.7 | 55.4 | 0 | 4131
50 | 12 | 5 | 3600.2 | 14439.5 | 5282.0 | 4455.9 | 9521.1 | 9186.5 | 63.4 | 44.5 | 36.4 | 53.2 | 0 | 2971
50 | 16 | 1 | 3600.2 | 10073.6 | 5186.7 | 4584.7 | 8693.5 | 8693.5 | 48.5 | 40.3 | 13.7 | 47.3 | 0 | 5200
50 | 16 | 2 | 3600.6 | 6050.0 | 3436.7 | 2923.1 | 5966.4 | 5966.4 | 43.2 | 42.4 | 1.4 | 51.0 | 0 | 3690
50 | 16 | 3 | 3600.2 | 13466.4 | 5498.5 | 4706.2 | 9239.6 | 9239.6 | 59.2 | 40.5 | 31.4 | 49.1 | 0 | 372
50 | 16 | 4 | 3600.4 | 8663.4 | 4316.4 | 3632.3 | 7453.7 | 7453.7 | 50.2 | 42.1 | 14.0 | 51.3 | 0 | 3022
50 | 16 | 5 | 3600.2 | 7773.5 | 3460.2 | 3213.4 | 6924.8 | 6924.8 | 55.5 | 50.0 | 10.9 | 53.6 | 0 | 964
50 | 25 | 1 | 3600.3 | 5584.0 | 3350.6 | 3106.5 | 5561.8 | 5561.8 | 40.0 | 39.8 | 0.4 | 44.1 | 0 | 2997
50 | 25 | 2 | 3600.3 | 7123.2 | 4435.2 | 4073.8 | 6891.1 | 6891.1 | 37.7 | 35.6 | 3.3 | 40.9 | 0 | 1471
50 | 25 | 3 | 3600.3 | 5615.5 | 3567.7 | 3320.2 | 5582.7 | 5582.7 | 36.5 | 36.1 | 0.6 | 40.5 | 0 | 2072
50 | 25 | 4 | 3600.3 | 6037.0 | 3509.4 | 3237.2 | 5900.7 | 5900.7 | 41.9 | 40.5 | 2.3 | 45.1 | 0 | 2660
50 | 25 | 5 | 3600.3 | 6780.0 | 3807.8 | 3536.6 | 6372.0 | 6372.0 | 43.8 | 40.2 | 6.0 | 44.5 | 0 | 1654
Table 76: Summary results table for model $F2_{x^{\ell}}^{flow}$ $|V|$ | p |  $|$#$|$ | cpu |  g$\overline{\text{U}}$R |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ | gUL | nod
---|---|---|---|---|---|---|---|---
20 | 5 | 1 | 3074.1 | 53.4 | 6.8 | 0.0 | 6.8 | 375240
20 | 6 | 0 | 3600.1 | 52.7 | 12.4 | 0.0 | 12.4 | 217176
20 | 10 | 4 | 2336.0 | 44.5 | 4.1 | 0.3 | 4.4 | 427577
30 | 7 | 0 | 3600.3 | 54.5 | 33.3 | 0.6 | 33.7 | 18260
30 | 10 | 0 | 3600.4 | 48.2 | 27.2 | 1.3 | 28.1 | 24844
30 | 15 | 0 | 3600.2 | 44.6 | 16.0 | 0.0 | 16.0 | 127160
40 | 10 | 0 | 3600.2 | 55.3 | 38.6 | 6.5 | 42.3 | 8581
40 | 13 | 0 | 3603.4 | 49.1 | 34.3 | 4.4 | 37.1 | 14066
40 | 20 | 0 | 3600.3 | 46.4 | 29.3 | 0.2 | 29.5 | 33511
50 | 12 | 0 | 3600.2 | 53.4 | 45.2 | 27.3 | 59.1 | 1777
50 | 16 | 0 | 3600.3 | 50.5 | 43.1 | 14.3 | 51.3 | 2650
50 | 25 | 0 | 3600.3 | 43.0 | 38.4 | 2.5 | 40.0 | 2171

Table 77: Instances results table for model $F2_{x^{\ell}}^{km}$ $|V|$ | p | ins | cpu | objU | objL | objR |  obj$\overline{\text{U}}$ |  obj$\overline{\text{L}}$ | gUL |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ |  g$\overline{\text{U}}$R | opt | nod
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
20 | 5 | 1 | 3600.1 | 24444.4 | 23230.6 | 11628.1 | 24444.4 | 24444.4 | 5.0 | 5.0 | 0.0 | 52.4 | 0 | 103359
20 | 5 | 2 | 3600.1 | 26585.3 | 24252.9 | 13320.5 | 26585.3 | 26585.3 | 8.8 | 8.8 | 0.0 | 49.9 | 0 | 122382
20 | 5 | 3 | 3600.4 | 26488.5 | 21151.2 | 11682.6 | 26159.6 | 26159.6 | 20.1 | 19.1 | 1.2 | 55.3 | 0 | 35880
20 | 5 | 4 | 393.2 | 16558.9 | 16558.9 | 6951.0 | 16558.9 | 16558.9 | 0.0 | 0.0 | 0.0 | 58.0 | 1 | 24512
20 | 5 | 5 | 699.9 | 29165.6 | 29165.6 | 14127.3 | 29165.6 | 29165.6 | 0.0 | 0.0 | 0.0 | 51.6 | 1 | 35418
20 | 6 | 1 | 3600.1 | 22648.4 | 16797.3 | 10139.9 | 22562.4 | 22562.4 | 25.8 | 25.6 | 0.4 | 55.1 | 0 | 41035
20 | 6 | 2 | 1132.2 | 20183.5 | 20183.5 | 10220.2 | 20183.5 | 20183.5 | 0.0 | 0.0 | 0.0 | 49.4 | 1 | 59818
20 | 6 | 3 | 3600.2 | 25238.2 | 18911.5 | 12124.6 | 25238.2 | 25238.2 | 25.1 | 25.1 | 0.0 | 52.0 | 0 | 31710
20 | 6 | 4 | 3600.1 | 20851.2 | 16632.7 | 9580.3 | 20161.1 | 20161.1 | 20.2 | 17.5 | 3.3 | 52.5 | 0 | 64429
20 | 6 | 5 | 3600.1 | 27296.4 | 20066.5 | 12384.4 | 27296.4 | 27296.4 | 26.5 | 26.5 | 0.0 | 54.6 | 0 | 39050
20 | 10 | 1 | 3329.6 | 15074.8 | 15074.8 | 8445.0 | 15074.8 | 15074.8 | 0.0 | 0.0 | 0.0 | 44.0 | 1 | 163800
20 | 10 | 2 | 1645.7 | 18092.9 | 18092.9 | 9917.5 | 18092.9 | 18092.9 | 0.0 | 0.0 | 0.0 | 45.2 | 1 | 90096
20 | 10 | 3 | 3556.6 | 14169.6 | 14169.6 | 7261.8 | 14169.6 | 14169.6 | 0.0 | 0.0 | 0.0 | 48.8 | 1 | 221463
20 | 10 | 4 | 1748.1 | 19027.0 | 19027.0 | 10680.8 | 19027.0 | 19027.0 | 0.0 | 0.0 | 0.0 | 43.9 | 1 | 85371
20 | 10 | 5 | 107.8 | 9742.5 | 9742.5 | 5785.7 | 9742.5 | 9742.5 | 0.0 | 0.0 | 0.0 | 40.6 | 1 | 6983
30 | 7 | 1 | 3600.2 | 15759.0 | 10092.6 | 7366.4 | 15759.0 | 15759.0 | 36.0 | 36.0 | 0.0 | 53.3 | 0 | 2563
30 | 7 | 2 | 3600.2 | 18179.7 | 10836.7 | 7335.1 | 17867.0 | 17867.0 | 40.4 | 39.4 | 1.7 | 59.0 | 0 | 1923
30 | 7 | 3 | 3600.2 | 15874.4 | 10333.1 | 7474.4 | 15619.6 | 15619.6 | 34.9 | 33.8 | 1.6 | 52.1 | 0 | 5299
30 | 7 | 4 | 3600.3 | 27455.8 | 11488.3 | 9136.9 | 18356.9 | 18356.9 | 58.2 | 37.4 | 33.1 | 50.2 | 0 | 1312
30 | 7 | 5 | 3600.2 | 16216.7 | 9331.6 | 6495.7 | 15460.6 | 15460.6 | 42.5 | 39.6 | 4.7 | 58.0 | 0 | 2755
30 | 10 | 1 | 3604.9 | 12853.2 | 9401.4 | 6404.5 | 12598.8 | 12598.8 | 26.9 | 25.4 | 2.0 | 49.2 | 0 | 10264
30 | 10 | 2 | 3600.0 | 9788.8 | 7806.6 | 5334.9 | 9620.6 | 9620.6 | 20.2 | 18.9 | 1.7 | 44.5 | 0 | 12058
30 | 10 | 3 | 3600.3 | 10039.3 | 7523.9 | 5107.6 | 9329.9 | 9329.9 | 25.1 | 19.4 | 7.1 | 45.3 | 0 | 14506
30 | 10 | 4 | 3600.4 | 15411.0 | 10475.0 | 7446.2 | 15224.5 | 15224.5 | 32.0 | 31.2 | 1.2 | 51.1 | 0 | 5225
30 | 10 | 5 | 3600.4 | 14954.4 | 9922.9 | 7183.9 | 14665.7 | 14665.7 | 33.6 | 32.3 | 1.9 | 51.0 | 0 | 4023
30 | 15 | 1 | 3600.1 | 10255.2 | 8006.5 | 4987.7 | 10085.3 | 10085.3 | 21.9 | 20.6 | 1.7 | 50.5 | 0 | 20353
30 | 15 | 2 | 3600.1 | 10658.1 | 9297.2 | 6108.2 | 10658.1 | 10658.1 | 12.8 | 12.8 | 0.0 | 42.7 | 0 | 36879
30 | 15 | 3 | 3600.2 | 8466.4 | 6956.2 | 4447.6 | 8466.4 | 8466.4 | 17.8 | 17.8 | 0.0 | 47.5 | 0 | 55110
30 | 15 | 4 | 3600.2 | 9980.5 | 8606.9 | 6027.4 | 9980.5 | 9980.5 | 13.8 | 13.8 | 0.0 | 39.6 | 0 | 76026
30 | 15 | 5 | 2670.0 | 9687.3 | 9687.3 | 5553.1 | 9687.3 | 9687.3 | 0.0 | 0.0 | 0.0 | 42.7 | 1 | 28
40 | 10 | 1 | 3600.3 | 20653.8 | 7588.6 | 6302.4 | 14500.9 | 14500.9 | 63.3 | 47.7 | 29.8 | 56.5 | 0 | 97
40 | 10 | 2 | 3600.3 | 19247.3 | 6392.8 | 5155.4 | 12213.5 | 12213.5 | 66.8 | 47.7 | 36.5 | 57.8 | 0 | 510
40 | 10 | 3 | 3600.2 | 11614.6 | 6793.9 | 5381.9 | 11071.1 | 11071.1 | 41.5 | 38.6 | 4.7 | 51.4 | 0 | 1995
40 | 10 | 4 | 3600.1 | 9739.6 | 5718.4 | 4294.9 | 9502.0 | 9502.1 | 41.3 | 39.8 | 2.4 | 54.8 | 0 | 1849
40 | 10 | 5 | 3600.3 | 18154.2 | 6306.1 | 4805.2 | 10972.0 | 10972.1 | 65.3 | 42.5 | 39.6 | 56.2 | 0 | 759
40 | 13 | 1 | 3600.6 | 11933.5 | 6162.9 | 5384.9 | 9885.2 | 9885.2 | 48.4 | 37.7 | 17.2 | 45.5 | 0 | 1426
40 | 13 | 2 | 3600.2 | 9987.2 | 6163.5 | 5015.9 | 9010.9 | 9010.9 | 38.3 | 31.6 | 9.8 | 44.3 | 0 | 1948
40 | 13 | 3 | 3600.4 | 10690.9 | 6585.4 | 5340.0 | 10645.3 | 10645.3 | 38.4 | 38.1 | 0.4 | 49.8 | 0 | 805
40 | 13 | 4 | 3600.2 | 9153.1 | 5505.3 | 4340.7 | 8911.8 | 8911.8 | 39.9 | 38.2 | 2.6 | 51.3 | 0 | 1836
40 | 13 | 5 | 3600.3 | 12333.7 | 6914.7 | 5300.9 | 11636.1 | 11636.1 | 43.9 | 40.6 | 5.7 | 54.4 | 0 | 273
40 | 20 | 1 | 3600.2 | 9731.4 | 6233.0 | 4913.9 | 9426.4 | 9426.4 | 36.0 | 33.9 | 3.1 | 47.9 | 0 | 2401
40 | 20 | 2 | 3600.2 | 6156.3 | 4552.4 | 3244.3 | 6156.3 | 6156.3 | 26.0 | 26.0 | 0.0 | 47.3 | 0 | 2396
40 | 20 | 3 | 3600.2 | 8481.4 | 5170.5 | 4057.7 | 8245.3 | 8245.3 | 39.0 | 37.3 | 2.8 | 50.8 | 0 | 3076
40 | 20 | 4 | 3600.2 | 8337.0 | 6226.3 | 4813.6 | 8315.2 | 8315.2 | 25.3 | 25.1 | 0.3 | 42.1 | 0 | 2189
40 | 20 | 5 | 3600.2 | 7181.3 | 5267.1 | 3912.2 | 6967.8 | 6967.8 | 26.7 | 24.4 | 3.0 | 43.9 | 0 | 3249
50 | 12 | 1 | 3600.1 | 20642.3 | 6238.6 | 5373.6 | 11063.0 | 10584.5 | 69.8 | 43.6 | 48.7 | 51.4 | 0 | 2
50 | 12 | 2 | 3600.2 | 17671.4 | 5582.5 | 4343.6 | 10517.5 | 9871.9 | 68.4 | 46.9 | 44.1 | 58.7 | 0 | 17
50 | 12 | 3 | 3600.1 | 15185.5 | 6387.4 | 5432.0 | 10501.1 | 10501.1 | 57.9 | 39.2 | 30.9 | 48.3 | 0 | 1
50 | 12 | 4 | 3600.1 | 12010.5 | 4701.1 | 3856.7 | 8653.6 | 8653.6 | 60.9 | 45.7 | 28.0 | 55.4 | 0 | 1
50 | 12 | 5 | 3600.1 | 18969.0 | 5516.3 | 4455.9 | 9521.1 | 9186.5 | 70.9 | 42.1 | 51.6 | 53.2 | 0 | 16
50 | 16 | 1 | 3600.4 | 10838.5 | 5230.5 | 4584.7 | 8693.5 | 8693.5 | 51.7 | 39.8 | 19.8 | 47.3 | 0 | 102
50 | 16 | 2 | 3600.2 | 9094.0 | 3497.8 | 2923.1 | 5966.4 | 5966.4 | 61.5 | 41.4 | 34.4 | 51.0 | 0 | 20
50 | 16 | 3 | 3600.2 | 16956.6 | 5468.9 | 4706.2 | 9239.6 | 9239.6 | 67.8 | 40.8 | 45.5 | 49.1 | 0 | 39
50 | 16 | 4 | 3600.3 | 10188.7 | 4332.2 | 3632.3 | 7453.7 | 7453.7 | 57.5 | 41.9 | 26.8 | 51.3 | 0 | 15
50 | 16 | 5 | 3600.2 | 9974.8 | 3791.0 | 3213.4 | 6924.8 | 6924.8 | 62.0 | 45.2 | 30.6 | 53.6 | 0 | 4
50 | 25 | 1 | 3600.2 | 6334.1 | 3369.6 | 3106.5 | 5561.8 | 5561.8 | 46.8 | 39.4 | 12.2 | 44.1 | 0 | 222
50 | 25 | 2 | 3600.3 | 7060.9 | 4449.2 | 4073.8 | 6891.1 | 6891.1 | 37.0 | 35.4 | 2.4 | 40.9 | 0 | 1035
50 | 25 | 3 | 3600.2 | 5614.4 | 3690.2 | 3320.2 | 5582.7 | 5582.7 | 34.3 | 33.9 | 0.6 | 40.5 | 0 | 29
50 | 25 | 4 | 3600.2 | 7183.9 | 3711.3 | 3237.2 | 5900.7 | 5900.7 | 48.3 | 37.1 | 17.9 | 45.1 | 0 | 14
50 | 25 | 5 | 3600.4 | 8265.3 | 3821.9 | 3536.6 | 6372.0 | 6372.0 | 53.8 | 40.0 | 22.9 | 44.5 | 0 | 517
Table 78: Summary results table for model $F2_{x^{\ell}}^{km}$ $|V|$ | p |  $|$#$|$ | cpu |  g$\overline{\text{U}}$R |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ | gUL | nod
---|---|---|---|---|---|---|---|---
20 | 5 | 2 | 2378.7 | 53.4 | 6.6 | 0.2 | 6.8 | 64310
20 | 6 | 1 | 3106.5 | 52.7 | 18.9 | 0.7 | 19.5 | 47208
20 | 10 | 5 | 2077.6 | 44.5 | 0.0 | 0.0 | 0.0 | 113543
30 | 7 | 0 | 3600.2 | 54.5 | 37.2 | 8.2 | 42.4 | 2770
30 | 10 | 0 | 3601.2 | 48.2 | 25.4 | 2.8 | 27.6 | 9215
30 | 15 | 1 | 3414.1 | 44.6 | 13.0 | 0.3 | 13.3 | 37679
40 | 10 | 0 | 3600.2 | 55.3 | 43.3 | 22.6 | 55.6 | 1042
40 | 13 | 0 | 3600.3 | 49.1 | 37.2 | 7.1 | 41.8 | 1258
40 | 20 | 0 | 3600.2 | 46.4 | 29.3 | 1.8 | 30.6 | 2662
50 | 12 | 0 | 3600.1 | 53.4 | 43.5 | 40.7 | 65.6 | 7
50 | 16 | 0 | 3600.3 | 50.5 | 41.8 | 31.4 | 60.1 | 36
50 | 25 | 0 | 3600.3 | 43.0 | 37.2 | 11.2 | 44.0 | 363

Table 79: Instances results table for model $F2_{x^{\ell}}^{sub}$ $|V|$ | p | ins | cpu | objU | objL | objR |  obj$\overline{\text{U}}$ |  obj$\overline{\text{L}}$ | gUL |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ |  g$\overline{\text{U}}$R | opt | nod
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
20 | 5 | 1 | 3600.1 | 24523.7 | 22557.9 | 11628.1 | 24444.4 | 24444.4 | 8.0 | 7.7 | 0.3 | 52.4 | 0 | 842897
20 | 5 | 2 | 3600.1 | 26585.3 | 23226.9 | 13320.5 | 26585.3 | 26585.3 | 12.6 | 12.6 | 0.0 | 49.9 | 0 | 451134
20 | 5 | 3 | 3255.6 | 26159.6 | 26159.6 | 11682.6 | 26159.6 | 26159.6 | 0.0 | 0.0 | 0.0 | 55.3 | 1 | 552918
20 | 5 | 4 | 447.1 | 16558.9 | 16558.9 | 6951.0 | 16558.9 | 16558.9 | 0.0 | 0.0 | 0.0 | 58.0 | 1 | 101941
20 | 5 | 5 | 3600.2 | 29165.6 | 26985.7 | 14127.3 | 29165.6 | 29165.6 | 7.5 | 7.5 | 0.0 | 51.6 | 0 | 827075
20 | 6 | 1 | 3600.0 | 23076.7 | 18507.7 | 10139.9 | 22562.4 | 22562.4 | 19.8 | 18.0 | 2.2 | 55.1 | 0 | 353637
20 | 6 | 2 | 785.7 | 20183.5 | 20183.5 | 10220.2 | 20183.5 | 20183.5 | 0.0 | 0.0 | 0.0 | 49.4 | 1 | 72061
20 | 6 | 3 | 3600.0 | 25883.3 | 19592.9 | 12124.6 | 25238.2 | 25238.2 | 24.3 | 22.4 | 2.5 | 52.0 | 0 | 355562
20 | 6 | 4 | 3600.0 | 21125.1 | 16320.6 | 9580.3 | 20161.1 | 20161.1 | 22.7 | 19.0 | 4.6 | 52.5 | 0 | 516484
20 | 6 | 5 | 3600.1 | 27308.9 | 21679.6 | 12384.4 | 27296.4 | 27296.4 | 20.6 | 20.6 | 0.0 | 54.6 | 0 | 306450
20 | 10 | 1 | 3600.1 | 15319.9 | 12664.8 | 8445.0 | 15074.8 | 15074.8 | 17.3 | 16.0 | 1.6 | 44.0 | 0 | 650827
20 | 10 | 2 | 3600.1 | 19592.2 | 13750.0 | 9917.5 | 18092.9 | 18092.9 | 29.8 | 24.0 | 7.7 | 45.2 | 0 | 647756
20 | 10 | 3 | 3600.0 | 14832.1 | 12390.0 | 7261.8 | 14169.6 | 14169.6 | 16.5 | 12.6 | 4.5 | 48.8 | 0 | 773252
20 | 10 | 4 | 3600.1 | 19370.0 | 17368.0 | 10680.8 | 19027.0 | 19027.0 | 10.3 | 8.7 | 1.8 | 43.9 | 0 | 580317
20 | 10 | 5 | 143.6 | 9742.5 | 9742.5 | 5785.7 | 9742.5 | 9742.5 | 0.0 | 0.0 | 0.0 | 40.6 | 1 | 15043
30 | 7 | 1 | 3600.1 | 24992.2 | 10686.2 | 7366.4 | 15759.0 | 15759.0 | 57.2 | 32.2 | 36.9 | 53.3 | 0 | 42182
30 | 7 | 2 | 3600.1 | 29799.6 | 11757.9 | 7335.1 | 17867.0 | 17867.0 | 60.5 | 34.2 | 40.0 | 59.0 | 0 | 14970
30 | 7 | 3 | 3600.0 | 20960.9 | 10792.6 | 7474.4 | 15619.6 | 15619.6 | 48.5 | 30.9 | 25.5 | 52.1 | 0 | 20961
30 | 7 | 4 | 3600.3 | 32341.1 | 12267.8 | 9136.9 | 18356.9 | 18356.9 | 62.1 | 33.2 | 43.2 | 50.2 | 0 | 30626
30 | 7 | 5 | 3600.5 | 24868.9 | 9593.4 | 6495.7 | 15460.6 | 15460.6 | 61.4 | 38.0 | 37.8 | 58.0 | 0 | 22543
30 | 10 | 1 | 3600.2 | 20526.1 | 8900.6 | 6404.5 | 12598.8 | 12598.8 | 56.6 | 29.4 | 38.6 | 49.2 | 0 | 29007
30 | 10 | 2 | 3600.8 | 21194.1 | 6898.7 | 5334.9 | 9620.6 | 9620.6 | 67.4 | 28.3 | 54.6 | 44.5 | 0 | 37405
30 | 10 | 3 | 3600.1 | 12977.5 | 7147.8 | 5107.6 | 9329.9 | 9329.9 | 44.9 | 23.4 | 28.1 | 45.3 | 0 | 40545
30 | 10 | 4 | 3600.1 | 42631.3 | 11970.9 | 7446.2 | 15224.5 | 15224.5 | 71.9 | 21.4 | 64.3 | 51.1 | 0 | 35769
30 | 10 | 5 | 3600.1 | 16520.9 | 9769.9 | 7183.9 | 14665.7 | 14665.7 | 40.9 | 33.4 | 11.2 | 51.0 | 0 | 84240
30 | 15 | 1 | 3600.2 | 13094.6 | 6424.1 | 4987.7 | 10085.3 | 10085.3 | 50.9 | 36.3 | 23.0 | 50.5 | 0 | 125131
30 | 15 | 2 | 3600.4 | 11268.8 | 8145.4 | 6108.2 | 10658.1 | 10658.1 | 27.7 | 23.6 | 5.4 | 42.7 | 0 | 181621
30 | 15 | 3 | 3600.2 | 10289.7 | 5989.5 | 4447.6 | 8466.4 | 8466.4 | 41.8 | 29.3 | 17.7 | 47.5 | 0 | 135377
30 | 15 | 4 | 3600.1 | 11512.6 | 7807.1 | 6027.4 | 9980.5 | 9980.5 | 32.2 | 21.8 | 13.3 | 39.6 | 0 | 171558
30 | 15 | 5 | 3600.2 | 10692.8 | 7693.0 | 5553.1 | 9687.3 | 9687.3 | 28.0 | 20.6 | 9.4 | 42.7 | 0 | 217480
40 | 10 | 1 | 3600.2 | 35693.0 | 7808.9 | 6302.4 | 14500.9 | 14500.9 | 78.1 | 46.1 | 59.4 | 56.5 | 0 | 10045
40 | 10 | 2 | 3600.2 | 60140.7 | 6717.6 | 5155.4 | 12213.5 | 12213.5 | 88.8 | 45.0 | 79.7 | 57.8 | 0 | 5660
40 | 10 | 3 | 3600.1 | 56043.2 | 7094.9 | 5381.9 | 11071.1 | 11071.1 | 87.3 | 35.9 | 80.2 | 51.4 | 0 | 5371
40 | 10 | 4 | 3600.3 | 62942.2 | 5869.1 | 4294.9 | 9502.0 | 9502.1 | 90.7 | 38.2 | 84.9 | 54.8 | 0 | 6360
40 | 10 | 5 | 3600.2 | 53025.1 | 5914.0 | 4805.2 | 10972.0 | 10972.1 | 88.8 | 46.1 | 79.3 | 56.2 | 0 | 9290
40 | 13 | 1 | 3600.2 | 68975.8 | 6357.6 | 5384.9 | 9885.2 | 9885.2 | 90.8 | 35.7 | 85.7 | 45.5 | 0 | 9353
40 | 13 | 2 | 3600.1 | 59359.5 | 6047.8 | 5015.9 | 9010.9 | 9010.9 | 89.8 | 32.9 | 84.8 | 44.3 | 0 | 6737
40 | 13 | 3 | 3600.3 | 61950.3 | 6594.5 | 5340.0 | 10645.3 | 10645.3 | 89.4 | 38.0 | 82.8 | 49.8 | 0 | 5723
40 | 13 | 4 | 3600.4 | 59327.0 | 5619.3 | 4340.7 | 8911.8 | 8911.8 | 90.5 | 36.9 | 85.0 | 51.3 | 0 | 19630
40 | 13 | 5 | 3600.2 | 57920.4 | 6406.8 | 5300.9 | 11636.1 | 11636.1 | 88.9 | 44.9 | 79.9 | 54.4 | 0 | 6768
40 | 20 | 1 | 3600.4 | 17322.8 | 5438.5 | 4913.9 | 9426.4 | 9426.4 | 68.6 | 42.3 | 45.6 | 47.9 | 0 | 23638
40 | 20 | 2 | 3600.3 | 15921.4 | 4021.9 | 3244.3 | 6156.3 | 6156.3 | 74.7 | 34.7 | 61.3 | 47.3 | 0 | 11831
40 | 20 | 3 | 3600.3 | 29067.0 | 4552.0 | 4057.7 | 8245.3 | 8245.3 | 84.3 | 44.8 | 71.6 | 50.8 | 0 | 22405
40 | 20 | 4 | 3600.3 | 27307.3 | 5459.4 | 4813.6 | 8315.2 | 8315.2 | 80.0 | 34.3 | 69.6 | 42.1 | 0 | 28703
40 | 20 | 5 | 3600.2 | 19952.0 | 4727.1 | 3912.2 | 6967.8 | 6967.8 | 76.3 | 32.2 | 65.1 | 43.9 | 0 | 33750
50 | 12 | 1 | 3600.9 | 57941.3 | 6245.5 | 5373.6 | 11063.0 | 10584.5 | 89.2 | 43.5 | 81.7 | 51.4 | 0 | 2950
50 | 12 | 2 | 3600.2 | 48435.9 | 5434.9 | 4343.6 | 10517.5 | 9871.9 | 88.8 | 48.3 | 79.6 | 58.7 | 0 | 3998
50 | 12 | 3 | 3600.3 | 45551.4 | 6373.0 | 5432.0 | 10501.1 | 10501.1 | 86.0 | 39.3 | 77.0 | 48.3 | 0 | 2666
50 | 12 | 4 | 3600.1 | 55258.1 | 4624.8 | 3856.7 | 8653.6 | 8653.6 | 91.6 | 46.6 | 84.3 | 55.4 | 0 | 2837
50 | 12 | 5 | 3601.9 | 59239.3 | 5306.9 | 4455.9 | 9521.1 | 9186.5 | 91.0 | 44.3 | 84.5 | 53.2 | 0 | 3933
50 | 16 | 1 | 3601.0 | 54053.5 | 5374.9 | 4584.7 | 8693.5 | 8693.5 | 90.1 | 38.2 | 83.9 | 47.3 | 0 | 3769
50 | 16 | 2 | 3600.2 | 55947.1 | 3483.0 | 2923.1 | 5966.4 | 5966.4 | 93.8 | 41.6 | 89.3 | 51.0 | 0 | 2424
50 | 16 | 3 | 3600.1 | 60344.6 | 5434.5 | 4706.2 | 9239.6 | 9239.6 | 91.0 | 41.2 | 84.7 | 49.1 | 0 | 4925
50 | 16 | 4 | 3601.5 | 48554.0 | 4375.0 | 3632.3 | 7453.7 | 7453.7 | 91.0 | 41.3 | 84.7 | 51.3 | 0 | 2735
50 | 16 | 5 | 3600.6 | 47985.6 | 3488.1 | 3213.4 | 6924.8 | 6924.8 | 92.7 | 49.6 | 85.6 | 53.6 | 0 | 3315
50 | 25 | 1 | 3600.7 | 51323.3 | 3459.3 | 3106.5 | 5561.8 | 5561.8 | 93.3 | 37.8 | 89.2 | 44.1 | 0 | 5624
50 | 25 | 2 | 3600.2 | 62091.2 | 4405.0 | 4073.8 | 6891.1 | 6891.1 | 92.9 | 36.1 | 88.9 | 40.9 | 0 | 5884
50 | 25 | 3 | 3600.3 | 48559.7 | 3756.3 | 3320.2 | 5582.7 | 5582.7 | 92.3 | 32.7 | 88.5 | 40.5 | 0 | 3689
50 | 25 | 4 | 3600.2 | 64320.5 | 3573.7 | 3237.2 | 5900.7 | 5900.7 | 94.4 | 39.4 | 90.8 | 45.1 | 0 | 5254
50 | 25 | 5 | 3600.3 | 63169.9 | 3970.1 | 3536.6 | 6372.0 | 6372.0 | 93.7 | 37.7 | 89.9 | 44.5 | 0 | 5548
Table 80: Summary results table for model $F2_{x^{\ell}}^{sub}$ $|V|$ | p |  $|$#$|$ | cpu |  g$\overline{\text{U}}$R |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ | gUL | nod
---|---|---|---|---|---|---|---|---
20 | 5 | 2 | 2900.6 | 53.4 | 5.6 | 0.1 | 5.6 | 555193
20 | 6 | 1 | 3037.2 | 52.7 | 16.0 | 1.9 | 17.5 | 320839
20 | 10 | 1 | 2908.8 | 44.5 | 12.3 | 3.1 | 14.8 | 533439
30 | 7 | 0 | 3600.2 | 54.5 | 33.7 | 36.7 | 57.9 | 26256
30 | 10 | 0 | 3600.3 | 48.2 | 27.2 | 39.4 | 56.3 | 45393
30 | 15 | 0 | 3600.2 | 44.6 | 26.3 | 13.8 | 36.1 | 166233
40 | 10 | 0 | 3600.2 | 55.3 | 42.3 | 76.7 | 86.7 | 7345
40 | 13 | 0 | 3600.2 | 49.1 | 37.7 | 83.6 | 89.9 | 9642
40 | 20 | 0 | 3600.3 | 46.4 | 37.7 | 62.6 | 76.8 | 24065
50 | 12 | 0 | 3600.7 | 53.4 | 44.4 | 81.4 | 89.3 | 3277
50 | 16 | 0 | 3600.7 | 50.5 | 42.4 | 85.6 | 91.7 | 3434
50 | 25 | 0 | 3600.3 | 43.0 | 36.7 | 89.5 | 93.3 | 5200

Table 81: Instances results table for model OMT Benders modern Kruskal $|V|$ | p | ins | cpu | objU | objL | objR |  obj$\overline{\text{U}}$ |  obj$\overline{\text{L}}$ | gUL |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ |  g$\overline{\text{U}}$R | opt | nod
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
20 | 5 | 1 | 3600.1 | 24996.1 | 16182.1 | 5459.2 | 24444.4 | 24444.4 | 35.3 | 33.8 | 2.2 | 77.7 | 0 | 1360306
20 | 5 | 2 | 3600.1 | 27981.6 | 13184.8 | 6947.0 | 26585.3 | 26585.3 | 52.9 | 50.4 | 5.0 | 73.9 | 0 | 1007270
20 | 5 | 3 | 3600.1 | 28294.2 | 14977.0 | 5859.3 | 26159.6 | 26159.6 | 47.1 | 42.8 | 7.5 | 77.6 | 0 | 959544
20 | 5 | 4 | 3600.1 | 17892.4 | 9863.0 | 3801.4 | 16558.9 | 16558.9 | 44.9 | 40.4 | 7.4 | 77.0 | 0 | 1623952
20 | 5 | 5 | 3600.1 | 31683.4 | 15903.0 | 7835.4 | 29165.6 | 29165.6 | 49.8 | 45.5 | 8.0 | 73.1 | 0 | 1623184
20 | 6 | 1 | 3600.0 | 25478.5 | 10767.0 | 4648.1 | 22562.4 | 22562.4 | 57.7 | 52.3 | 11.4 | 79.4 | 0 | 564187
20 | 6 | 2 | 3600.1 | 22691.7 | 16423.0 | 6014.2 | 20183.5 | 20183.5 | 27.6 | 18.6 | 11.1 | 70.2 | 0 | 730717
20 | 6 | 3 | 3600.2 | 31048.3 | 10386.4 | 5204.0 | 25238.2 | 25238.2 | 66.6 | 58.9 | 18.7 | 79.4 | 0 | 712630
20 | 6 | 4 | 3600.1 | 24290.7 | 8848.8 | 4394.6 | 20161.1 | 20161.1 | 63.6 | 56.1 | 17.0 | 78.2 | 0 | 1180410
20 | 6 | 5 | 3600.0 | 30583.4 | 11319.3 | 5184.1 | 27296.4 | 27296.4 | 63.0 | 58.5 | 10.8 | 81.0 | 0 | 566821
20 | 10 | 1 | 3600.3 | 16515.2 | 7010.6 | 2419.6 | 15074.8 | 15074.8 | 57.5 | 53.5 | 8.7 | 84.0 | 0 | 272366
20 | 10 | 2 | 3600.2 | 18092.9 | 8868.5 | 2372.4 | 18092.9 | 18092.9 | 51.0 | 51.0 | 0.0 | 86.9 | 0 | 418981
20 | 10 | 3 | 3600.1 | 16441.3 | 4450.1 | 1828.8 | 14169.6 | 14169.6 | 72.9 | 68.6 | 13.8 | 87.1 | 0 | 396395
20 | 10 | 4 | 3600.1 | 20029.0 | 6025.6 | 2316.8 | 19027.0 | 19027.0 | 69.9 | 68.3 | 5.0 | 87.8 | 0 | 303864
20 | 10 | 5 | 3600.4 | 10519.6 | 2977.7 | 806.2 | 9742.5 | 9742.5 | 71.7 | 69.4 | 7.4 | 91.7 | 0 | 339872
30 | 7 | 1 | 3600.1 | 26587.5 | 5120.3 | 3461.6 | 15759.0 | 15759.0 | 80.7 | 67.5 | 40.7 | 78.0 | 0 | 96075
30 | 7 | 2 | 3600.1 | 42056.1 | 5897.9 | 4139.3 | 17867.0 | 17867.0 | 86.0 | 67.0 | 57.5 | 76.8 | 0 | 110973
30 | 7 | 3 | 3600.4 | 19362.7 | 5597.2 | 4202.6 | 15619.6 | 15619.6 | 71.1 | 64.2 | 19.3 | 73.1 | 0 | 148751
30 | 7 | 4 | 3600.1 | 30078.9 | 6463.7 | 4464.4 | 18356.9 | 18356.9 | 78.5 | 64.8 | 39.0 | 75.7 | 0 | 113766
30 | 7 | 5 | 3600.1 | 24946.9 | 5183.6 | 3479.7 | 15460.6 | 15460.6 | 79.2 | 66.5 | 38.0 | 77.5 | 0 | 94087
30 | 10 | 1 | 3600.4 | 19821.1 | 4047.4 | 2800.6 | 12598.8 | 12598.8 | 79.6 | 67.9 | 36.4 | 77.8 | 0 | 161044
30 | 10 | 2 | 3600.1 | 19950.2 | 2764.4 | 1911.3 | 9620.6 | 9620.6 | 86.1 | 71.3 | 51.8 | 80.1 | 0 | 94000
30 | 10 | 3 | 3600.3 | 20033.1 | 3525.4 | 1887.8 | 9329.9 | 9329.9 | 82.4 | 62.2 | 53.4 | 79.8 | 0 | 239316
30 | 10 | 4 | 3600.4 | 25477.0 | 4952.4 | 3146.7 | 15224.5 | 15224.5 | 80.6 | 67.5 | 40.2 | 79.3 | 0 | 77779
30 | 10 | 5 | 3600.1 | 22623.6 | 4323.1 | 2907.3 | 14665.7 | 14665.7 | 80.9 | 70.5 | 35.2 | 80.2 | 0 | 129159
30 | 15 | 1 | 3600.4 | 14409.4 | 1825.2 | 912.7 | 10085.3 | 10085.3 | 87.3 | 81.9 | 30.0 | 91.0 | 0 | 366363
30 | 15 | 2 | 3600.2 | 12309.5 | 1742.9 | 1018.6 | 10658.1 | 10658.1 | 85.8 | 83.7 | 13.4 | 90.4 | 0 | 326819
30 | 15 | 3 | 3600.2 | 10595.7 | 2432.2 | 709.7 | 8466.4 | 8466.4 | 77.0 | 71.3 | 20.1 | 91.6 | 0 | 581290
30 | 15 | 4 | 3600.2 | 13025.6 | 1838.7 | 1096.1 | 9980.5 | 9980.5 | 85.9 | 81.6 | 23.4 | 89.0 | 0 | 362971
30 | 15 | 5 | 3600.2 | 13613.6 | 2158.2 | 1192.2 | 9687.3 | 9687.3 | 84.2 | 77.7 | 28.8 | 87.7 | 0 | 634002
40 | 10 | 1 | 3600.2 | 23446.6 | 4193.7 | 3838.9 | 14500.9 | 14500.9 | 82.1 | 71.1 | 38.1 | 73.5 | 0 | 35406
40 | 10 | 2 | 3600.3 | 19671.4 | 3388.7 | 2783.6 | 12213.5 | 12213.5 | 82.8 | 72.2 | 37.9 | 77.2 | 0 | 24936
40 | 10 | 3 | 3600.2 | 16026.1 | 3596.5 | 3126.0 | 11071.1 | 11071.1 | 77.6 | 67.5 | 30.9 | 71.8 | 0 | 13349
40 | 10 | 4 | 3600.2 | 22805.1 | 3135.8 | 2756.6 | 9502.0 | 9502.1 | 86.2 | 67.0 | 58.3 | 71.0 | 0 | 34038
40 | 10 | 5 | 3600.2 | 24665.8 | 2576.6 | 2338.7 | 10972.0 | 10972.1 | 89.6 | 76.5 | 55.5 | 78.7 | 0 | 26960
40 | 13 | 1 | 3600.2 | 22308.9 | 2477.1 | 2196.2 | 9885.2 | 9885.2 | 88.9 | 74.9 | 55.7 | 77.8 | 0 | 14311
40 | 13 | 2 | 3600.3 | 17862.6 | 2669.4 | 2241.2 | 9010.9 | 9010.9 | 85.1 | 70.4 | 49.5 | 75.1 | 0 | 22046
40 | 13 | 3 | 3600.2 | 18740.5 | 2280.6 | 1979.4 | 10645.3 | 10645.3 | 87.8 | 78.6 | 43.2 | 81.4 | 0 | 13643
40 | 13 | 4 | 3600.1 | 18720.8 | 2182.6 | 1734.5 | 8911.8 | 8911.8 | 88.3 | 75.5 | 52.4 | 80.5 | 0 | 17962
40 | 13 | 5 | 3600.2 | 21386.1 | 3372.6 | 2568.0 | 11636.1 | 11636.1 | 84.2 | 71.0 | 45.6 | 77.9 | 0 | 14648
40 | 20 | 1 | 3600.2 | 13092.8 | 1754.1 | 1119.3 | 9426.4 | 9426.4 | 86.6 | 81.4 | 28.0 | 88.1 | 0 | 70126
40 | 20 | 2 | 3600.2 | 9717.6 | 1016.4 | 640.6 | 6156.3 | 6156.3 | 89.5 | 83.5 | 36.6 | 89.6 | 0 | 102720
40 | 20 | 3 | 3600.5 | 12031.8 | 1954.5 | 878.1 | 8245.3 | 8245.3 | 83.8 | 76.3 | 31.5 | 89.3 | 0 | 134024
40 | 20 | 4 | 3600.5 | 9288.7 | 2646.6 | 1002.8 | 8315.2 | 8315.2 | 71.5 | 68.2 | 10.5 | 87.9 | 0 | 260735
40 | 20 | 5 | 3601.1 | 12035.9 | 1124.7 | 813.2 | 6967.8 | 6967.8 | 90.7 | 83.9 | 42.1 | 88.3 | 0 | 53697
50 | 12 | 1 | 3601.5 | 22867.2 | 3075.8 | 2881.5 | 11063.0 | 10584.5 | 86.6 | 72.2 | 53.7 | 74.0 | 0 | 5128
50 | 12 | 2 | 3600.1 | 17671.4 | 2478.4 | 2275.6 | 10517.5 | 9871.9 | 86.0 | 76.4 | 44.1 | 78.4 | 0 | 2703
50 | 12 | 3 | 3600.3 | 15553.4 | 2813.8 | 2652.7 | 10501.1 | 10501.1 | 81.9 | 73.2 | 32.5 | 74.7 | 0 | 5149
50 | 12 | 4 | 3600.1 | 12573.3 | 2342.9 | 2159.6 | 8653.6 | 8653.6 | 81.4 | 72.9 | 31.2 | 75.0 | 0 | 5369
50 | 12 | 5 | 3600.8 | 16531.4 | 2284.1 | 2067.8 | 9521.1 | 9186.5 | 86.2 | 76.0 | 44.4 | 78.3 | 0 | 5362
50 | 16 | 1 | 3600.2 | 16633.5 | 2173.6 | 2058.3 | 8693.5 | 8693.5 | 86.9 | 75.0 | 47.7 | 76.3 | 0 | 5353
50 | 16 | 2 | 3600.2 | 11776.8 | 1228.8 | 1104.4 | 5966.4 | 5966.4 | 89.6 | 79.4 | 49.3 | 81.5 | 0 | 5629
50 | 16 | 3 | 3600.2 | 19662.9 | 2108.9 | 1845.8 | 9239.6 | 9239.6 | 89.3 | 77.2 | 53.0 | 80.0 | 0 | 5606
50 | 16 | 4 | 3600.1 | 12907.2 | 1883.3 | 1663.3 | 7453.7 | 7453.7 | 85.4 | 74.7 | 42.2 | 77.7 | 0 | 6296
50 | 16 | 5 | 3600.2 | 14471.3 | 1663.2 | 1504.9 | 6924.8 | 6924.8 | 88.5 | 76.0 | 52.1 | 78.3 | 0 | 5882
50 | 25 | 1 | 3600.2 | 8443.0 | 647.8 | 579.1 | 5561.8 | 5561.8 | 92.3 | 88.3 | 34.1 | 89.6 | 0 | 11499
50 | 25 | 2 | 3600.2 | 11549.1 | 970.0 | 884.8 | 6891.1 | 6891.1 | 91.6 | 85.9 | 40.3 | 87.2 | 0 | 18602
50 | 25 | 3 | 3600.5 | 9091.8 | 857.9 | 741.7 | 5582.7 | 5582.7 | 90.6 | 84.6 | 38.6 | 86.7 | 0 | 5862
50 | 25 | 4 | 3600.4 | 8648.7 | 780.7 | 636.9 | 5900.7 | 5900.7 | 91.0 | 86.8 | 31.8 | 89.2 | 0 | 5819
50 | 25 | 5 | 3600.4 | 9614.2 | 880.0 | 686.8 | 6372.0 | 6372.0 | 90.8 | 86.2 | 33.7 | 89.2 | 0 | 10480
Table 82: Summary results table for model OMT Benders modern Kruskal $|V|$ | p |  $|$#$|$ | cpu |  g$\overline{\text{U}}$R |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ | gUL | nod
---|---|---|---|---|---|---|---|---
20 | 5 | 0 | 3600.1 | 75.9 | 42.6 | 6.0 | 46.0 | 1314851
20 | 6 | 0 | 3600.1 | 77.6 | 48.9 | 13.8 | 55.7 | 750953
20 | 10 | 0 | 3600.2 | 87.5 | 62.2 | 7.0 | 64.6 | 346296
30 | 7 | 0 | 3600.2 | 76.2 | 66.0 | 38.9 | 79.1 | 112730
30 | 10 | 0 | 3600.3 | 79.4 | 67.9 | 43.4 | 81.9 | 140260
30 | 15 | 0 | 3600.2 | 89.9 | 79.2 | 23.1 | 84.0 | 454289
40 | 10 | 0 | 3600.2 | 74.4 | 70.9 | 44.1 | 83.7 | 26938
40 | 13 | 0 | 3600.2 | 78.5 | 74.1 | 49.3 | 86.9 | 16522
40 | 20 | 0 | 3600.5 | 88.6 | 78.7 | 29.7 | 84.4 | 124260
50 | 12 | 0 | 3600.6 | 76.1 | 74.1 | 41.2 | 84.4 | 4742
50 | 16 | 0 | 3600.2 | 78.8 | 76.5 | 48.9 | 87.9 | 5753
50 | 25 | 0 | 3600.3 | 88.4 | 86.4 | 35.7 | 91.3 | 10452

Table 83: Instances results table for model OMT Benders modern $km$ $|V|$ | p | ins | cpu | objU | objL | objR |  obj$\overline{\text{U}}$ |  obj$\overline{\text{L}}$ | gUL |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ |  g$\overline{\text{U}}$R | opt | nod
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
20 | 5 | 1 | 879.6 | 24444.4 | 24444.4 | 5459.2 | 24444.4 | 24444.4 | 0.0 | 0.0 | 0.0 | 77.7 | 1 | 374298
20 | 5 | 2 | 1761.9 | 26585.3 | 26585.3 | 6947.0 | 26585.3 | 26585.3 | 0.0 | 0.0 | 0.0 | 73.9 | 1 | 306014
20 | 5 | 3 | 1433.9 | 26159.6 | 26159.6 | 5859.3 | 26159.6 | 26159.6 | 0.0 | 0.0 | 0.0 | 77.6 | 1 | 522739
20 | 5 | 4 | 3600.1 | 17949.8 | 11298.5 | 3801.4 | 16558.9 | 16558.9 | 37.1 | 31.8 | 7.8 | 77.0 | 0 | 1183169
20 | 5 | 5 | 3600.1 | 29165.6 | 27884.8 | 7835.4 | 29165.6 | 29165.6 | 4.4 | 4.4 | 0.0 | 73.1 | 0 | 2181222
20 | 6 | 1 | 3600.0 | 24198.5 | 11388.4 | 4648.1 | 22562.4 | 22562.4 | 52.9 | 49.5 | 6.8 | 79.4 | 0 | 669949
20 | 6 | 2 | 1868.3 | 20183.5 | 20183.5 | 6014.2 | 20183.5 | 20183.5 | 0.0 | 0.0 | 0.0 | 70.2 | 1 | 470660
20 | 6 | 3 | 1728.8 | 25238.2 | 25238.2 | 5204.0 | 25238.2 | 25238.2 | 0.0 | 0.0 | 0.0 | 79.4 | 1 | 347013
20 | 6 | 4 | 2483.1 | 20161.1 | 20161.1 | 4394.6 | 20161.1 | 20161.1 | 0.0 | 0.0 | 0.0 | 78.2 | 1 | 450740
20 | 6 | 5 | 3050.6 | 27296.4 | 27296.4 | 5184.1 | 27296.4 | 27296.4 | 0.0 | 0.0 | 0.0 | 81.0 | 1 | 489603
20 | 10 | 1 | 3601.8 | 15756.5 | 9626.8 | 2419.6 | 15074.8 | 15074.8 | 38.9 | 36.1 | 4.3 | 84.0 | 0 | 1029702
20 | 10 | 2 | 3600.0 | 18728.4 | 13126.7 | 2372.4 | 18092.9 | 18092.9 | 29.9 | 27.4 | 3.4 | 86.9 | 0 | 898861
20 | 10 | 3 | 3600.0 | 14763.4 | 9797.6 | 1828.8 | 14169.6 | 14169.6 | 33.6 | 30.9 | 4.0 | 87.1 | 0 | 377127
20 | 10 | 4 | 3600.0 | 20396.0 | 12682.0 | 2316.8 | 19027.0 | 19027.0 | 37.8 | 33.4 | 6.7 | 87.8 | 0 | 646552
20 | 10 | 5 | 3580.2 | 9742.5 | 9742.5 | 806.2 | 9742.5 | 9742.5 | 0.0 | 0.0 | 0.0 | 91.7 | 1 | 676850
30 | 7 | 1 | 3600.1 | 26587.5 | 5010.6 | 3461.6 | 15759.0 | 15759.0 | 81.2 | 68.2 | 40.7 | 78.0 | 0 | 195930
30 | 7 | 2 | 3600.3 | 42056.1 | 5790.5 | 4139.3 | 17867.0 | 17867.0 | 86.2 | 67.6 | 57.5 | 76.8 | 0 | 108281
30 | 7 | 3 | 3600.2 | 19362.7 | 5686.2 | 4202.6 | 15619.6 | 15619.6 | 70.6 | 63.6 | 19.3 | 73.1 | 0 | 137972
30 | 7 | 4 | 3600.1 | 27035.9 | 6153.6 | 4464.4 | 18356.9 | 18356.9 | 77.2 | 66.5 | 32.1 | 75.7 | 0 | 100324
30 | 7 | 5 | 3600.1 | 24946.9 | 4726.8 | 3479.7 | 15460.6 | 15460.6 | 81.0 | 69.4 | 38.0 | 77.5 | 0 | 77714
30 | 10 | 1 | 3600.1 | 17201.9 | 5990.3 | 2800.6 | 12598.8 | 12598.8 | 65.2 | 52.5 | 26.8 | 77.8 | 0 | 137999
30 | 10 | 2 | 3600.1 | 20288.4 | 3996.4 | 1911.3 | 9620.6 | 9620.6 | 80.3 | 58.5 | 52.6 | 80.1 | 0 | 144084
30 | 10 | 3 | 3600.3 | 18041.1 | 2626.4 | 1887.8 | 9329.9 | 9329.9 | 85.4 | 71.8 | 48.3 | 79.8 | 0 | 113743
30 | 10 | 4 | 3600.1 | 28987.4 | 4448.3 | 3146.7 | 15224.5 | 15224.5 | 84.7 | 70.8 | 47.5 | 79.3 | 0 | 140330
30 | 10 | 5 | 3600.3 | 28287.1 | 3898.8 | 2907.3 | 14665.7 | 14665.7 | 86.2 | 73.4 | 48.1 | 80.2 | 0 | 127312
30 | 15 | 1 | 3614.4 | 15705.3 | 1891.0 | 912.7 | 10085.3 | 10085.3 | 88.0 | 81.2 | 35.8 | 91.0 | 0 | 243711
30 | 15 | 2 | 3600.3 | 13140.4 | 1783.2 | 1018.6 | 10658.1 | 10658.1 | 86.4 | 83.3 | 18.9 | 90.4 | 0 | 299609
30 | 15 | 3 | 3600.3 | 12005.0 | 1391.0 | 709.7 | 8466.4 | 8466.4 | 88.4 | 83.6 | 29.5 | 91.6 | 0 | 259698
30 | 15 | 4 | 3626.2 | 12275.6 | 3428.4 | 1096.1 | 9980.5 | 9980.5 | 72.1 | 65.7 | 18.7 | 89.0 | 0 | 190840
30 | 15 | 5 | 3600.1 | 12551.5 | 2450.9 | 1192.2 | 9687.3 | 9687.3 | 80.5 | 74.7 | 22.8 | 87.7 | 0 | 267386
40 | 10 | 1 | 3600.2 | 23446.6 | 4243.9 | 3838.9 | 14500.9 | 14500.9 | 81.9 | 70.7 | 38.1 | 73.5 | 0 | 18370
40 | 10 | 2 | 3600.3 | 19671.4 | 3092.4 | 2783.6 | 12213.5 | 12213.5 | 84.3 | 74.7 | 37.9 | 77.2 | 0 | 27322
40 | 10 | 3 | 3600.2 | 16026.1 | 3605.7 | 3126.0 | 11071.1 | 11071.1 | 77.5 | 67.4 | 30.9 | 71.8 | 0 | 27824
40 | 10 | 4 | 3600.1 | 22805.1 | 3249.2 | 2756.6 | 9502.0 | 9502.1 | 85.8 | 65.8 | 58.3 | 71.0 | 0 | 18557
40 | 10 | 5 | 3600.2 | 21958.0 | 2708.5 | 2338.7 | 10972.0 | 10972.1 | 87.7 | 75.3 | 50.0 | 78.7 | 0 | 40345
40 | 13 | 1 | 3600.2 | 22308.9 | 3686.7 | 2196.2 | 9885.2 | 9885.2 | 83.5 | 62.7 | 55.7 | 77.8 | 0 | 37421
40 | 13 | 2 | 3600.2 | 17862.6 | 2646.4 | 2241.2 | 9010.9 | 9010.9 | 85.2 | 70.6 | 49.5 | 75.1 | 0 | 29951
40 | 13 | 3 | 3600.7 | 18740.5 | 3390.5 | 1979.4 | 10645.3 | 10645.3 | 81.9 | 68.2 | 43.2 | 81.4 | 0 | 98378
40 | 13 | 4 | 3600.2 | 16089.4 | 2117.2 | 1734.5 | 8911.8 | 8911.8 | 86.8 | 76.2 | 44.6 | 80.5 | 0 | 17848
40 | 13 | 5 | 3600.3 | 21386.1 | 3190.7 | 2568.0 | 11636.1 | 11636.1 | 85.1 | 72.6 | 45.6 | 77.9 | 0 | 43725
40 | 20 | 1 | 3600.1 | 13269.3 | 1559.1 | 1119.3 | 9426.4 | 9426.4 | 88.2 | 83.5 | 29.0 | 88.1 | 0 | 18432
40 | 20 | 2 | 3615.6 | 9784.4 | 1515.9 | 640.6 | 6156.3 | 6156.3 | 84.5 | 75.4 | 37.1 | 89.6 | 0 | 103999
40 | 20 | 3 | 3687.5 | 12258.4 | 1206.7 | 878.1 | 8245.3 | 8245.3 | 90.2 | 85.4 | 32.7 | 89.3 | 0 | 11799
40 | 20 | 4 | 3847.4 | 9809.5 | 2865.2 | 1002.8 | 8315.2 | 8315.2 | 70.8 | 65.5 | 15.2 | 87.9 | 0 | 17313
40 | 20 | 5 | 3600.9 | 10785.5 | 1086.7 | 813.2 | 6967.8 | 6967.8 | 89.9 | 84.4 | 35.4 | 88.3 | 0 | 42996
50 | 12 | 1 | 3600.6 | 22867.2 | 3069.3 | 2881.5 | 11063.0 | 10584.5 | 86.6 | 72.3 | 53.7 | 74.0 | 0 | 5270
50 | 12 | 2 | 3600.4 | 17671.4 | 2447.3 | 2275.6 | 10517.5 | 9871.9 | 86.2 | 76.7 | 44.1 | 78.4 | 0 | 5123
50 | 12 | 3 | 3600.1 | 15553.4 | 2772.1 | 2652.7 | 10501.1 | 10501.1 | 82.2 | 73.6 | 32.5 | 74.7 | 0 | 5216
50 | 12 | 4 | 3601.0 | 12573.3 | 2321.9 | 2159.6 | 8653.6 | 8653.6 | 81.5 | 73.2 | 31.2 | 75.0 | 0 | 5240
50 | 12 | 5 | 3600.6 | 16531.4 | 2203.2 | 2067.8 | 9521.1 | 9186.5 | 86.7 | 76.9 | 44.4 | 78.3 | 0 | 5421
50 | 16 | 1 | 3600.3 | 16633.5 | 2173.2 | 2058.3 | 8693.5 | 8693.5 | 86.9 | 75.0 | 47.7 | 76.3 | 0 | 5494
50 | 16 | 2 | 3600.2 | 11776.8 | 1233.3 | 1104.4 | 5966.4 | 5966.4 | 89.5 | 79.3 | 49.3 | 81.5 | 0 | 5356
50 | 16 | 3 | 3600.2 | 19662.9 | 2074.5 | 1845.8 | 9239.6 | 9239.6 | 89.4 | 77.6 | 53.0 | 80.0 | 0 | 5654
50 | 16 | 4 | 3601.4 | 12907.2 | 1855.2 | 1663.3 | 7453.7 | 7453.7 | 85.6 | 75.1 | 42.2 | 77.7 | 0 | 5767
50 | 16 | 5 | 3602.8 | 14471.3 | 1645.6 | 1504.9 | 6924.8 | 6924.8 | 88.6 | 76.2 | 52.1 | 78.3 | 0 | 5769
50 | 25 | 1 | 3600.4 | 8443.0 | 728.2 | 579.1 | 5561.8 | 5561.8 | 91.4 | 86.9 | 34.1 | 89.6 | 0 | 3062
50 | 25 | 2 | 3796.7 | 11549.1 | 937.6 | 884.8 | 6891.1 | 6891.1 | 91.9 | 86.4 | 40.3 | 87.2 | 0 | 14136
50 | 25 | 3 | 3600.1 | 9091.8 | 837.1 | 741.7 | 5582.7 | 5582.7 | 90.8 | 85.0 | 38.6 | 86.7 | 0 | 5308
50 | 25 | 4 | 3600.7 | 8648.7 | 768.6 | 636.9 | 5900.7 | 5900.7 | 91.1 | 87.0 | 31.8 | 89.2 | 0 | 5219
50 | 25 | 5 | 3600.2 | 9614.2 | 814.2 | 686.8 | 6372.0 | 6372.0 | 91.5 | 87.2 | 33.7 | 89.2 | 0 | 5498
Table 84: Summary results table for model OMT Benders modern $km$ $|V|$ | p |  $|$#$|$ | cpu |  g$\overline{\text{U}}$R |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ | gUL | nod
---|---|---|---|---|---|---|---|---
20 | 5 | 3 | 2255.1 | 75.9 | 7.2 | 1.6 | 8.3 | 913488
20 | 6 | 4 | 2546.2 | 77.6 | 9.9 | 1.4 | 10.6 | 485593
20 | 10 | 1 | 3596.4 | 87.5 | 25.6 | 3.7 | 28.0 | 725818
30 | 7 | 0 | 3600.2 | 76.2 | 67.1 | 37.5 | 79.2 | 124044
30 | 10 | 0 | 3600.2 | 79.4 | 65.4 | 44.7 | 80.4 | 132694
30 | 15 | 0 | 3608.3 | 89.9 | 77.7 | 25.1 | 83.1 | 252249
40 | 10 | 0 | 3600.2 | 74.4 | 70.8 | 43.0 | 83.4 | 26484
40 | 13 | 0 | 3600.3 | 78.5 | 70.1 | 47.7 | 84.5 | 45465
40 | 20 | 0 | 3670.3 | 88.6 | 78.8 | 29.9 | 84.7 | 38908
50 | 12 | 0 | 3600.5 | 76.1 | 74.5 | 41.2 | 84.6 | 5254
50 | 16 | 0 | 3601.0 | 78.8 | 76.6 | 48.9 | 88.0 | 5608
50 | 25 | 0 | 3639.6 | 88.4 | 86.5 | 35.7 | 91.3 | 6645

Table 85: Instances results table for model OMT Benders classic $km$ $|V|$ | p | ins | cpu | objU | objL | objR |  obj$\overline{\text{U}}$ |  obj$\overline{\text{L}}$ | gUL |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ |  g$\overline{\text{U}}$R | opt | nod
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
20 | 5 | 1 | 3600.8 | 27234.9 | 14738.9 | 5501.0 | 24444.4 | 24444.4 | 45.9 | 39.7 | 10.2 | 77.5 | 0 |
20 | 5 | 2 | 3600.8 | 27981.6 | 16388.0 | 6991.2 | 26585.3 | 26585.3 | 41.4 | 38.4 | 5.0 | 73.7 | 0 |
20 | 5 | 3 | 3600.8 | 35106.7 | 17205.5 | 5859.3 | 26159.6 | 26159.6 | 51.0 | 34.2 | 25.5 | 77.6 | 0 |
20 | 5 | 4 | 3600.9 | 24368.0 | 10919.8 | 3801.4 | 16558.9 | 16558.9 | 55.2 | 34.0 | 32.0 | 77.0 | 0 |
20 | 5 | 5 | 3600.8 | 44078.0 | 18183.9 | 7835.4 | 29165.6 | 29165.6 | 58.8 | 37.6 | 33.8 | 73.1 | 0 |
20 | 6 | 1 | 3601.2 | 28016.2 | 11817.1 | 4648.1 | 22562.4 | 22562.4 | 57.8 | 47.6 | 19.5 | 79.4 | 0 |
20 | 6 | 2 | 3601.3 | 31841.1 | 14341.4 | 6019.6 | 20183.5 | 20183.5 | 55.0 | 28.9 | 36.6 | 70.2 | 0 |
20 | 6 | 3 | 3601.4 | 37765.8 | 13205.0 | 5204.0 | 25238.2 | 25238.2 | 65.0 | 47.7 | 33.2 | 79.4 | 0 |
20 | 6 | 4 | 3601.2 | 29045.1 | 10523.7 | 4399.0 | 20161.1 | 20161.1 | 63.8 | 47.8 | 30.6 | 78.2 | 0 |
20 | 6 | 5 | 3601.6 | 33855.1 | 13570.4 | 5343.7 | 27296.4 | 27296.4 | 59.9 | 50.3 | 19.4 | 80.4 | 0 |
20 | 10 | 1 | 3601.5 | 22286.5 | 6415.2 | 2432.2 | 15074.8 | 15074.8 | 71.2 | 57.4 | 32.4 | 83.9 | 0 |
20 | 10 | 2 | 3601.3 | 20605.4 | 7974.1 | 2729.6 | 18092.9 | 18092.9 | 61.3 | 55.9 | 12.2 | 84.9 | 0 |
20 | 10 | 3 | 3601.6 | 16246.4 | 5942.7 | 1992.4 | 14169.6 | 14169.6 | 63.4 | 58.1 | 12.8 | 85.9 | 0 |
20 | 10 | 4 | 3601.2 | 20818.6 | 8503.7 | 2467.5 | 19027.0 | 19027.0 | 59.1 | 55.3 | 8.6 | 87.0 | 0 |
20 | 10 | 5 | 3601.6 | 10519.6 | 4279.3 | 879.1 | 9742.5 | 9742.5 | 59.3 | 56.1 | 7.4 | 91.0 | 0 |
30 | 7 | 1 | 3607.9 | 26587.5 | 0.0 | 3461.6 | 15759.0 | 15759.0 | 100.0 | 100.0 | 40.7 | 78.0 | 0 |
30 | 7 | 2 | 3617.2 | 42056.1 | 0.0 | 4139.3 | 17867.0 | 17867.0 | 100.0 | 100.0 | 57.5 | 76.8 | 0 |
30 | 7 | 3 | 3614.4 | 43839.0 | 0.0 | 4202.6 | 15619.6 | 15619.6 | 100.0 | 100.0 | 64.4 | 73.1 | 0 |
30 | 7 | 4 | 3610.1 | 30892.7 | 0.0 | 4464.4 | 18356.9 | 18356.9 | 100.0 | 100.0 | 40.6 | 75.7 | 0 |
30 | 7 | 5 | 3610.9 | 30533.0 | 0.0 | 3479.7 | 15460.6 | 15460.6 | 100.0 | 100.0 | 49.4 | 77.5 | 0 |
30 | 10 | 1 | 3615.3 | 23798.2 | 7047.2 | 2800.6 | 12598.8 | 12598.8 | 70.4 | 44.1 | 47.1 | 77.8 | 0 |
30 | 10 | 2 | 3614.9 | 18069.1 | 4512.3 | 1918.3 | 9620.6 | 9620.6 | 75.0 | 53.1 | 46.8 | 80.1 | 0 |
30 | 10 | 3 | 3610.8 | 20033.1 | 4317.1 | 1887.8 | 9329.9 | 9329.9 | 78.4 | 53.7 | 53.4 | 79.8 | 0 |
30 | 10 | 4 | 3618.6 | 28987.4 | 0.0 | 3146.7 | 15224.5 | 15224.5 | 100.0 | 100.0 | 47.5 | 79.3 | 0 |
30 | 10 | 5 | 3622.6 | 29380.1 | 0.0 | 2907.3 | 14665.7 | 14665.7 | 100.0 | 100.0 | 50.1 | 80.2 | 0 |
30 | 15 | 1 | 3604.0 | 14332.3 | 2805.1 | 946.4 | 10085.3 | 10085.3 | 80.4 | 72.2 | 29.6 | 90.6 | 0 |
30 | 15 | 2 | 3604.3 | 12780.3 | 3081.1 | 1018.6 | 10658.1 | 10658.1 | 75.9 | 71.1 | 16.6 | 90.4 | 0 |
30 | 15 | 3 | 3603.9 | 11640.8 | 2437.1 | 725.8 | 8466.4 | 8466.4 | 79.1 | 71.2 | 27.3 | 91.4 | 0 |
30 | 15 | 4 | 3604.6 | 13062.8 | 3086.4 | 1168.9 | 9980.5 | 9980.5 | 76.4 | 69.1 | 23.6 | 88.3 | 0 |
30 | 15 | 5 | 3604.1 | 12884.0 | 3786.3 | 1258.8 | 9687.3 | 9687.3 | 70.6 | 60.9 | 24.8 | 87.0 | 0 |
40 | 10 | 1 | 3613.7 | 23446.6 | 0.0 | 3838.9 | 14500.9 | 14500.9 | 100.0 | 100.0 | 38.1 | 73.5 | 0 |
40 | 10 | 2 | 3613.2 | 19671.4 | 0.0 | 2783.6 | 12213.5 | 12213.5 | 100.0 | 100.0 | 37.9 | 77.2 | 0 |
40 | 10 | 3 | 3613.0 | 16026.1 | 0.0 | 3126.0 | 11071.1 | 11071.1 | 100.0 | 100.0 | 30.9 | 71.8 | 0 |
40 | 10 | 4 | 3615.6 | 22805.1 | 0.0 | 2756.6 | 9502.0 | 9502.1 | 100.0 | 100.0 | 58.3 | 71.0 | 0 |
40 | 10 | 5 | 3613.9 | 26717.0 | 0.0 | 2338.7 | 10972.0 | 10972.1 | 100.0 | 100.0 | 58.9 | 78.7 | 0 |
40 | 13 | 1 | 3613.0 | 17220.8 | 0.0 | 2196.2 | 9885.2 | 9885.2 | 100.0 | 100.0 | 42.6 | 77.8 | 0 |
40 | 13 | 2 | 3613.7 | 16095.8 | 0.0 | 2241.2 | 9010.9 | 9010.9 | 100.0 | 100.0 | 44.0 | 75.1 | 0 |
40 | 13 | 3 | 3613.4 | 17412.3 | 4727.1 | 1979.4 | 10645.3 | 10645.3 | 72.8 | 55.6 | 38.9 | 81.4 | 0 |
40 | 13 | 4 | 3619.1 | 15710.6 | 0.0 | 1734.5 | 8911.8 | 8911.8 | 100.0 | 100.0 | 43.3 | 80.5 | 0 |
40 | 13 | 5 | 3619.4 | 21386.1 | 0.0 | 2568.0 | 11636.1 | 11636.1 | 100.0 | 100.0 | 45.6 | 77.9 | 0 |
40 | 20 | 1 | 3615.3 | 12939.5 | 2908.4 | 1119.3 | 9426.4 | 9426.4 | 77.5 | 69.2 | 27.1 | 88.1 | 0 |
40 | 20 | 2 | 3615.2 | 9983.7 | 1796.4 | 642.5 | 6156.3 | 6156.3 | 82.0 | 70.8 | 38.3 | 89.6 | 0 |
40 | 20 | 3 | 3615.1 | 12650.3 | 0.0 | 878.1 | 8245.3 | 8245.3 | 100.0 | 100.0 | 34.8 | 89.3 | 0 |
40 | 20 | 4 | 3615.3 | 10296.1 | 2721.9 | 1069.1 | 8315.2 | 8315.2 | 73.6 | 67.3 | 19.2 | 87.1 | 0 |
40 | 20 | 5 | 3614.2 | 11002.2 | 2181.8 | 822.4 | 6967.8 | 6967.8 | 80.2 | 68.7 | 36.7 | 88.2 | 0 |
50 | 12 | 1 | 3886.5 | 22867.2 | 0.0 | 2881.5 | 11063.0 | 10584.5 | 100.0 | 100.0 | 53.7 | 74.0 | 0 |
50 | 12 | 2 | 3887.7 | 17671.4 | 0.0 | 2275.6 | 10517.5 | 9871.9 | 100.0 | 100.0 | 44.1 | 78.4 | 0 |
50 | 12 | 3 | 3892.9 | 14064.6 | 0.0 | 2652.7 | 10501.1 | 10501.1 | 100.0 | 100.0 | 25.3 | 74.7 | 0 |
50 | 12 | 4 | 3851.4 | 12597.6 | 0.0 | 2159.6 | 8653.6 | 8653.6 | 100.0 | 100.0 | 31.3 | 75.0 | 0 |
50 | 12 | 5 | 3851.7 | 18371.8 | 0.0 | 2067.8 | 9521.1 | 9186.5 | 100.0 | 100.0 | 50.0 | 78.3 | 0 |
50 | 16 | 1 | 3873.8 | 16633.5 | 0.0 | 2058.3 | 8693.5 | 8693.5 | 100.0 | 100.0 | 47.7 | 76.3 | 0 |
50 | 16 | 2 | 3895.8 | 11776.8 | 0.0 | 1104.4 | 5966.4 | 5966.4 | 100.0 | 100.0 | 49.3 | 81.5 | 0 |
50 | 16 | 3 | 3885.6 | 19662.9 | 0.0 | 1845.8 | 9239.6 | 9239.6 | 100.0 | 100.0 | 53.0 | 80.0 | 0 |
50 | 16 | 4 | 3866.5 | 12391.8 | 0.0 | 1663.3 | 7453.7 | 7453.7 | 100.0 | 100.0 | 39.9 | 77.7 | 0 |
50 | 16 | 5 | 3852.7 | 14606.1 | 0.0 | 1504.9 | 6924.8 | 6924.8 | 100.0 | 100.0 | 52.6 | 78.3 | 0 |
50 | 25 | 1 | 3880.5 | 8443.0 | 0.0 | 579.1 | 5561.8 | 5561.8 | 100.0 | 100.0 | 34.1 | 89.6 | 0 |
50 | 25 | 2 | 3905.2 | 11549.1 | 0.0 | 884.8 | 6891.1 | 6891.1 | 100.0 | 100.0 | 40.3 | 87.2 | 0 |
50 | 25 | 3 | 3841.7 | 8849.4 | 1827.9 | 741.7 | 5582.7 | 5582.7 | 79.3 | 67.3 | 36.9 | 86.7 | 0 |
50 | 25 | 4 | 3905.3 | 8648.7 | 0.0 | 636.9 | 5900.7 | 5900.7 | 100.0 | 100.0 | 31.8 | 89.2 | 0 |
50 | 25 | 5 | 3954.9 | 9141.2 | 1849.1 | 710.0 | 6372.0 | 6372.0 | 79.8 | 71.0 | 30.3 | 88.9 | 0 |
Table 86: Summary results table for model OMT Benders classic $km$ $|V|$ | p |  $|$#$|$ | cpu |  g$\overline{\text{U}}$R |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ | gUL | nod
---|---|---|---|---|---|---|---|---
20 | 5 | 0 | 3600.8 | 75.8 | 36.8 | 21.3 | 50.5 |
20 | 6 | 0 | 3601.3 | 77.5 | 44.5 | 27.9 | 60.3 |
20 | 10 | 0 | 3601.4 | 86.5 | 56.6 | 14.7 | 62.9 |
30 | 7 | 0 | 3612.1 | 76.2 | 100.0 | 50.5 | 100.0 |
30 | 10 | 0 | 3616.4 | 79.4 | 70.2 | 49.0 | 84.8 |
30 | 15 | 0 | 3604.2 | 89.5 | 68.9 | 24.4 | 76.5 |
40 | 10 | 0 | 3613.9 | 74.4 | 100.0 | 44.8 | 100.0 |
40 | 13 | 0 | 3615.7 | 78.5 | 91.1 | 42.9 | 94.6 |
40 | 20 | 0 | 3615.0 | 88.5 | 75.2 | 31.2 | 82.7 |
50 | 12 | 0 | 3874.0 | 76.1 | 100.0 | 40.9 | 100.0 |
50 | 16 | 0 | 3874.9 | 78.8 | 100.0 | 48.5 | 100.0 |
50 | 25 | 0 | 3897.5 | 88.3 | 87.7 | 34.7 | 91.8 |

Table 87: Instances results table for model $F1_{u}^{mtz}$ $|V|$ | p | ins | cpu | objU | objL | objR |  obj$\overline{\text{U}}$ |  obj$\overline{\text{L}}$ | gUL |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ |  g$\overline{\text{U}}$R | opt | nod
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
20 | 5 | 1 | 9.6 | 24444.4 | 24444.4 | 8678.2 | 24444.4 | 24444.4 | 0.0 | 0.0 | 0.0 | 64.5 | 1 | 5728
20 | 5 | 2 | 9.3 | 26585.3 | 26585.3 | 11464.7 | 26585.3 | 26585.3 | 0.0 | 0.0 | 0.0 | 56.9 | 1 | 1506
20 | 5 | 3 | 9.0 | 26159.6 | 26159.6 | 8966.5 | 26159.6 | 26159.6 | 0.0 | 0.0 | 0.0 | 65.7 | 1 | 3077
20 | 5 | 4 | 9.0 | 16558.9 | 16558.9 | 5449.0 | 16558.9 | 16558.9 | 0.0 | 0.0 | 0.0 | 67.1 | 1 | 1508
20 | 5 | 5 | 6.6 | 29165.6 | 29165.6 | 11867.1 | 29165.6 | 29165.6 | 0.0 | 0.0 | 0.0 | 59.3 | 1 | 2300
20 | 6 | 1 | 15.2 | 22562.4 | 22562.4 | 7620.6 | 22562.4 | 22562.4 | 0.0 | 0.0 | 0.0 | 66.2 | 1 | 4547
20 | 6 | 2 | 2.4 | 20183.5 | 20183.5 | 8736.0 | 20183.5 | 20183.5 | 0.0 | 0.0 | 0.0 | 56.7 | 1 | 1
20 | 6 | 3 | 11.5 | 25238.2 | 25238.2 | 8642.1 | 25238.2 | 25238.2 | 0.0 | 0.0 | 0.0 | 65.8 | 1 | 2574
20 | 6 | 4 | 15.5 | 20161.1 | 20161.1 | 7071.6 | 20161.1 | 20161.1 | 0.0 | 0.0 | 0.0 | 64.9 | 1 | 4996
20 | 6 | 5 | 31.3 | 27296.4 | 27296.4 | 7825.1 | 27296.4 | 27296.4 | 0.0 | 0.0 | 0.0 | 71.3 | 1 | 3844
20 | 10 | 1 | 8.9 | 15074.8 | 15074.8 | 7443.9 | 15074.8 | 15074.8 | 0.0 | 0.0 | 0.0 | 50.6 | 1 | 3107
20 | 10 | 2 | 5.7 | 18092.9 | 18092.9 | 7781.0 | 18092.9 | 18092.9 | 0.0 | 0.0 | 0.0 | 57.0 | 1 | 1308
20 | 10 | 3 | 18.5 | 14169.6 | 14169.6 | 6073.0 | 14169.6 | 14169.6 | 0.0 | 0.0 | 0.0 | 57.1 | 1 | 6797
20 | 10 | 4 | 2.8 | 19027.0 | 19025.6 | 7807.7 | 19027.0 | 19027.0 | 0.0 | 0.0 | 0.0 | 59.0 | 1 | 1
20 | 10 | 5 | 3.6 | 9742.5 | 9742.5 | 3873.3 | 9742.5 | 9742.5 | 0.0 | 0.0 | 0.0 | 60.2 | 1 | 349
30 | 7 | 1 | 153.0 | 15759.0 | 15759.0 | 4913.7 | 15759.0 | 15759.0 | 0.0 | 0.0 | 0.0 | 68.8 | 1 | 2775
30 | 7 | 2 | 132.1 | 17867.0 | 17867.0 | 5869.8 | 17867.0 | 17867.0 | 0.0 | 0.0 | 0.0 | 67.2 | 1 | 3473
30 | 7 | 3 | 111.3 | 15619.6 | 15619.6 | 6348.0 | 15619.6 | 15619.6 | 0.0 | 0.0 | 0.0 | 59.4 | 1 | 4646
30 | 7 | 4 | 148.0 | 18356.9 | 18356.9 | 6956.1 | 18356.9 | 18356.9 | 0.0 | 0.0 | 0.0 | 62.1 | 1 | 7094
30 | 7 | 5 | 399.9 | 15460.6 | 15460.6 | 4669.8 | 15460.6 | 15460.6 | 0.0 | 0.0 | 0.0 | 69.8 | 1 | 21022
30 | 10 | 1 | 26.8 | 12598.8 | 12598.8 | 4558.6 | 12598.8 | 12598.8 | 0.0 | 0.0 | 0.0 | 63.8 | 1 | 1737
30 | 10 | 2 | 33.3 | 9620.6 | 9620.6 | 4067.0 | 9620.6 | 9620.6 | 0.0 | 0.0 | 0.0 | 57.7 | 1 | 3359
30 | 10 | 3 | 55.8 | 9329.9 | 9329.9 | 3745.2 | 9329.9 | 9329.9 | 0.0 | 0.0 | 0.0 | 59.9 | 1 | 4067
30 | 10 | 4 | 54.0 | 15224.5 | 15224.5 | 5750.3 | 15224.5 | 15224.5 | 0.0 | 0.0 | 0.0 | 62.2 | 1 | 4096
30 | 10 | 5 | 1074.0 | 14665.7 | 14665.7 | 5544.5 | 14665.7 | 14665.7 | 0.0 | 0.0 | 0.0 | 62.2 | 1 | 41782
30 | 15 | 1 | 65.6 | 10085.3 | 10085.3 | 3267.5 | 10085.3 | 10085.3 | 0.0 | 0.0 | 0.0 | 67.6 | 1 | 6727
30 | 15 | 2 | 65.7 | 10658.1 | 10658.1 | 4098.7 | 10658.1 | 10658.1 | 0.0 | 0.0 | 0.0 | 61.5 | 1 | 6566
30 | 15 | 3 | 161.5 | 8466.4 | 8466.4 | 3070.2 | 8466.4 | 8466.4 | 0.0 | 0.0 | 0.0 | 63.7 | 1 | 20002
30 | 15 | 4 | 22.2 | 9980.5 | 9980.5 | 4609.0 | 9980.5 | 9980.5 | 0.0 | 0.0 | 0.0 | 53.8 | 1 | 4916
30 | 15 | 5 | 16.9 | 9687.3 | 9687.3 | 4582.8 | 9687.3 | 9687.3 | 0.0 | 0.0 | 0.0 | 52.7 | 1 | 156
40 | 10 | 1 | 1643.7 | 14500.9 | 14500.9 | 5513.9 | 14500.9 | 14500.9 | 0.0 | 0.0 | 0.0 | 62.0 | 1 | 54317
40 | 10 | 2 | 2285.2 | 12213.5 | 12213.5 | 3884.9 | 12213.5 | 12213.5 | 0.0 | 0.0 | 0.0 | 68.2 | 1 | 108392
40 | 10 | 3 | 309.0 | 11071.1 | 11071.1 | 4374.9 | 11071.1 | 11071.1 | 0.0 | 0.0 | 0.0 | 60.5 | 1 | 3655
40 | 10 | 4 | 244.2 | 9502.1 | 9502.1 | 3676.7 | 9502.0 | 9502.1 | 0.0 | 0.0 | 0.0 | 61.3 | 1 | 7639
40 | 10 | 5 | 1706.7 | 10972.1 | 10972.0 | 3593.4 | 10972.0 | 10972.1 | 0.0 | 0.0 | 0.0 | 67.2 | 1 | 51879
40 | 13 | 1 | 256.6 | 9885.2 | 9885.1 | 4092.9 | 9885.2 | 9885.2 | 0.0 | 0.0 | 0.0 | 58.6 | 1 | 2815
40 | 13 | 2 | 77.1 | 9010.9 | 9010.9 | 4280.9 | 9010.9 | 9010.9 | 0.0 | 0.0 | 0.0 | 52.5 | 1 | 3602
40 | 13 | 3 | 503.0 | 10645.3 | 10645.3 | 3675.2 | 10645.3 | 10645.3 | 0.0 | 0.0 | 0.0 | 65.5 | 1 | 7240
40 | 13 | 4 | 385.6 | 8911.8 | 8911.8 | 3069.5 | 8911.8 | 8911.8 | 0.0 | 0.0 | 0.0 | 65.6 | 1 | 8027
40 | 13 | 5 | 1426.0 | 11636.1 | 11636.1 | 4354.2 | 11636.1 | 11636.1 | 0.0 | 0.0 | 0.0 | 62.6 | 1 | 66217
40 | 20 | 1 | 3600.5 | 9426.4 | 8962.8 | 3793.6 | 9426.4 | 9426.4 | 4.9 | 4.9 | 0.0 | 59.8 | 0 | 87775
40 | 20 | 2 | 180.3 | 6156.3 | 6156.3 | 2372.8 | 6156.3 | 6156.3 | 0.0 | 0.0 | 0.0 | 61.5 | 1 | 3137
40 | 20 | 3 | 455.9 | 8245.3 | 8245.3 | 3012.1 | 8245.3 | 8245.3 | 0.0 | 0.0 | 0.0 | 63.5 | 1 | 28023
40 | 20 | 4 | 44.6 | 8315.2 | 8315.2 | 3834.2 | 8315.2 | 8315.2 | 0.0 | 0.0 | 0.0 | 53.9 | 1 | 2585
40 | 20 | 5 | 261.9 | 6967.8 | 6967.8 | 3044.4 | 6967.8 | 6967.8 | 0.0 | 0.0 | 0.0 | 56.3 | 1 | 11067
50 | 12 | 1 | 3600.2 | 11063.0 | 10584.5 | 4500.3 | 11063.0 | 10584.5 | 4.3 | 4.3 | 4.3 | 59.3 | 0 | 28684
50 | 12 | 2 | 3600.7 | 10517.5 | 9652.5 | 3372.3 | 10517.5 | 9871.9 | 8.2 | 8.2 | 6.1 | 67.9 | 0 | 20859
50 | 12 | 3 | 2731.4 | 10501.1 | 10501.1 | 4310.6 | 10501.1 | 10501.1 | 0.0 | 0.0 | 0.0 | 59.0 | 1 | 29140
50 | 12 | 4 | 3600.7 | 8653.6 | 8264.7 | 3130.6 | 8653.6 | 8653.6 | 4.5 | 4.5 | 0.0 | 63.8 | 0 | 33306
50 | 12 | 5 | 3600.5 | 9576.8 | 8917.2 | 3049.1 | 9521.1 | 9186.5 | 6.9 | 6.3 | 4.1 | 68.0 | 0 | 31144
50 | 16 | 1 | 1265.0 | 8693.5 | 8693.5 | 3630.9 | 8693.5 | 8693.5 | 0.0 | 0.0 | 0.0 | 58.2 | 1 | 14838
50 | 16 | 2 | 1476.2 | 5966.4 | 5966.4 | 1945.6 | 5966.4 | 5966.4 | 0.0 | 0.0 | 0.0 | 67.4 | 1 | 20118
50 | 16 | 3 | 1384.5 | 9239.6 | 9239.6 | 3403.9 | 9239.6 | 9239.6 | 0.0 | 0.0 | 0.0 | 63.2 | 1 | 15605
50 | 16 | 4 | 2050.2 | 7453.7 | 7453.7 | 2731.0 | 7453.7 | 7453.7 | 0.0 | 0.0 | 0.0 | 63.4 | 1 | 21038
50 | 16 | 5 | 3600.4 | 6924.8 | 6785.8 | 2416.9 | 6924.8 | 6924.8 | 2.0 | 2.0 | 0.0 | 65.1 | 0 | 48350
50 | 25 | 1 | 371.1 | 5561.8 | 5561.8 | 2203.8 | 5561.8 | 5561.8 | 0.0 | 0.0 | 0.0 | 60.4 | 1 | 1496
50 | 25 | 2 | 298.7 | 6891.1 | 6891.1 | 3287.8 | 6891.1 | 6891.1 | 0.0 | 0.0 | 0.0 | 52.3 | 1 | 5307
50 | 25 | 3 | 3600.4 | 5582.7 | 5514.5 | 2560.5 | 5582.7 | 5582.7 | 1.2 | 1.2 | 0.0 | 54.1 | 0 | 135341
50 | 25 | 4 | 593.4 | 5900.7 | 5900.6 | 2401.7 | 5900.7 | 5900.7 | 0.0 | 0.0 | 0.0 | 59.3 | 1 | 19241
50 | 25 | 5 | 307.0 | 6372.0 | 6372.0 | 2718.2 | 6372.0 | 6372.0 | 0.0 | 0.0 | 0.0 | 57.3 | 1 | 1201
Table 88: Summary results table for model $F1_{u}^{mtz}$ $|V|$ | p |  $|$#$|$ | cpu |  g$\overline{\text{U}}$R |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ | gUL | nod
---|---|---|---|---|---|---|---|---
20 | 5 | 5 | 8.7 | 62.7 | 0.0 | 0.0 | 0.0 | 2824
20 | 6 | 5 | 15.2 | 65.0 | 0.0 | 0.0 | 0.0 | 3192
20 | 10 | 5 | 7.9 | 56.8 | 0.0 | 0.0 | 0.0 | 2312
30 | 7 | 5 | 188.9 | 65.5 | 0.0 | 0.0 | 0.0 | 7802
30 | 10 | 5 | 248.8 | 61.2 | 0.0 | 0.0 | 0.0 | 11008
30 | 15 | 5 | 66.4 | 59.9 | 0.0 | 0.0 | 0.0 | 7673
40 | 10 | 5 | 1237.8 | 63.8 | 0.0 | 0.0 | 0.0 | 45176
40 | 13 | 5 | 529.7 | 61.0 | 0.0 | 0.0 | 0.0 | 17580
40 | 20 | 4 | 908.6 | 59.0 | 1.0 | 0.0 | 1.0 | 26517
50 | 12 | 1 | 3426.7 | 63.6 | 4.7 | 2.9 | 4.8 | 28627
50 | 16 | 4 | 1955.3 | 63.5 | 0.4 | 0.0 | 0.4 | 23990
50 | 25 | 4 | 1034.1 | 56.7 | 0.2 | 0.0 | 0.2 | 32517

Table 89: Instances results table for model $F1_{u}^{flow1}$ $|V|$ | p | ins | cpu | objU | objL | objR |  obj$\overline{\text{U}}$ |  obj$\overline{\text{L}}$ | gUL |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ |  g$\overline{\text{U}}$R | opt | nod
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
20 | 5 | 1 | 8.3 | 24444.4 | 24444.4 | 8678.2 | 24444.4 | 24444.4 | 0.0 | 0.0 | 0.0 | 64.5 | 1 | 1292
20 | 5 | 2 | 4.6 | 26585.3 | 26582.7 | 11464.7 | 26585.3 | 26585.3 | 0.0 | 0.0 | 0.0 | 56.9 | 1 | 1
20 | 5 | 3 | 9.1 | 26159.6 | 26159.6 | 8966.5 | 26159.6 | 26159.6 | 0.0 | 0.0 | 0.0 | 65.7 | 1 | 1720
20 | 5 | 4 | 10.1 | 16558.9 | 16558.9 | 5449.0 | 16558.9 | 16558.9 | 0.0 | 0.0 | 0.0 | 67.1 | 1 | 1105
20 | 5 | 5 | 6.3 | 29165.6 | 29163.8 | 11867.1 | 29165.6 | 29165.6 | 0.0 | 0.0 | 0.0 | 59.3 | 1 | 1382
20 | 6 | 1 | 10.0 | 22562.4 | 22562.4 | 7620.6 | 22562.4 | 22562.4 | 0.0 | 0.0 | 0.0 | 66.2 | 1 | 1940
20 | 6 | 2 | 1.5 | 20183.5 | 20183.5 | 8736.0 | 20183.5 | 20183.5 | 0.0 | 0.0 | 0.0 | 56.7 | 1 | 1
20 | 6 | 3 | 10.4 | 25238.2 | 25238.2 | 8642.1 | 25238.2 | 25238.2 | 0.0 | 0.0 | 0.0 | 65.8 | 1 | 1320
20 | 6 | 4 | 7.9 | 20161.1 | 20161.1 | 7071.6 | 20161.1 | 20161.1 | 0.0 | 0.0 | 0.0 | 64.9 | 1 | 915
20 | 6 | 5 | 6.5 | 27296.4 | 27296.4 | 7825.1 | 27296.4 | 27296.4 | 0.0 | 0.0 | 0.0 | 71.3 | 1 | 1787
20 | 10 | 1 | 7.8 | 15074.8 | 15074.8 | 7443.9 | 15074.8 | 15074.8 | 0.0 | 0.0 | 0.0 | 50.6 | 1 | 437
20 | 10 | 2 | 9.0 | 18092.9 | 18092.9 | 7781.0 | 18092.9 | 18092.9 | 0.0 | 0.0 | 0.0 | 57.0 | 1 | 931
20 | 10 | 3 | 3.3 | 14169.6 | 14169.6 | 6073.0 | 14169.6 | 14169.6 | 0.0 | 0.0 | 0.0 | 57.1 | 1 | 241
20 | 10 | 4 | 2.7 | 19027.0 | 19027.0 | 7807.7 | 19027.0 | 19027.0 | 0.0 | 0.0 | 0.0 | 59.0 | 1 | 148
20 | 10 | 5 | 1.4 | 9742.5 | 9742.5 | 3873.3 | 9742.5 | 9742.5 | 0.0 | 0.0 | 0.0 | 60.2 | 1 | 1
30 | 7 | 1 | 53.1 | 15759.0 | 15759.0 | 4913.7 | 15759.0 | 15759.0 | 0.0 | 0.0 | 0.0 | 68.8 | 1 | 2038
30 | 7 | 2 | 49.2 | 17867.0 | 17867.0 | 5869.8 | 17867.0 | 17867.0 | 0.0 | 0.0 | 0.0 | 67.2 | 1 | 4076
30 | 7 | 3 | 47.0 | 15619.6 | 15619.6 | 6348.0 | 15619.6 | 15619.6 | 0.0 | 0.0 | 0.0 | 59.4 | 1 | 3808
30 | 7 | 4 | 66.5 | 18356.9 | 18356.9 | 6956.1 | 18356.9 | 18356.9 | 0.0 | 0.0 | 0.0 | 62.1 | 1 | 3244
30 | 7 | 5 | 159.3 | 15460.6 | 15460.6 | 4669.8 | 15460.6 | 15460.6 | 0.0 | 0.0 | 0.0 | 69.8 | 1 | 7361
30 | 10 | 1 | 31.4 | 12598.8 | 12598.8 | 4558.6 | 12598.8 | 12598.8 | 0.0 | 0.0 | 0.0 | 63.8 | 1 | 857
30 | 10 | 2 | 43.6 | 9620.6 | 9620.6 | 4067.0 | 9620.6 | 9620.6 | 0.0 | 0.0 | 0.0 | 57.7 | 1 | 1204
30 | 10 | 3 | 39.5 | 9329.9 | 9329.9 | 3745.2 | 9329.9 | 9329.9 | 0.0 | 0.0 | 0.0 | 59.9 | 1 | 1190
30 | 10 | 4 | 78.3 | 15224.5 | 15224.5 | 5750.3 | 15224.5 | 15224.5 | 0.0 | 0.0 | 0.0 | 62.2 | 1 | 4687
30 | 10 | 5 | 155.5 | 14665.7 | 14665.7 | 5544.5 | 14665.7 | 14665.7 | 0.0 | 0.0 | 0.0 | 62.2 | 1 | 8375
30 | 15 | 1 | 36.8 | 10085.3 | 10085.3 | 3267.5 | 10085.3 | 10085.3 | 0.0 | 0.0 | 0.0 | 67.6 | 1 | 4714
30 | 15 | 2 | 29.8 | 10658.1 | 10658.1 | 4098.7 | 10658.1 | 10658.1 | 0.0 | 0.0 | 0.0 | 61.5 | 1 | 3774
30 | 15 | 3 | 30.8 | 8466.4 | 8466.4 | 3070.2 | 8466.4 | 8466.4 | 0.0 | 0.0 | 0.0 | 63.7 | 1 | 1152
30 | 15 | 4 | 21.8 | 9980.5 | 9980.5 | 4609.0 | 9980.5 | 9980.5 | 0.0 | 0.0 | 0.0 | 53.8 | 1 | 748
30 | 15 | 5 | 3.7 | 9687.3 | 9687.3 | 4582.8 | 9687.3 | 9687.3 | 0.0 | 0.0 | 0.0 | 52.7 | 1 | 1
40 | 10 | 1 | 1032.0 | 14500.9 | 14500.9 | 5513.9 | 14500.9 | 14500.9 | 0.0 | 0.0 | 0.0 | 62.0 | 1 | 37737
40 | 10 | 2 | 1016.6 | 12213.5 | 12213.5 | 3884.9 | 12213.5 | 12213.5 | 0.0 | 0.0 | 0.0 | 68.2 | 1 | 51402
40 | 10 | 3 | 365.9 | 11071.1 | 11071.1 | 4374.9 | 11071.1 | 11071.1 | 0.0 | 0.0 | 0.0 | 60.5 | 1 | 2867
40 | 10 | 4 | 110.7 | 9502.1 | 9501.8 | 3676.7 | 9502.0 | 9502.1 | 0.0 | 0.0 | 0.0 | 61.3 | 1 | 7181
40 | 10 | 5 | 986.5 | 10972.1 | 10972.1 | 3593.4 | 10972.0 | 10972.1 | 0.0 | 0.0 | 0.0 | 67.2 | 1 | 24997
40 | 13 | 1 | 395.6 | 9885.2 | 9885.2 | 4092.9 | 9885.2 | 9885.2 | 0.0 | 0.0 | 0.0 | 58.6 | 1 | 7481
40 | 13 | 2 | 69.0 | 9010.9 | 9010.9 | 4280.9 | 9010.9 | 9010.9 | 0.0 | 0.0 | 0.0 | 52.5 | 1 | 4108
40 | 13 | 3 | 652.5 | 10645.3 | 10645.3 | 3675.2 | 10645.3 | 10645.3 | 0.0 | 0.0 | 0.0 | 65.5 | 1 | 25872
40 | 13 | 4 | 646.4 | 8911.8 | 8911.8 | 3069.5 | 8911.8 | 8911.8 | 0.0 | 0.0 | 0.0 | 65.6 | 1 | 4191
40 | 13 | 5 | 493.9 | 11636.1 | 11636.1 | 4354.2 | 11636.1 | 11636.1 | 0.0 | 0.0 | 0.0 | 62.6 | 1 | 11874
40 | 20 | 1 | 300.3 | 9426.4 | 9426.4 | 3793.6 | 9426.4 | 9426.4 | 0.0 | 0.0 | 0.0 | 59.8 | 1 | 2458
40 | 20 | 2 | 97.7 | 6156.3 | 6156.3 | 2372.8 | 6156.3 | 6156.3 | 0.0 | 0.0 | 0.0 | 61.5 | 1 | 12035
40 | 20 | 3 | 263.4 | 8245.3 | 8245.3 | 3012.1 | 8245.3 | 8245.3 | 0.0 | 0.0 | 0.0 | 63.5 | 1 | 3605
40 | 20 | 4 | 135.2 | 8315.2 | 8315.2 | 3834.2 | 8315.2 | 8315.2 | 0.0 | 0.0 | 0.0 | 53.9 | 1 | 2290
40 | 20 | 5 | 94.7 | 6967.8 | 6967.8 | 3044.4 | 6967.8 | 6967.8 | 0.0 | 0.0 | 0.0 | 56.3 | 1 | 2984
50 | 12 | 1 | 3600.2 | 11063.0 | 10431.6 | 4500.3 | 11063.0 | 10584.5 | 5.7 | 5.7 | 4.3 | 59.3 | 0 | 28919
50 | 12 | 2 | 3600.3 | 10545.7 | 9694.5 | 3372.3 | 10517.5 | 9871.9 | 8.1 | 7.8 | 6.4 | 67.9 | 0 | 24501
50 | 12 | 3 | 3600.3 | 10501.1 | 9630.6 | 4310.6 | 10501.1 | 10501.1 | 8.3 | 8.3 | 0.0 | 59.0 | 0 | 20790
50 | 12 | 4 | 3364.1 | 8653.6 | 8653.6 | 3130.6 | 8653.6 | 8653.6 | 0.0 | 0.0 | 0.0 | 63.8 | 1 | 26844
50 | 12 | 5 | 3600.4 | 9576.8 | 8961.9 | 3049.1 | 9521.1 | 9186.5 | 6.4 | 5.9 | 4.1 | 68.0 | 0 | 24696
50 | 16 | 1 | 808.3 | 8693.5 | 8693.5 | 3630.9 | 8693.5 | 8693.5 | 0.0 | 0.0 | 0.0 | 58.2 | 1 | 8758
50 | 16 | 2 | 586.4 | 5966.4 | 5966.4 | 1945.6 | 5966.4 | 5966.4 | 0.0 | 0.0 | 0.0 | 67.4 | 1 | 5195
50 | 16 | 3 | 1587.6 | 9239.6 | 9239.6 | 3403.9 | 9239.6 | 9239.6 | 0.0 | 0.0 | 0.0 | 63.2 | 1 | 10307
50 | 16 | 4 | 1993.7 | 7453.7 | 7453.7 | 2731.0 | 7453.7 | 7453.7 | 0.0 | 0.0 | 0.0 | 63.4 | 1 | 27040
50 | 16 | 5 | 3345.6 | 6924.8 | 6924.8 | 2416.9 | 6924.8 | 6924.8 | 0.0 | 0.0 | 0.0 | 65.1 | 1 | 54551
50 | 25 | 1 | 248.4 | 5561.8 | 5561.8 | 2203.8 | 5561.8 | 5561.8 | 0.0 | 0.0 | 0.0 | 60.4 | 1 | 1472
50 | 25 | 2 | 489.9 | 6891.1 | 6891.1 | 3287.8 | 6891.1 | 6891.1 | 0.0 | 0.0 | 0.0 | 52.3 | 1 | 5455
50 | 25 | 3 | 390.4 | 5582.7 | 5582.7 | 2560.5 | 5582.7 | 5582.7 | 0.0 | 0.0 | 0.0 | 54.1 | 1 | 3790
50 | 25 | 4 | 1330.6 | 5900.7 | 5900.7 | 2401.7 | 5900.7 | 5900.7 | 0.0 | 0.0 | 0.0 | 59.3 | 1 | 38948
50 | 25 | 5 | 243.4 | 6372.0 | 6372.0 | 2718.2 | 6372.0 | 6372.0 | 0.0 | 0.0 | 0.0 | 57.3 | 1 | 2370
Table 90: Summary results table for model $F1_{u}^{flow1}$ $|V|$ | p |  $|$#$|$ | cpu |  g$\overline{\text{U}}$R |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ | gUL | nod
---|---|---|---|---|---|---|---|---
20 | 5 | 5 | 7.7 | 62.7 | 0.0 | 0.0 | 0.0 | 1100
20 | 6 | 5 | 7.3 | 65.0 | 0.0 | 0.0 | 0.0 | 1193
20 | 10 | 5 | 4.8 | 56.8 | 0.0 | 0.0 | 0.0 | 352
30 | 7 | 5 | 75.0 | 65.5 | 0.0 | 0.0 | 0.0 | 4105
30 | 10 | 5 | 69.7 | 61.2 | 0.0 | 0.0 | 0.0 | 3263
30 | 15 | 5 | 24.6 | 59.9 | 0.0 | 0.0 | 0.0 | 2078
40 | 10 | 5 | 702.3 | 63.8 | 0.0 | 0.0 | 0.0 | 24837
40 | 13 | 5 | 451.5 | 61.0 | 0.0 | 0.0 | 0.0 | 10705
40 | 20 | 5 | 178.3 | 59.0 | 0.0 | 0.0 | 0.0 | 4674
50 | 12 | 1 | 3553.1 | 63.6 | 5.5 | 3.0 | 5.7 | 25150
50 | 16 | 5 | 1664.3 | 63.5 | 0.0 | 0.0 | 0.0 | 21170
50 | 25 | 5 | 540.5 | 56.7 | 0.0 | 0.0 | 0.0 | 10407

Table 91: Instances results table for model $F1_{u}^{flow2}$ $|V|$ | p | ins | cpu | objU | objL | objR |  obj$\overline{\text{U}}$ |  obj$\overline{\text{L}}$ | gUL |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ |  g$\overline{\text{U}}$R | opt | nod
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
20 | 5 | 1 | 8.8 | 24444.4 | 24444.4 | 9971.1 | 24444.4 | 24444.4 | 0.0 | 0.0 | 0.0 | 59.2 | 1 | 2868
20 | 5 | 2 | 7.7 | 26585.3 | 26585.3 | 11774.1 | 26585.3 | 26585.3 | 0.0 | 0.0 | 0.0 | 55.7 | 1 | 1083
20 | 5 | 3 | 10.9 | 26159.6 | 26159.6 | 9314.1 | 26159.6 | 26159.6 | 0.0 | 0.0 | 0.0 | 64.4 | 1 | 1788
20 | 5 | 4 | 7.3 | 16558.9 | 16558.9 | 5798.7 | 16558.9 | 16558.9 | 0.0 | 0.0 | 0.0 | 65.0 | 1 | 978
20 | 5 | 5 | 5.2 | 29165.6 | 29165.6 | 12647.6 | 29165.6 | 29165.6 | 0.0 | 0.0 | 0.0 | 56.6 | 1 | 638
20 | 6 | 1 | 9.8 | 22562.4 | 22562.4 | 7904.6 | 22562.4 | 22562.4 | 0.0 | 0.0 | 0.0 | 65.0 | 1 | 1305
20 | 6 | 2 | 1.0 | 20183.5 | 20183.5 | 9439.0 | 20183.5 | 20183.5 | 0.0 | 0.0 | 0.0 | 53.2 | 1 | 1
20 | 6 | 3 | 11.1 | 25238.2 | 25238.2 | 9227.7 | 25238.2 | 25238.2 | 0.0 | 0.0 | 0.0 | 63.4 | 1 | 1353
20 | 6 | 4 | 4.2 | 20161.1 | 20160.7 | 7338.0 | 20161.1 | 20161.1 | 0.0 | 0.0 | 0.0 | 63.6 | 1 | 1268
20 | 6 | 5 | 7.2 | 27296.4 | 27296.4 | 8757.3 | 27296.4 | 27296.4 | 0.0 | 0.0 | 0.0 | 67.9 | 1 | 1703
20 | 10 | 1 | 5.8 | 15074.8 | 15074.8 | 7588.5 | 15074.8 | 15074.8 | 0.0 | 0.0 | 0.0 | 49.7 | 1 | 224
20 | 10 | 2 | 7.3 | 18092.9 | 18092.9 | 8361.4 | 18092.9 | 18092.9 | 0.0 | 0.0 | 0.0 | 53.8 | 1 | 492
20 | 10 | 3 | 2.8 | 14169.6 | 14169.6 | 6973.3 | 14169.6 | 14169.6 | 0.0 | 0.0 | 0.0 | 50.8 | 1 | 449
20 | 10 | 4 | 1.3 | 19027.0 | 19027.0 | 8063.7 | 19027.0 | 19027.0 | 0.0 | 0.0 | 0.0 | 57.6 | 1 | 1
20 | 10 | 5 | 1.8 | 9742.5 | 9742.5 | 4051.0 | 9742.5 | 9742.5 | 0.0 | 0.0 | 0.0 | 58.4 | 1 | 1
30 | 7 | 1 | 57.9 | 15759.0 | 15759.0 | 5403.4 | 15759.0 | 15759.0 | 0.0 | 0.0 | 0.0 | 65.7 | 1 | 1434
30 | 7 | 2 | 47.6 | 17867.0 | 17867.0 | 6197.5 | 17867.0 | 17867.0 | 0.0 | 0.0 | 0.0 | 65.3 | 1 | 2931
30 | 7 | 3 | 45.8 | 15619.6 | 15619.6 | 6572.6 | 15619.6 | 15619.6 | 0.0 | 0.0 | 0.0 | 57.9 | 1 | 2683
30 | 7 | 4 | 65.3 | 18356.9 | 18356.9 | 7554.1 | 18356.9 | 18356.9 | 0.0 | 0.0 | 0.0 | 58.9 | 1 | 2743
30 | 7 | 5 | 117.6 | 15460.6 | 15460.6 | 4939.9 | 15460.6 | 15460.6 | 0.0 | 0.0 | 0.0 | 68.0 | 1 | 5402
30 | 10 | 1 | 32.2 | 12598.8 | 12598.8 | 5073.4 | 12598.8 | 12598.8 | 0.0 | 0.0 | 0.0 | 59.7 | 1 | 1035
30 | 10 | 2 | 60.8 | 9620.6 | 9620.6 | 4258.8 | 9620.6 | 9620.6 | 0.0 | 0.0 | 0.0 | 55.7 | 1 | 674
30 | 10 | 3 | 50.0 | 9329.9 | 9329.9 | 4015.2 | 9329.9 | 9329.9 | 0.0 | 0.0 | 0.0 | 57.0 | 1 | 802
30 | 10 | 4 | 55.0 | 15224.5 | 15224.5 | 6063.4 | 15224.5 | 15224.5 | 0.0 | 0.0 | 0.0 | 60.2 | 1 | 3170
30 | 10 | 5 | 185.8 | 14665.7 | 14665.7 | 5890.0 | 14665.7 | 14665.7 | 0.0 | 0.0 | 0.0 | 59.8 | 1 | 8672
30 | 15 | 1 | 32.6 | 10085.3 | 10085.3 | 3488.0 | 10085.3 | 10085.3 | 0.0 | 0.0 | 0.0 | 65.4 | 1 | 3945
30 | 15 | 2 | 19.7 | 10658.1 | 10658.1 | 4186.7 | 10658.1 | 10658.1 | 0.0 | 0.0 | 0.0 | 60.7 | 1 | 824
30 | 15 | 3 | 13.8 | 8466.4 | 8466.4 | 3192.9 | 8466.4 | 8466.4 | 0.0 | 0.0 | 0.0 | 62.3 | 1 | 260
30 | 15 | 4 | 7.5 | 9980.5 | 9979.5 | 4666.7 | 9980.5 | 9980.5 | 0.0 | 0.0 | 0.0 | 53.2 | 1 | 20
30 | 15 | 5 | 9.4 | 9687.3 | 9686.7 | 4655.6 | 9687.3 | 9687.3 | 0.0 | 0.0 | 0.0 | 51.9 | 1 | 1
40 | 10 | 1 | 696.5 | 14500.9 | 14500.9 | 5660.0 | 14500.9 | 14500.9 | 0.0 | 0.0 | 0.0 | 61.0 | 1 | 26726
40 | 10 | 2 | 683.0 | 12213.5 | 12213.5 | 4252.5 | 12213.5 | 12213.5 | 0.0 | 0.0 | 0.0 | 65.2 | 1 | 22333
40 | 10 | 3 | 498.8 | 11071.1 | 11071.1 | 4613.9 | 11071.1 | 11071.1 | 0.0 | 0.0 | 0.0 | 58.3 | 1 | 5097
40 | 10 | 4 | 269.3 | 9502.1 | 9502.1 | 3997.8 | 9502.0 | 9502.1 | 0.0 | 0.0 | 0.0 | 57.9 | 1 | 4021
40 | 10 | 5 | 881.1 | 10972.0 | 10972.0 | 3721.2 | 10972.0 | 10972.1 | 0.0 | 0.0 | 0.0 | 66.1 | 1 | 19198
40 | 13 | 1 | 435.9 | 9885.2 | 9885.2 | 4284.4 | 9885.2 | 9885.2 | 0.0 | 0.0 | 0.0 | 56.7 | 1 | 6583
40 | 13 | 2 | 75.3 | 9010.9 | 9010.9 | 4376.4 | 9010.9 | 9010.9 | 0.0 | 0.0 | 0.0 | 51.4 | 1 | 3696
40 | 13 | 3 | 463.9 | 10645.3 | 10645.3 | 3778.7 | 10645.3 | 10645.3 | 0.0 | 0.0 | 0.0 | 64.5 | 1 | 8637
40 | 13 | 4 | 277.8 | 8911.8 | 8911.8 | 3419.7 | 8911.8 | 8911.8 | 0.0 | 0.0 | 0.0 | 61.6 | 1 | 6230
40 | 13 | 5 | 505.0 | 11636.1 | 11636.1 | 4540.4 | 11636.1 | 11636.1 | 0.0 | 0.0 | 0.0 | 61.0 | 1 | 5191
40 | 20 | 1 | 126.2 | 9426.4 | 9426.4 | 3908.0 | 9426.4 | 9426.4 | 0.0 | 0.0 | 0.0 | 58.5 | 1 | 4815
40 | 20 | 2 | 82.6 | 6156.3 | 6156.3 | 2429.8 | 6156.3 | 6156.3 | 0.0 | 0.0 | 0.0 | 60.5 | 1 | 733
40 | 20 | 3 | 105.6 | 8245.3 | 8245.3 | 3105.4 | 8245.3 | 8245.3 | 0.0 | 0.0 | 0.0 | 62.3 | 1 | 7055
40 | 20 | 4 | 58.7 | 8315.2 | 8315.2 | 3907.4 | 8315.2 | 8315.2 | 0.0 | 0.0 | 0.0 | 53.0 | 1 | 3453
40 | 20 | 5 | 99.7 | 6967.8 | 6967.8 | 3161.9 | 6967.8 | 6967.8 | 0.0 | 0.0 | 0.0 | 54.6 | 1 | 4232
50 | 12 | 1 | 3600.2 | 11063.0 | 10462.7 | 4631.4 | 11063.0 | 10584.5 | 5.4 | 5.4 | 4.3 | 58.1 | 0 | 17105
50 | 12 | 2 | 3600.7 | 10545.7 | 9395.3 | 3592.2 | 10517.5 | 9871.9 | 10.9 | 10.7 | 6.4 | 65.8 | 0 | 21065
50 | 12 | 3 | 3600.2 | 10501.1 | 10348.8 | 4392.7 | 10501.1 | 10501.1 | 1.4 | 1.4 | 0.0 | 58.2 | 0 | 27363
50 | 12 | 4 | 2817.6 | 8653.6 | 8653.6 | 3273.0 | 8653.6 | 8653.6 | 0.0 | 0.0 | 0.0 | 62.2 | 1 | 22371
50 | 12 | 5 | 3600.2 | 9576.8 | 8895.4 | 3229.1 | 9521.1 | 9186.5 | 7.1 | 6.6 | 4.1 | 66.1 | 0 | 21376
50 | 16 | 1 | 843.7 | 8693.5 | 8693.5 | 3779.4 | 8693.5 | 8693.5 | 0.0 | 0.0 | 0.0 | 56.5 | 1 | 9535
50 | 16 | 2 | 713.9 | 5966.4 | 5966.4 | 2123.4 | 5966.4 | 5966.4 | 0.0 | 0.0 | 0.0 | 64.4 | 1 | 5947
50 | 16 | 3 | 870.0 | 9239.6 | 9239.6 | 3562.0 | 9239.6 | 9239.6 | 0.0 | 0.0 | 0.0 | 61.5 | 1 | 7047
50 | 16 | 4 | 1247.9 | 7453.7 | 7453.7 | 2814.7 | 7453.7 | 7453.7 | 0.0 | 0.0 | 0.0 | 62.2 | 1 | 11386
50 | 16 | 5 | 3600.3 | 6924.8 | 6851.0 | 2615.8 | 6924.8 | 6924.8 | 1.1 | 1.1 | 0.0 | 62.2 | 0 | 45867
50 | 25 | 1 | 212.5 | 5561.8 | 5561.8 | 2305.2 | 5561.8 | 5561.8 | 0.0 | 0.0 | 0.0 | 58.5 | 1 | 1228
50 | 25 | 2 | 234.4 | 6891.1 | 6891.1 | 3357.6 | 6891.1 | 6891.1 | 0.0 | 0.0 | 0.0 | 51.3 | 1 | 3038
50 | 25 | 3 | 228.6 | 5582.7 | 5582.7 | 2620.3 | 5582.7 | 5582.7 | 0.0 | 0.0 | 0.0 | 53.1 | 1 | 4695
50 | 25 | 4 | 496.3 | 5900.7 | 5900.7 | 2440.8 | 5900.7 | 5900.7 | 0.0 | 0.0 | 0.0 | 58.6 | 1 | 8090
50 | 25 | 5 | 272.5 | 6372.0 | 6372.0 | 2743.5 | 6372.0 | 6372.0 | 0.0 | 0.0 | 0.0 | 56.9 | 1 | 1467
Table 92: Summary results table for model $F1_{u}^{flow2}$ $|V|$ | p |  $|$#$|$ | cpu |  g$\overline{\text{U}}$R |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ | gUL | nod
---|---|---|---|---|---|---|---|---
20 | 5 | 5 | 8.0 | 60.2 | 0.0 | 0.0 | 0.0 | 1471
20 | 6 | 5 | 6.7 | 62.6 | 0.0 | 0.0 | 0.0 | 1126
20 | 10 | 5 | 3.8 | 54.1 | 0.0 | 0.0 | 0.0 | 233
30 | 7 | 5 | 66.8 | 63.2 | 0.0 | 0.0 | 0.0 | 3039
30 | 10 | 5 | 76.8 | 58.5 | 0.0 | 0.0 | 0.0 | 2871
30 | 15 | 5 | 16.6 | 58.7 | 0.0 | 0.0 | 0.0 | 1010
40 | 10 | 5 | 605.7 | 61.7 | 0.0 | 0.0 | 0.0 | 15475
40 | 13 | 5 | 351.6 | 59.0 | 0.0 | 0.0 | 0.0 | 6067
40 | 20 | 5 | 94.6 | 57.8 | 0.0 | 0.0 | 0.0 | 4058
50 | 12 | 1 | 3443.8 | 62.1 | 4.8 | 3.0 | 5.0 | 21856
50 | 16 | 4 | 1455.2 | 61.4 | 0.2 | 0.0 | 0.2 | 15956
50 | 25 | 5 | 288.9 | 55.7 | 0.0 | 0.0 | 0.0 | 3704

Table 93: Instances results table for model $F1_{u}^{km}$ $|V|$ | p | ins | cpu | objU | objL | objR |  obj$\overline{\text{U}}$ |  obj$\overline{\text{L}}$ | gUL |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ |  g$\overline{\text{U}}$R | opt | nod
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
20 | 5 | 1 | 5.9 | 24444.4 | 24443.2 | 8678.2 | 24444.4 | 24444.4 | 0.0 | 0.0 | 0.0 | 64.5 | 1 | 1
20 | 5 | 2 | 10.3 | 26585.3 | 26582.9 | 11464.7 | 26585.3 | 26585.3 | 0.0 | 0.0 | 0.0 | 56.9 | 1 | 1
20 | 5 | 3 | 10.9 | 26159.6 | 26159.6 | 8966.5 | 26159.6 | 26159.6 | 0.0 | 0.0 | 0.0 | 65.7 | 1 | 1496
20 | 5 | 4 | 14.3 | 16558.9 | 16558.9 | 5449.0 | 16558.9 | 16558.9 | 0.0 | 0.0 | 0.0 | 67.1 | 1 | 1175
20 | 5 | 5 | 12.1 | 29165.6 | 29165.6 | 11867.1 | 29165.6 | 29165.6 | 0.0 | 0.0 | 0.0 | 59.3 | 1 | 900
20 | 6 | 1 | 17.7 | 22562.4 | 22562.4 | 7620.6 | 22562.4 | 22562.4 | 0.0 | 0.0 | 0.0 | 66.2 | 1 | 1206
20 | 6 | 2 | 2.6 | 20183.5 | 20182.9 | 8736.0 | 20183.5 | 20183.5 | 0.0 | 0.0 | 0.0 | 56.7 | 1 | 1
20 | 6 | 3 | 14.1 | 25238.2 | 25238.2 | 8642.1 | 25238.2 | 25238.2 | 0.0 | 0.0 | 0.0 | 65.8 | 1 | 1273
20 | 6 | 4 | 19.3 | 20161.1 | 20161.1 | 7071.6 | 20161.1 | 20161.1 | 0.0 | 0.0 | 0.0 | 64.9 | 1 | 1143
20 | 6 | 5 | 11.5 | 27296.4 | 27296.4 | 7825.1 | 27296.4 | 27296.4 | 0.0 | 0.0 | 0.0 | 71.3 | 1 | 1291
20 | 10 | 1 | 2.8 | 15074.8 | 15073.6 | 7443.9 | 15074.8 | 15074.8 | 0.0 | 0.0 | 0.0 | 50.6 | 1 | 1
20 | 10 | 2 | 2.9 | 18092.9 | 18091.5 | 7781.0 | 18092.9 | 18092.9 | 0.0 | 0.0 | 0.0 | 57.0 | 1 | 1
20 | 10 | 3 | 3.0 | 14169.6 | 14168.8 | 6073.0 | 14169.6 | 14169.6 | 0.0 | 0.0 | 0.0 | 57.1 | 1 | 1
20 | 10 | 4 | 1.6 | 19027.0 | 19027.0 | 7807.7 | 19027.0 | 19027.0 | 0.0 | 0.0 | 0.0 | 59.0 | 1 | 1
20 | 10 | 5 | 2.5 | 9742.5 | 9742.5 | 3873.3 | 9742.5 | 9742.5 | 0.0 | 0.0 | 0.0 | 60.2 | 1 | 1
30 | 7 | 1 | 101.4 | 15759.0 | 15759.0 | 4913.7 | 15759.0 | 15759.0 | 0.0 | 0.0 | 0.0 | 68.8 | 1 | 1853
30 | 7 | 2 | 139.0 | 17867.0 | 17867.0 | 5869.8 | 17867.0 | 17867.0 | 0.0 | 0.0 | 0.0 | 67.2 | 1 | 2842
30 | 7 | 3 | 50.8 | 15619.6 | 15619.6 | 6348.0 | 15619.6 | 15619.6 | 0.0 | 0.0 | 0.0 | 59.4 | 1 | 1943
30 | 7 | 4 | 173.8 | 18356.9 | 18356.9 | 6956.1 | 18356.9 | 18356.9 | 0.0 | 0.0 | 0.0 | 62.1 | 1 | 3575
30 | 7 | 5 | 216.8 | 15460.6 | 15460.6 | 4669.8 | 15460.6 | 15460.6 | 0.0 | 0.0 | 0.0 | 69.8 | 1 | 4477
30 | 10 | 1 | 38.6 | 12598.8 | 12598.8 | 4558.6 | 12598.8 | 12598.8 | 0.0 | 0.0 | 0.0 | 63.8 | 1 | 285
30 | 10 | 2 | 35.1 | 9620.6 | 9620.6 | 4067.0 | 9620.6 | 9620.6 | 0.0 | 0.0 | 0.0 | 57.7 | 1 | 722
30 | 10 | 3 | 89.9 | 9329.9 | 9329.9 | 3745.2 | 9329.9 | 9329.9 | 0.0 | 0.0 | 0.0 | 59.9 | 1 | 710
30 | 10 | 4 | 102.0 | 15224.5 | 15224.5 | 5750.3 | 15224.5 | 15224.5 | 0.0 | 0.0 | 0.0 | 62.2 | 1 | 3835
30 | 10 | 5 | 211.2 | 14665.7 | 14665.7 | 5544.5 | 14665.7 | 14665.7 | 0.0 | 0.0 | 0.0 | 62.2 | 1 | 4512
30 | 15 | 1 | 31.1 | 10085.3 | 10085.3 | 3267.5 | 10085.3 | 10085.3 | 0.0 | 0.0 | 0.0 | 67.6 | 1 | 696
30 | 15 | 2 | 28.3 | 10658.1 | 10658.1 | 4098.7 | 10658.1 | 10658.1 | 0.0 | 0.0 | 0.0 | 61.5 | 1 | 537
30 | 15 | 3 | 40.1 | 8466.4 | 8466.4 | 3070.2 | 8466.4 | 8466.4 | 0.0 | 0.0 | 0.0 | 63.7 | 1 | 1301
30 | 15 | 4 | 22.2 | 9980.5 | 9980.2 | 4609.0 | 9980.5 | 9980.5 | 0.0 | 0.0 | 0.0 | 53.8 | 1 | 489
30 | 15 | 5 | 21.2 | 9687.3 | 9687.3 | 4582.8 | 9687.3 | 9687.3 | 0.0 | 0.0 | 0.0 | 52.7 | 1 | 93
40 | 10 | 1 | 1063.3 | 14500.9 | 14500.9 | 5513.9 | 14500.9 | 14500.9 | 0.0 | 0.0 | 0.0 | 62.0 | 1 | 25409
40 | 10 | 2 | 904.7 | 12213.5 | 12213.5 | 3884.9 | 12213.5 | 12213.5 | 0.0 | 0.0 | 0.0 | 68.2 | 1 | 19218
40 | 10 | 3 | 363.7 | 11071.1 | 11071.1 | 4374.9 | 11071.1 | 11071.1 | 0.0 | 0.0 | 0.0 | 60.5 | 1 | 5127
40 | 10 | 4 | 143.5 | 9502.1 | 9502.1 | 3676.7 | 9502.0 | 9502.1 | 0.0 | 0.0 | 0.0 | 61.3 | 1 | 5213
40 | 10 | 5 | 630.7 | 10972.1 | 10972.1 | 3593.4 | 10972.0 | 10972.1 | 0.0 | 0.0 | 0.0 | 67.2 | 1 | 10438
40 | 13 | 1 | 265.1 | 9885.2 | 9885.2 | 4092.9 | 9885.2 | 9885.2 | 0.0 | 0.0 | 0.0 | 58.6 | 1 | 6778
40 | 13 | 2 | 157.1 | 9010.9 | 9010.6 | 4280.9 | 9010.9 | 9010.9 | 0.0 | 0.0 | 0.0 | 52.5 | 1 | 1395
40 | 13 | 3 | 233.6 | 10645.3 | 10645.3 | 3675.2 | 10645.3 | 10645.3 | 0.0 | 0.0 | 0.0 | 65.5 | 1 | 4559
40 | 13 | 4 | 439.5 | 8911.8 | 8911.8 | 3069.5 | 8911.8 | 8911.8 | 0.0 | 0.0 | 0.0 | 65.6 | 1 | 3759
40 | 13 | 5 | 330.6 | 11636.1 | 11636.1 | 4354.2 | 11636.1 | 11636.1 | 0.0 | 0.0 | 0.0 | 62.6 | 1 | 7761
40 | 20 | 1 | 701.7 | 9426.4 | 9426.4 | 3793.6 | 9426.4 | 9426.4 | 0.0 | 0.0 | 0.0 | 59.8 | 1 | 2782
40 | 20 | 2 | 167.3 | 6156.3 | 6156.3 | 2372.8 | 6156.3 | 6156.3 | 0.0 | 0.0 | 0.0 | 61.5 | 1 | 5396
40 | 20 | 3 | 446.6 | 8245.3 | 8245.3 | 3012.1 | 8245.3 | 8245.3 | 0.0 | 0.0 | 0.0 | 63.5 | 1 | 4400
40 | 20 | 4 | 233.4 | 8315.2 | 8315.2 | 3834.2 | 8315.2 | 8315.2 | 0.0 | 0.0 | 0.0 | 53.9 | 1 | 3699
40 | 20 | 5 | 122.4 | 6967.8 | 6967.8 | 3044.4 | 6967.8 | 6967.8 | 0.0 | 0.0 | 0.0 | 56.3 | 1 | 2861
50 | 12 | 1 | 3600.4 | 11063.0 | 10395.0 | 4500.3 | 11063.0 | 10584.5 | 6.0 | 6.0 | 4.3 | 59.3 | 0 | 11183
50 | 12 | 2 | 3600.6 | 10714.0 | 9871.9 | 3372.3 | 10517.5 | 9871.9 | 7.9 | 6.1 | 7.9 | 67.9 | 0 | 15170
50 | 12 | 3 | 3600.2 | 10501.1 | 10295.0 | 4310.6 | 10501.1 | 10501.1 | 2.0 | 2.0 | 0.0 | 59.0 | 0 | 14210
50 | 12 | 4 | 2284.2 | 8653.6 | 8653.6 | 3130.6 | 8653.6 | 8653.6 | 0.0 | 0.0 | 0.0 | 63.8 | 1 | 15098
50 | 12 | 5 | 3600.3 | 9521.1 | 9186.5 | 3049.1 | 9521.1 | 9186.5 | 3.5 | 3.5 | 3.5 | 68.0 | 0 | 18649
50 | 16 | 1 | 1254.9 | 8693.5 | 8693.5 | 3630.9 | 8693.5 | 8693.5 | 0.0 | 0.0 | 0.0 | 58.2 | 1 | 5741
50 | 16 | 2 | 948.1 | 5966.4 | 5966.4 | 1945.6 | 5966.4 | 5966.4 | 0.0 | 0.0 | 0.0 | 67.4 | 1 | 3948
50 | 16 | 3 | 1807.9 | 9239.6 | 9239.6 | 3403.9 | 9239.6 | 9239.6 | 0.0 | 0.0 | 0.0 | 63.2 | 1 | 5586
50 | 16 | 4 | 1288.3 | 7453.7 | 7453.7 | 2731.0 | 7453.7 | 7453.7 | 0.0 | 0.0 | 0.0 | 63.4 | 1 | 3713
50 | 16 | 5 | 1257.3 | 6924.8 | 6924.8 | 2416.9 | 6924.8 | 6924.8 | 0.0 | 0.0 | 0.0 | 65.1 | 1 | 7182
50 | 25 | 1 | 1165.3 | 5561.8 | 5561.8 | 2203.8 | 5561.8 | 5561.8 | 0.0 | 0.0 | 0.0 | 60.4 | 1 | 1618
50 | 25 | 2 | 950.1 | 6891.1 | 6891.1 | 3287.8 | 6891.1 | 6891.1 | 0.0 | 0.0 | 0.0 | 52.3 | 1 | 1859
50 | 25 | 3 | 427.5 | 5582.7 | 5582.7 | 2560.5 | 5582.7 | 5582.7 | 0.0 | 0.0 | 0.0 | 54.1 | 1 | 2085
50 | 25 | 4 | 1166.3 | 5900.7 | 5900.7 | 2401.7 | 5900.7 | 5900.7 | 0.0 | 0.0 | 0.0 | 59.3 | 1 | 1746
50 | 25 | 5 | 1294.4 | 6372.0 | 6372.0 | 2718.2 | 6372.0 | 6372.0 | 0.0 | 0.0 | 0.0 | 57.3 | 1 | 1597
Table 94: Summary results table for model $F1_{u}^{km}$ $|V|$ | p |  $|$#$|$ | cpu |  g$\overline{\text{U}}$R |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ | gUL | nod
---|---|---|---|---|---|---|---|---
20 | 5 | 5 | 10.7 | 62.7 | 0.0 | 0.0 | 0.0 | 715
20 | 6 | 5 | 13.0 | 65.0 | 0.0 | 0.0 | 0.0 | 983
20 | 10 | 5 | 2.6 | 56.8 | 0.0 | 0.0 | 0.0 | 1
30 | 7 | 5 | 136.4 | 65.5 | 0.0 | 0.0 | 0.0 | 2938
30 | 10 | 5 | 95.4 | 61.2 | 0.0 | 0.0 | 0.0 | 2013
30 | 15 | 5 | 28.6 | 59.9 | 0.0 | 0.0 | 0.0 | 623
40 | 10 | 5 | 621.2 | 63.8 | 0.0 | 0.0 | 0.0 | 13081
40 | 13 | 5 | 285.2 | 61.0 | 0.0 | 0.0 | 0.0 | 4850
40 | 20 | 5 | 334.3 | 59.0 | 0.0 | 0.0 | 0.0 | 3828
50 | 12 | 1 | 3337.1 | 63.6 | 3.5 | 3.1 | 3.9 | 14862
50 | 16 | 5 | 1311.3 | 63.5 | 0.0 | 0.0 | 0.0 | 5234
50 | 25 | 5 | 1000.7 | 56.7 | 0.0 | 0.0 | 0.0 | 1781

Table 95: Instances results table for model $F1_{u}^{sub1}$ $|V|$ | p | ins | cpu | objU | objL | objR |  obj$\overline{\text{U}}$ |  obj$\overline{\text{L}}$ | gUL |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ |  g$\overline{\text{U}}$R | opt | nod
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
20 | 5 | 1 | 8.5 | 24444.4 | 24444.4 | 8678.2 | 24444.4 | 24444.4 | 0.0 | 0.0 | 0.0 | 64.5 | 1 | 3120
20 | 5 | 2 | 5.4 | 26585.3 | 26585.3 | 11464.7 | 26585.3 | 26585.3 | 0.0 | 0.0 | 0.0 | 56.9 | 1 | 892
20 | 5 | 3 | 8.9 | 26159.6 | 26159.6 | 8966.5 | 26159.6 | 26159.6 | 0.0 | 0.0 | 0.0 | 65.7 | 1 | 2177
20 | 5 | 4 | 6.0 | 16558.9 | 16558.9 | 5449.0 | 16558.9 | 16558.9 | 0.0 | 0.0 | 0.0 | 67.1 | 1 | 1742
20 | 5 | 5 | 8.4 | 29165.6 | 29165.6 | 11867.1 | 29165.6 | 29165.6 | 0.0 | 0.0 | 0.0 | 59.3 | 1 | 3266
20 | 6 | 1 | 14.2 | 22562.4 | 22562.4 | 7620.6 | 22562.4 | 22562.4 | 0.0 | 0.0 | 0.0 | 66.2 | 1 | 3569
20 | 6 | 2 | 4.0 | 20183.5 | 20183.5 | 8736.0 | 20183.5 | 20183.5 | 0.0 | 0.0 | 0.0 | 56.7 | 1 | 1
20 | 6 | 3 | 6.1 | 25238.2 | 25238.2 | 8642.1 | 25238.2 | 25238.2 | 0.0 | 0.0 | 0.0 | 65.8 | 1 | 2246
20 | 6 | 4 | 23.9 | 20161.1 | 20161.1 | 7071.6 | 20161.1 | 20161.1 | 0.0 | 0.0 | 0.0 | 64.9 | 1 | 2478
20 | 6 | 5 | 5.7 | 27296.4 | 27296.4 | 7825.1 | 27296.4 | 27296.4 | 0.0 | 0.0 | 0.0 | 71.3 | 1 | 2540
20 | 10 | 1 | 18.9 | 15074.8 | 15074.8 | 7443.9 | 15074.8 | 15074.8 | 0.0 | 0.0 | 0.0 | 50.6 | 1 | 2696
20 | 10 | 2 | 6.1 | 18092.9 | 18092.9 | 7781.0 | 18092.9 | 18092.9 | 0.0 | 0.0 | 0.0 | 57.0 | 1 | 3055
20 | 10 | 3 | 30.5 | 14169.6 | 14169.6 | 6073.0 | 14169.6 | 14169.6 | 0.0 | 0.0 | 0.0 | 57.1 | 1 | 7456
20 | 10 | 4 | 2.9 | 19027.0 | 19027.0 | 7807.7 | 19027.0 | 19027.0 | 0.0 | 0.0 | 0.0 | 59.0 | 1 | 1065
20 | 10 | 5 | 4.8 | 9742.5 | 9742.5 | 3873.3 | 9742.5 | 9742.5 | 0.0 | 0.0 | 0.0 | 60.2 | 1 | 905
30 | 7 | 1 | 38.0 | 15759.0 | 15759.0 | 4913.7 | 15759.0 | 15759.0 | 0.0 | 0.0 | 0.0 | 68.8 | 1 | 4587
30 | 7 | 2 | 90.3 | 17867.0 | 17867.0 | 5869.8 | 17867.0 | 17867.0 | 0.0 | 0.0 | 0.0 | 67.2 | 1 | 2455
30 | 7 | 3 | 65.9 | 15619.6 | 15619.6 | 6348.0 | 15619.6 | 15619.6 | 0.0 | 0.0 | 0.0 | 59.4 | 1 | 3242
30 | 7 | 4 | 82.9 | 18356.9 | 18356.9 | 6956.1 | 18356.9 | 18356.9 | 0.0 | 0.0 | 0.0 | 62.1 | 1 | 3767
30 | 7 | 5 | 320.6 | 15460.6 | 15460.6 | 4669.8 | 15460.6 | 15460.6 | 0.0 | 0.0 | 0.0 | 69.8 | 1 | 19345
30 | 10 | 1 | 19.6 | 12598.8 | 12598.8 | 4558.6 | 12598.8 | 12598.8 | 0.0 | 0.0 | 0.0 | 63.8 | 1 | 1991
30 | 10 | 2 | 59.5 | 9620.6 | 9620.6 | 4067.0 | 9620.6 | 9620.6 | 0.0 | 0.0 | 0.0 | 57.7 | 1 | 2434
30 | 10 | 3 | 28.7 | 9329.9 | 9329.9 | 3745.2 | 9329.9 | 9329.9 | 0.0 | 0.0 | 0.0 | 59.9 | 1 | 1645
30 | 10 | 4 | 49.9 | 15224.5 | 15224.3 | 5750.3 | 15224.5 | 15224.5 | 0.0 | 0.0 | 0.0 | 62.2 | 1 | 4684
30 | 10 | 5 | 780.9 | 14665.7 | 14665.7 | 5544.5 | 14665.7 | 14665.7 | 0.0 | 0.0 | 0.0 | 62.2 | 1 | 92094
30 | 15 | 1 | 340.5 | 10085.3 | 10085.3 | 3267.5 | 10085.3 | 10085.3 | 0.0 | 0.0 | 0.0 | 67.6 | 1 | 59795
30 | 15 | 2 | 106.1 | 10658.1 | 10658.1 | 4098.7 | 10658.1 | 10658.1 | 0.0 | 0.0 | 0.0 | 61.5 | 1 | 10294
30 | 15 | 3 | 162.9 | 8466.4 | 8466.4 | 3070.2 | 8466.4 | 8466.4 | 0.0 | 0.0 | 0.0 | 63.7 | 1 | 25634
30 | 15 | 4 | 61.3 | 9980.5 | 9980.0 | 4609.0 | 9980.5 | 9980.5 | 0.0 | 0.0 | 0.0 | 53.8 | 1 | 1971
30 | 15 | 5 | 14.5 | 9687.3 | 9687.1 | 4582.8 | 9687.3 | 9687.3 | 0.0 | 0.0 | 0.0 | 52.7 | 1 | 117
40 | 10 | 1 | 3600.3 | 14500.9 | 14211.8 | 5513.9 | 14500.9 | 14500.9 | 2.0 | 2.0 | 0.0 | 62.0 | 0 | 194273
40 | 10 | 2 | 2026.9 | 12213.5 | 12213.5 | 3884.9 | 12213.5 | 12213.5 | 0.0 | 0.0 | 0.0 | 68.2 | 1 | 104324
40 | 10 | 3 | 218.3 | 11071.1 | 11071.1 | 4374.9 | 11071.1 | 11071.1 | 0.0 | 0.0 | 0.0 | 60.5 | 1 | 4503
40 | 10 | 4 | 257.2 | 9502.1 | 9502.1 | 3676.7 | 9502.0 | 9502.1 | 0.0 | 0.0 | 0.0 | 61.3 | 1 | 2586
40 | 10 | 5 | 1458.9 | 10972.1 | 10972.1 | 3593.4 | 10972.0 | 10972.1 | 0.0 | 0.0 | 0.0 | 67.2 | 1 | 62975
40 | 13 | 1 | 598.1 | 9885.2 | 9885.2 | 4092.9 | 9885.2 | 9885.2 | 0.0 | 0.0 | 0.0 | 58.6 | 1 | 43464
40 | 13 | 2 | 333.4 | 9010.9 | 9010.9 | 4280.9 | 9010.9 | 9010.9 | 0.0 | 0.0 | 0.0 | 52.5 | 1 | 3180
40 | 13 | 3 | 1232.1 | 10645.3 | 10645.3 | 3675.2 | 10645.3 | 10645.3 | 0.0 | 0.0 | 0.0 | 65.5 | 1 | 86000
40 | 13 | 4 | 546.9 | 8911.8 | 8911.8 | 3069.5 | 8911.8 | 8911.8 | 0.0 | 0.0 | 0.0 | 65.6 | 1 | 22461
40 | 13 | 5 | 1316.5 | 11636.1 | 11636.1 | 4354.2 | 11636.1 | 11636.1 | 0.0 | 0.0 | 0.0 | 62.6 | 1 | 175695
40 | 20 | 1 | 3600.7 | 10038.1 | 8226.5 | 3793.6 | 9426.4 | 9426.4 | 18.0 | 12.7 | 6.1 | 59.8 | 0 | 287338
40 | 20 | 2 | 702.4 | 6156.3 | 6156.3 | 2372.8 | 6156.3 | 6156.3 | 0.0 | 0.0 | 0.0 | 61.5 | 1 | 64652
40 | 20 | 3 | 3600.5 | 8440.9 | 7844.6 | 3012.1 | 8245.3 | 8245.3 | 7.1 | 4.9 | 2.3 | 63.5 | 0 | 181565
40 | 20 | 4 | 3601.0 | 8628.5 | 7942.1 | 3834.2 | 8315.2 | 8315.2 | 8.0 | 4.5 | 3.6 | 53.9 | 0 | 248509
40 | 20 | 5 | 493.4 | 6967.8 | 6967.8 | 3044.4 | 6967.8 | 6967.8 | 0.0 | 0.0 | 0.0 | 56.3 | 1 | 49917
50 | 12 | 1 | 3600.5 | 14196.5 | 10019.1 | 4500.3 | 11063.0 | 10584.5 | 29.4 | 9.4 | 25.4 | 59.3 | 0 | 38310
50 | 12 | 2 | 3600.4 | 10742.3 | 9645.9 | 3372.3 | 10517.5 | 9871.9 | 10.2 | 8.3 | 8.1 | 67.9 | 0 | 44910
50 | 12 | 3 | 3600.2 | 10501.1 | 10148.1 | 4310.6 | 10501.1 | 10501.1 | 3.4 | 3.4 | 0.0 | 59.0 | 0 | 61538
50 | 12 | 4 | 3600.3 | 8682.3 | 7976.8 | 3130.6 | 8653.6 | 8653.6 | 8.1 | 7.8 | 0.3 | 63.8 | 0 | 50129
50 | 12 | 5 | 3600.2 | 9521.1 | 8930.7 | 3049.1 | 9521.1 | 9186.5 | 6.2 | 6.2 | 3.5 | 68.0 | 0 | 54054
50 | 16 | 1 | 1241.7 | 8693.5 | 8693.5 | 3630.9 | 8693.5 | 8693.5 | 0.0 | 0.0 | 0.0 | 58.2 | 1 | 18107
50 | 16 | 2 | 1145.5 | 5966.4 | 5966.4 | 1945.6 | 5966.4 | 5966.4 | 0.0 | 0.0 | 0.0 | 67.4 | 1 | 20820
50 | 16 | 3 | 3600.1 | 9239.6 | 9069.6 | 3403.9 | 9239.6 | 9239.6 | 1.8 | 1.8 | 0.0 | 63.2 | 0 | 71473
50 | 16 | 4 | 1511.5 | 7453.7 | 7453.7 | 2731.0 | 7453.7 | 7453.7 | 0.0 | 0.0 | 0.0 | 63.4 | 1 | 19142
50 | 16 | 5 | 3600.3 | 8209.9 | 6287.5 | 2416.9 | 6924.8 | 6924.8 | 23.4 | 9.2 | 15.7 | 65.1 | 0 | 57101
50 | 25 | 1 | 3600.4 | 51323.3 | 5361.6 | 2203.8 | 5561.8 | 5561.8 | 89.6 | 3.6 | 89.2 | 60.4 | 0 | 86655
50 | 25 | 2 | 3601.3 | 7185.8 | 6720.1 | 3287.8 | 6891.1 | 6891.1 | 6.5 | 2.5 | 4.1 | 52.3 | 0 | 113437
50 | 25 | 3 | 3600.8 | 48559.7 | 5322.8 | 2560.5 | 5582.7 | 5582.7 | 89.0 | 4.7 | 88.5 | 54.1 | 0 | 83815
50 | 25 | 4 | 3600.5 | 6524.9 | 5690.4 | 2401.7 | 5900.7 | 5900.7 | 12.8 | 3.6 | 9.6 | 59.3 | 0 | 97945
50 | 25 | 5 | 2070.7 | 6372.0 | 6371.4 | 2718.2 | 6372.0 | 6372.0 | 0.0 | 0.0 | 0.0 | 57.3 | 1 | 66467
Table 96: Summary results table for model $F1_{u}^{sub1}$ $|V|$ | p |  $|$#$|$ | cpu |  g$\overline{\text{U}}$R |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ | gUL | nod
---|---|---|---|---|---|---|---|---
20 | 5 | 5 | 7.4 | 62.7 | 0.0 | 0.0 | 0.0 | 2239
20 | 6 | 5 | 10.8 | 65.0 | 0.0 | 0.0 | 0.0 | 2167
20 | 10 | 5 | 12.6 | 56.8 | 0.0 | 0.0 | 0.0 | 3035
30 | 7 | 5 | 119.5 | 65.5 | 0.0 | 0.0 | 0.0 | 6679
30 | 10 | 5 | 187.7 | 61.2 | 0.0 | 0.0 | 0.0 | 20570
30 | 15 | 5 | 137.1 | 59.9 | 0.0 | 0.0 | 0.0 | 19562
40 | 10 | 4 | 1512.3 | 63.8 | 0.4 | 0.0 | 0.4 | 73732
40 | 13 | 5 | 805.4 | 61.0 | 0.0 | 0.0 | 0.0 | 66160
40 | 20 | 2 | 2399.6 | 59.0 | 4.4 | 2.4 | 6.6 | 166396
50 | 12 | 0 | 3600.3 | 63.6 | 7.0 | 7.5 | 11.5 | 49788
50 | 16 | 3 | 2219.8 | 63.5 | 2.2 | 3.1 | 5.0 | 37329
50 | 25 | 1 | 3294.7 | 56.7 | 2.9 | 38.3 | 39.6 | 89664

Table 97: Instances results table for model $F1_{u}^{sub2}$ $|V|$ | p | ins | cpu | objU | objL | objR |  obj$\overline{\text{U}}$ |  obj$\overline{\text{L}}$ | gUL |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ |  g$\overline{\text{U}}$R | opt | nod
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
20 | 5 | 1 | 19.4 | 24444.4 | 24444.4 | 8678.2 | 24444.4 | 24444.4 | 0.0 | 0.0 | 0.0 | 64.5 | 1 | 5663
20 | 5 | 2 | 5.0 | 26585.3 | 26585.3 | 11464.7 | 26585.3 | 26585.3 | 0.0 | 0.0 | 0.0 | 56.9 | 1 | 924
20 | 5 | 3 | 8.9 | 26159.6 | 26159.6 | 8966.5 | 26159.6 | 26159.6 | 0.0 | 0.0 | 0.0 | 65.7 | 1 | 2177
20 | 5 | 4 | 7.3 | 16558.9 | 16558.9 | 5449.0 | 16558.9 | 16558.9 | 0.0 | 0.0 | 0.0 | 67.1 | 1 | 1742
20 | 5 | 5 | 6.2 | 29165.6 | 29165.6 | 11867.1 | 29165.6 | 29165.6 | 0.0 | 0.0 | 0.0 | 59.3 | 1 | 2540
20 | 6 | 1 | 24.2 | 22562.4 | 22562.4 | 7620.6 | 22562.4 | 22562.4 | 0.0 | 0.0 | 0.0 | 66.2 | 1 | 2931
20 | 6 | 2 | 3.5 | 20183.5 | 20183.5 | 8736.0 | 20183.5 | 20183.5 | 0.0 | 0.0 | 0.0 | 56.7 | 1 | 26
20 | 6 | 3 | 7.7 | 25238.2 | 25238.2 | 8642.1 | 25238.2 | 25238.2 | 0.0 | 0.0 | 0.0 | 65.8 | 1 | 2807
20 | 6 | 4 | 13.4 | 20161.1 | 20161.1 | 7071.6 | 20161.1 | 20161.1 | 0.0 | 0.0 | 0.0 | 64.9 | 1 | 3150
20 | 6 | 5 | 10.1 | 27296.4 | 27296.4 | 7825.1 | 27296.4 | 27296.4 | 0.0 | 0.0 | 0.0 | 71.3 | 1 | 3794
20 | 10 | 1 | 9.3 | 15074.8 | 15074.8 | 7443.9 | 15074.8 | 15074.8 | 0.0 | 0.0 | 0.0 | 50.6 | 1 | 857
20 | 10 | 2 | 14.2 | 18092.9 | 18092.9 | 7781.0 | 18092.9 | 18092.9 | 0.0 | 0.0 | 0.0 | 57.0 | 1 | 2198
20 | 10 | 3 | 4.2 | 14169.6 | 14169.6 | 6073.0 | 14169.6 | 14169.6 | 0.0 | 0.0 | 0.0 | 57.1 | 1 | 181
20 | 10 | 4 | 2.3 | 19027.0 | 19027.0 | 7807.7 | 19027.0 | 19027.0 | 0.0 | 0.0 | 0.0 | 59.0 | 1 | 675
20 | 10 | 5 | 2.6 | 9742.5 | 9742.5 | 3873.3 | 9742.5 | 9742.5 | 0.0 | 0.0 | 0.0 | 60.2 | 1 | 142
30 | 7 | 1 | 68.3 | 15759.0 | 15759.0 | 4913.7 | 15759.0 | 15759.0 | 0.0 | 0.0 | 0.0 | 68.8 | 1 | 2370
30 | 7 | 2 | 161.0 | 17867.0 | 17867.0 | 5869.8 | 17867.0 | 17867.0 | 0.0 | 0.0 | 0.0 | 67.2 | 1 | 3554
30 | 7 | 3 | 62.2 | 15619.6 | 15619.6 | 6348.0 | 15619.6 | 15619.6 | 0.0 | 0.0 | 0.0 | 59.4 | 1 | 3558
30 | 7 | 4 | 147.8 | 18356.9 | 18356.9 | 6956.1 | 18356.9 | 18356.9 | 0.0 | 0.0 | 0.0 | 62.1 | 1 | 9245
30 | 7 | 5 | 413.1 | 15460.6 | 15460.6 | 4669.8 | 15460.6 | 15460.6 | 0.0 | 0.0 | 0.0 | 69.8 | 1 | 30683
30 | 10 | 1 | 46.7 | 12598.8 | 12598.8 | 4558.6 | 12598.8 | 12598.8 | 0.0 | 0.0 | 0.0 | 63.8 | 1 | 1365
30 | 10 | 2 | 62.8 | 9620.6 | 9620.6 | 4067.0 | 9620.6 | 9620.6 | 0.0 | 0.0 | 0.0 | 57.7 | 1 | 2335
30 | 10 | 3 | 80.1 | 9329.9 | 9329.9 | 3745.2 | 9329.9 | 9329.9 | 0.0 | 0.0 | 0.0 | 59.9 | 1 | 1742
30 | 10 | 4 | 76.1 | 15224.5 | 15224.5 | 5750.3 | 15224.5 | 15224.5 | 0.0 | 0.0 | 0.0 | 62.2 | 1 | 2482
30 | 10 | 5 | 1029.5 | 14665.7 | 14665.7 | 5544.5 | 14665.7 | 14665.7 | 0.0 | 0.0 | 0.0 | 62.2 | 1 | 72013
30 | 15 | 1 | 76.0 | 10085.3 | 10085.3 | 3267.5 | 10085.3 | 10085.3 | 0.0 | 0.0 | 0.0 | 67.6 | 1 | 2307
30 | 15 | 2 | 84.1 | 10658.1 | 10658.1 | 4098.7 | 10658.1 | 10658.1 | 0.0 | 0.0 | 0.0 | 61.5 | 1 | 4139
30 | 15 | 3 | 26.2 | 8466.4 | 8466.4 | 3070.2 | 8466.4 | 8466.4 | 0.0 | 0.0 | 0.0 | 63.7 | 1 | 1977
30 | 15 | 4 | 14.7 | 9980.5 | 9980.5 | 4609.0 | 9980.5 | 9980.5 | 0.0 | 0.0 | 0.0 | 53.8 | 1 | 646
30 | 15 | 5 | 9.6 | 9687.3 | 9687.3 | 4582.8 | 9687.3 | 9687.3 | 0.0 | 0.0 | 0.0 | 52.7 | 1 | 479
40 | 10 | 1 | 3600.3 | 14500.9 | 14084.3 | 5513.9 | 14500.9 | 14500.9 | 2.9 | 2.9 | 0.0 | 62.0 | 0 | 231176
40 | 10 | 2 | 3249.0 | 12213.5 | 12213.5 | 3884.9 | 12213.5 | 12213.5 | 0.0 | 0.0 | 0.0 | 68.2 | 1 | 184174
40 | 10 | 3 | 216.7 | 11071.1 | 11071.1 | 4374.9 | 11071.1 | 11071.1 | 0.0 | 0.0 | 0.0 | 60.5 | 1 | 10117
40 | 10 | 4 | 206.4 | 9502.1 | 9502.1 | 3676.7 | 9502.0 | 9502.1 | 0.0 | 0.0 | 0.0 | 61.3 | 1 | 3870
40 | 10 | 5 | 3600.4 | 10972.1 | 10315.8 | 3593.4 | 10972.0 | 10972.1 | 6.0 | 6.0 | 0.0 | 67.2 | 0 | 154997
40 | 13 | 1 | 1541.0 | 9885.2 | 9885.2 | 4092.9 | 9885.2 | 9885.2 | 0.0 | 0.0 | 0.0 | 58.6 | 1 | 84126
40 | 13 | 2 | 302.4 | 9010.9 | 9010.9 | 4280.9 | 9010.9 | 9010.9 | 0.0 | 0.0 | 0.0 | 52.5 | 1 | 11164
40 | 13 | 3 | 1894.9 | 10645.3 | 10645.3 | 3675.2 | 10645.3 | 10645.3 | 0.0 | 0.0 | 0.0 | 65.5 | 1 | 133655
40 | 13 | 4 | 773.3 | 8911.8 | 8911.8 | 3069.5 | 8911.8 | 8911.8 | 0.0 | 0.0 | 0.0 | 65.6 | 1 | 22957
40 | 13 | 5 | 2787.0 | 11636.1 | 11636.1 | 4354.2 | 11636.1 | 11636.1 | 0.0 | 0.0 | 0.0 | 62.6 | 1 | 189003
40 | 20 | 1 | 458.7 | 9426.4 | 9426.4 | 3793.6 | 9426.4 | 9426.4 | 0.0 | 0.0 | 0.0 | 59.8 | 1 | 7245
40 | 20 | 2 | 152.4 | 6156.3 | 6155.6 | 2372.8 | 6156.3 | 6156.3 | 0.0 | 0.0 | 0.0 | 61.5 | 1 | 3172
40 | 20 | 3 | 510.9 | 8245.3 | 8245.3 | 3012.1 | 8245.3 | 8245.3 | 0.0 | 0.0 | 0.0 | 63.5 | 1 | 36971
40 | 20 | 4 | 122.4 | 8315.2 | 8315.2 | 3834.2 | 8315.2 | 8315.2 | 0.0 | 0.0 | 0.0 | 53.9 | 1 | 3831
40 | 20 | 5 | 200.1 | 6967.8 | 6967.8 | 3044.4 | 6967.8 | 6967.8 | 0.0 | 0.0 | 0.0 | 56.3 | 1 | 3693
50 | 12 | 1 | 3600.7 | 11063.0 | 10124.3 | 4500.3 | 11063.0 | 10584.5 | 8.5 | 8.5 | 4.3 | 59.3 | 0 | 36054
50 | 12 | 2 | 3600.2 | 10517.5 | 9744.8 | 3372.3 | 10517.5 | 9871.9 | 7.3 | 7.3 | 6.1 | 67.9 | 0 | 37097
50 | 12 | 3 | 3600.4 | 11025.8 | 9738.0 | 4310.6 | 10501.1 | 10501.1 | 11.7 | 7.3 | 4.8 | 59.0 | 0 | 38674
50 | 12 | 4 | 3600.3 | 8682.3 | 7879.6 | 3130.6 | 8653.6 | 8653.6 | 9.2 | 8.9 | 0.3 | 63.8 | 0 | 39769
50 | 12 | 5 | 3600.8 | 9834.0 | 8285.9 | 3049.1 | 9521.1 | 9186.5 | 15.7 | 13.0 | 6.6 | 68.0 | 0 | 27464
50 | 16 | 1 | 3600.4 | 8697.4 | 8481.7 | 3630.9 | 8693.5 | 8693.5 | 2.5 | 2.4 | 0.0 | 58.2 | 0 | 51639
50 | 16 | 2 | 1368.1 | 5966.4 | 5966.4 | 1945.6 | 5966.4 | 5966.4 | 0.0 | 0.0 | 0.0 | 67.4 | 1 | 14440
50 | 16 | 3 | 3600.3 | 9239.6 | 8935.9 | 3403.9 | 9239.6 | 9239.6 | 3.3 | 3.3 | 0.0 | 63.2 | 0 | 36158
50 | 16 | 4 | 3600.5 | 7725.8 | 7002.0 | 2731.0 | 7453.7 | 7453.7 | 9.4 | 6.1 | 3.5 | 63.4 | 0 | 38522
50 | 16 | 5 | 3600.4 | 8042.7 | 6198.1 | 2416.9 | 6924.8 | 6924.8 | 22.9 | 10.5 | 13.9 | 65.1 | 0 | 56885
50 | 25 | 1 | 363.5 | 5561.8 | 5561.8 | 2203.8 | 5561.8 | 5561.8 | 0.0 | 0.0 | 0.0 | 60.4 | 1 | 1809
50 | 25 | 2 | 1000.4 | 6891.1 | 6891.1 | 3287.8 | 6891.1 | 6891.1 | 0.0 | 0.0 | 0.0 | 52.3 | 1 | 13728
50 | 25 | 3 | 795.1 | 5582.7 | 5582.7 | 2560.5 | 5582.7 | 5582.7 | 0.0 | 0.0 | 0.0 | 54.1 | 1 | 2393
50 | 25 | 4 | 1066.5 | 5900.7 | 5900.7 | 2401.7 | 5900.7 | 5900.7 | 0.0 | 0.0 | 0.0 | 59.3 | 1 | 18599
50 | 25 | 5 | 326.3 | 6372.0 | 6372.0 | 2718.2 | 6372.0 | 6372.0 | 0.0 | 0.0 | 0.0 | 57.3 | 1 | 2105
Table 98: Summary results table for model $F1_{u}^{sub2}$ $|V|$ | p |  $|$#$|$ | cpu |  g$\overline{\text{U}}$R |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ | gUL | nod
---|---|---|---|---|---|---|---|---
20 | 5 | 5 | 9.4 | 62.7 | 0.0 | 0.0 | 0.0 | 2609
20 | 6 | 5 | 11.8 | 65.0 | 0.0 | 0.0 | 0.0 | 2542
20 | 10 | 5 | 6.5 | 56.8 | 0.0 | 0.0 | 0.0 | 811
30 | 7 | 5 | 170.5 | 65.5 | 0.0 | 0.0 | 0.0 | 9882
30 | 10 | 5 | 259.0 | 61.2 | 0.0 | 0.0 | 0.0 | 15987
30 | 15 | 5 | 42.1 | 59.9 | 0.0 | 0.0 | 0.0 | 1910
40 | 10 | 3 | 2174.6 | 63.8 | 1.8 | 0.0 | 1.8 | 116867
40 | 13 | 5 | 1459.7 | 61.0 | 0.0 | 0.0 | 0.0 | 88181
40 | 20 | 5 | 288.9 | 59.0 | 0.0 | 0.0 | 0.0 | 10982
50 | 12 | 0 | 3600.5 | 63.6 | 9.0 | 4.4 | 10.5 | 35812
50 | 16 | 1 | 3153.9 | 63.5 | 4.5 | 3.5 | 7.6 | 39529
50 | 25 | 5 | 710.4 | 56.7 | 0.0 | 0.0 | 0.0 | 7727

Table 99: Instances results table for model $F2_{u}^{mtz}$ $|V|$ | p | ins | cpu | objU | objL | objR |  obj$\overline{\text{U}}$ |  obj$\overline{\text{L}}$ | gUL |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ |  g$\overline{\text{U}}$R | opt | nod
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
20 | 5 | 1 | 18.2 | 24444.4 | 24444.4 | 11628.1 | 24444.4 | 24444.4 | 0.0 | 0.0 | 0.0 | 52.4 | 1 | 7897
20 | 5 | 2 | 25.4 | 26585.3 | 26585.3 | 13320.5 | 26585.3 | 26585.3 | 0.0 | 0.0 | 0.0 | 49.9 | 1 | 7165
20 | 5 | 3 | 38.1 | 26159.6 | 26158.8 | 11682.6 | 26159.6 | 26159.6 | 0.0 | 0.0 | 0.0 | 55.3 | 1 | 13743
20 | 5 | 4 | 14.9 | 16558.9 | 16558.9 | 6951.0 | 16558.9 | 16558.9 | 0.0 | 0.0 | 0.0 | 58.0 | 1 | 4842
20 | 5 | 5 | 22.2 | 29165.6 | 29165.6 | 14127.3 | 29165.6 | 29165.6 | 0.0 | 0.0 | 0.0 | 51.6 | 1 | 6846
20 | 6 | 1 | 99.5 | 22562.4 | 22562.4 | 10139.9 | 22562.4 | 22562.4 | 0.0 | 0.0 | 0.0 | 55.1 | 1 | 5234
20 | 6 | 2 | 2.0 | 20183.5 | 20183.5 | 10220.2 | 20183.5 | 20183.5 | 0.0 | 0.0 | 0.0 | 49.4 | 1 | 1
20 | 6 | 3 | 47.7 | 25238.2 | 25238.2 | 12124.6 | 25238.2 | 25238.2 | 0.0 | 0.0 | 0.0 | 52.0 | 1 | 3699
20 | 6 | 4 | 61.3 | 20161.1 | 20161.1 | 9580.3 | 20161.1 | 20161.1 | 0.0 | 0.0 | 0.0 | 52.5 | 1 | 1792
20 | 6 | 5 | 55.8 | 27296.4 | 27296.4 | 12384.4 | 27296.4 | 27296.4 | 0.0 | 0.0 | 0.0 | 54.6 | 1 | 3806
20 | 10 | 1 | 7.3 | 15074.8 | 15074.8 | 8445.0 | 15074.8 | 15074.8 | 0.0 | 0.0 | 0.0 | 44.0 | 1 | 294
20 | 10 | 2 | 11.5 | 18092.9 | 18092.9 | 9917.5 | 18092.9 | 18092.9 | 0.0 | 0.0 | 0.0 | 45.2 | 1 | 2163
20 | 10 | 3 | 9.2 | 14169.6 | 14169.6 | 7261.8 | 14169.6 | 14169.6 | 0.0 | 0.0 | 0.0 | 48.8 | 1 | 82
20 | 10 | 4 | 3.2 | 19027.0 | 19025.6 | 10680.8 | 19027.0 | 19027.0 | 0.0 | 0.0 | 0.0 | 43.9 | 1 | 1
20 | 10 | 5 | 2.1 | 9742.5 | 9742.5 | 5785.7 | 9742.5 | 9742.5 | 0.0 | 0.0 | 0.0 | 40.6 | 1 | 1
30 | 7 | 1 | 261.7 | 15759.0 | 15759.0 | 7366.4 | 15759.0 | 15759.0 | 0.0 | 0.0 | 0.0 | 53.3 | 1 | 4099
30 | 7 | 2 | 312.9 | 17867.0 | 17867.0 | 7335.1 | 17867.0 | 17867.0 | 0.0 | 0.0 | 0.0 | 59.0 | 1 | 3832
30 | 7 | 3 | 312.7 | 15619.6 | 15619.6 | 7474.4 | 15619.6 | 15619.6 | 0.0 | 0.0 | 0.0 | 52.1 | 1 | 6690
30 | 7 | 4 | 400.7 | 18356.9 | 18356.9 | 9136.9 | 18356.9 | 18356.9 | 0.0 | 0.0 | 0.0 | 50.2 | 1 | 5727
30 | 7 | 5 | 531.9 | 15460.6 | 15460.6 | 6495.7 | 15460.6 | 15460.6 | 0.0 | 0.0 | 0.0 | 58.0 | 1 | 12499
30 | 10 | 1 | 161.8 | 12598.8 | 12598.8 | 6404.5 | 12598.8 | 12598.8 | 0.0 | 0.0 | 0.0 | 49.2 | 1 | 2347
30 | 10 | 2 | 182.2 | 9620.6 | 9620.6 | 5334.9 | 9620.6 | 9620.6 | 0.0 | 0.0 | 0.0 | 44.5 | 1 | 2577
30 | 10 | 3 | 197.4 | 9329.9 | 9329.9 | 5107.6 | 9329.9 | 9329.9 | 0.0 | 0.0 | 0.0 | 45.3 | 1 | 2061
30 | 10 | 4 | 219.7 | 15224.5 | 15224.5 | 7446.2 | 15224.5 | 15224.5 | 0.0 | 0.0 | 0.0 | 51.1 | 1 | 4160
30 | 10 | 5 | 377.3 | 14665.7 | 14665.7 | 7183.9 | 14665.7 | 14665.7 | 0.0 | 0.0 | 0.0 | 51.0 | 1 | 10933
30 | 15 | 1 | 41.3 | 10085.3 | 10085.3 | 4987.7 | 10085.3 | 10085.3 | 0.0 | 0.0 | 0.0 | 50.5 | 1 | 4641
30 | 15 | 2 | 21.9 | 10658.1 | 10658.1 | 6108.2 | 10658.1 | 10658.1 | 0.0 | 0.0 | 0.0 | 42.7 | 1 | 1163
30 | 15 | 3 | 25.5 | 8466.4 | 8466.4 | 4447.6 | 8466.4 | 8466.4 | 0.0 | 0.0 | 0.0 | 47.5 | 1 | 1168
30 | 15 | 4 | 20.6 | 9980.5 | 9980.5 | 6027.4 | 9980.5 | 9980.5 | 0.0 | 0.0 | 0.0 | 39.6 | 1 | 1303
30 | 15 | 5 | 18.9 | 9687.3 | 9687.3 | 5553.1 | 9687.3 | 9687.3 | 0.0 | 0.0 | 0.0 | 42.7 | 1 | 602
40 | 10 | 1 | 3366.8 | 14500.9 | 14500.9 | 6302.4 | 14500.9 | 14500.9 | 0.0 | 0.0 | 0.0 | 56.5 | 1 | 73325
40 | 10 | 2 | 3246.1 | 12213.5 | 12213.5 | 5155.4 | 12213.5 | 12213.5 | 0.0 | 0.0 | 0.0 | 57.8 | 1 | 72635
40 | 10 | 3 | 790.3 | 11071.1 | 11071.1 | 5381.9 | 11071.1 | 11071.1 | 0.0 | 0.0 | 0.0 | 51.4 | 1 | 7037
40 | 10 | 4 | 574.1 | 9502.1 | 9502.1 | 4294.9 | 9502.0 | 9502.1 | 0.0 | 0.0 | 0.0 | 54.8 | 1 | 6895
40 | 10 | 5 | 2654.1 | 10972.1 | 10972.0 | 4805.2 | 10972.0 | 10972.1 | 0.0 | 0.0 | 0.0 | 56.2 | 1 | 49635
40 | 13 | 1 | 1183.4 | 9885.2 | 9885.2 | 5384.9 | 9885.2 | 9885.2 | 0.0 | 0.0 | 0.0 | 45.5 | 1 | 18922
40 | 13 | 2 | 587.2 | 9010.9 | 9010.9 | 5015.9 | 9010.9 | 9010.9 | 0.0 | 0.0 | 0.0 | 44.3 | 1 | 5292
40 | 13 | 3 | 950.1 | 10645.3 | 10645.3 | 5340.0 | 10645.3 | 10645.3 | 0.0 | 0.0 | 0.0 | 49.8 | 1 | 10068
40 | 13 | 4 | 769.1 | 8911.8 | 8911.8 | 4340.7 | 8911.8 | 8911.8 | 0.0 | 0.0 | 0.0 | 51.3 | 1 | 10415
40 | 13 | 5 | 3425.2 | 11636.1 | 11636.1 | 5300.9 | 11636.1 | 11636.1 | 0.0 | 0.0 | 0.0 | 54.4 | 1 | 55410
40 | 20 | 1 | 690.0 | 9426.4 | 9426.4 | 4913.9 | 9426.4 | 9426.4 | 0.0 | 0.0 | 0.0 | 47.9 | 1 | 68048
40 | 20 | 2 | 35.6 | 6156.3 | 6156.3 | 3244.3 | 6156.3 | 6156.3 | 0.0 | 0.0 | 0.0 | 47.3 | 1 | 4564
40 | 20 | 3 | 766.9 | 8245.3 | 8245.3 | 4057.7 | 8245.3 | 8245.3 | 0.0 | 0.0 | 0.0 | 50.8 | 1 | 75300
40 | 20 | 4 | 132.4 | 8315.2 | 8315.2 | 4813.6 | 8315.2 | 8315.2 | 0.0 | 0.0 | 0.0 | 42.1 | 1 | 2376
40 | 20 | 5 | 39.1 | 6967.8 | 6967.8 | 3912.2 | 6967.8 | 6967.8 | 0.0 | 0.0 | 0.0 | 43.9 | 1 | 4062
50 | 12 | 1 | 3600.3 | 11063.0 | 9802.6 | 5373.6 | 11063.0 | 10584.5 | 11.4 | 11.4 | 4.3 | 51.4 | 0 | 6389
50 | 12 | 2 | 3600.2 | 10887.2 | 8760.3 | 4343.6 | 10517.5 | 9871.9 | 19.5 | 16.7 | 9.3 | 58.7 | 0 | 4772
50 | 12 | 3 | 3600.4 | 10501.1 | 9306.6 | 5432.0 | 10501.1 | 10501.1 | 11.4 | 11.4 | 0.0 | 48.3 | 0 | 2540
50 | 12 | 4 | 3600.7 | 8682.3 | 7499.1 | 3856.7 | 8653.6 | 8653.6 | 13.6 | 13.3 | 0.3 | 55.4 | 0 | 4321
50 | 12 | 5 | 3600.4 | 9521.1 | 8596.1 | 4455.9 | 9521.1 | 9186.5 | 9.7 | 9.7 | 3.5 | 53.2 | 0 | 6794
50 | 16 | 1 | 3165.7 | 8693.5 | 8693.5 | 4584.7 | 8693.5 | 8693.5 | 0.0 | 0.0 | 0.0 | 47.3 | 1 | 10877
50 | 16 | 2 | 3600.3 | 5966.4 | 5849.6 | 2923.1 | 5966.4 | 5966.4 | 2.0 | 2.0 | 0.0 | 51.0 | 0 | 9022
50 | 16 | 3 | 3600.3 | 9239.6 | 8920.9 | 4706.2 | 9239.6 | 9239.6 | 3.5 | 3.5 | 0.0 | 49.1 | 0 | 8507
50 | 16 | 4 | 3600.2 | 7453.7 | 7203.1 | 3632.3 | 7453.7 | 7453.7 | 3.4 | 3.4 | 0.0 | 51.3 | 0 | 11699
50 | 16 | 5 | 3600.3 | 6924.8 | 6446.6 | 3213.4 | 6924.8 | 6924.8 | 6.9 | 6.9 | 0.0 | 53.6 | 0 | 8528
50 | 25 | 1 | 174.0 | 5561.8 | 5561.8 | 3106.5 | 5561.8 | 5561.8 | 0.0 | 0.0 | 0.0 | 44.1 | 1 | 1825
50 | 25 | 2 | 146.7 | 6891.1 | 6891.1 | 4073.8 | 6891.1 | 6891.1 | 0.0 | 0.0 | 0.0 | 40.9 | 1 | 1947
50 | 25 | 3 | 189.1 | 5582.7 | 5582.7 | 3320.2 | 5582.7 | 5582.7 | 0.0 | 0.0 | 0.0 | 40.5 | 1 | 2184
50 | 25 | 4 | 280.1 | 5900.7 | 5900.7 | 3237.2 | 5900.7 | 5900.7 | 0.0 | 0.0 | 0.0 | 45.1 | 1 | 4012
50 | 25 | 5 | 227.8 | 6372.0 | 6372.0 | 3536.6 | 6372.0 | 6372.0 | 0.0 | 0.0 | 0.0 | 44.5 | 1 | 2595
Table 100: Summary results table for model $F2_{u}^{mtz}$ $|V|$ | p |  $|$#$|$ | cpu |  g$\overline{\text{U}}$R |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ | gUL | nod
---|---|---|---|---|---|---|---|---
20 | 5 | 5 | 23.8 | 53.4 | 0.0 | 0.0 | 0.0 | 8099
20 | 6 | 5 | 53.3 | 52.7 | 0.0 | 0.0 | 0.0 | 2906
20 | 10 | 5 | 6.7 | 44.5 | 0.0 | 0.0 | 0.0 | 508
30 | 7 | 5 | 364.0 | 54.5 | 0.0 | 0.0 | 0.0 | 6569
30 | 10 | 5 | 227.7 | 48.2 | 0.0 | 0.0 | 0.0 | 4416
30 | 15 | 5 | 25.6 | 44.6 | 0.0 | 0.0 | 0.0 | 1775
40 | 10 | 5 | 2126.3 | 55.3 | 0.0 | 0.0 | 0.0 | 41905
40 | 13 | 5 | 1383.0 | 49.1 | 0.0 | 0.0 | 0.0 | 20021
40 | 20 | 5 | 332.8 | 46.4 | 0.0 | 0.0 | 0.0 | 30870
50 | 12 | 0 | 3600.4 | 53.4 | 12.5 | 3.5 | 13.1 | 4963
50 | 16 | 1 | 3513.4 | 50.5 | 3.2 | 0.0 | 3.2 | 9727
50 | 25 | 5 | 203.5 | 43.0 | 0.0 | 0.0 | 0.0 | 2513

Table 101: Instances results table for model $F2_{u}^{flow}$ $|V|$ | p | ins | cpu | objU | objL | objR |  obj$\overline{\text{U}}$ |  obj$\overline{\text{L}}$ | gUL |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ |  g$\overline{\text{U}}$R | opt | nod
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
20 | 5 | 1 | 33.6 | 24444.4 | 24444.4 | 11628.1 | 24444.4 | 24444.4 | 0.0 | 0.0 | 0.0 | 52.4 | 1 | 4175
20 | 5 | 2 | 16.6 | 26585.3 | 26585.3 | 13320.5 | 26585.3 | 26585.3 | 0.0 | 0.0 | 0.0 | 49.9 | 1 | 11085
20 | 5 | 3 | 53.8 | 26159.6 | 26159.6 | 11682.6 | 26159.6 | 26159.6 | 0.0 | 0.0 | 0.0 | 55.3 | 1 | 3156
20 | 5 | 4 | 16.2 | 16558.9 | 16558.9 | 6951.0 | 16558.9 | 16558.9 | 0.0 | 0.0 | 0.0 | 58.0 | 1 | 5335
20 | 5 | 5 | 29.5 | 29165.6 | 29165.6 | 14127.3 | 29165.6 | 29165.6 | 0.0 | 0.0 | 0.0 | 51.6 | 1 | 2856
20 | 6 | 1 | 70.1 | 22562.4 | 22562.4 | 10139.9 | 22562.4 | 22562.4 | 0.0 | 0.0 | 0.0 | 55.1 | 1 | 4579
20 | 6 | 2 | 3.0 | 20183.5 | 20183.5 | 10220.2 | 20183.5 | 20183.5 | 0.0 | 0.0 | 0.0 | 49.4 | 1 | 1
20 | 6 | 3 | 46.4 | 25238.2 | 25238.2 | 12124.6 | 25238.2 | 25238.2 | 0.0 | 0.0 | 0.0 | 52.0 | 1 | 3628
20 | 6 | 4 | 38.8 | 20161.1 | 20161.1 | 9580.3 | 20161.1 | 20161.1 | 0.0 | 0.0 | 0.0 | 52.5 | 1 | 1740
20 | 6 | 5 | 53.1 | 27296.4 | 27296.4 | 12384.4 | 27296.4 | 27296.4 | 0.0 | 0.0 | 0.0 | 54.6 | 1 | 3210
20 | 10 | 1 | 12.2 | 15074.8 | 15074.8 | 8445.0 | 15074.8 | 15074.8 | 0.0 | 0.0 | 0.0 | 44.0 | 1 | 3845
20 | 10 | 2 | 22.6 | 18092.9 | 18092.9 | 9917.5 | 18092.9 | 18092.9 | 0.0 | 0.0 | 0.0 | 45.2 | 1 | 3877
20 | 10 | 3 | 5.1 | 14169.6 | 14169.6 | 7261.8 | 14169.6 | 14169.6 | 0.0 | 0.0 | 0.0 | 48.8 | 1 | 499
20 | 10 | 4 | 7.1 | 19027.0 | 19027.0 | 10680.8 | 19027.0 | 19027.0 | 0.0 | 0.0 | 0.0 | 43.9 | 1 | 132
20 | 10 | 5 | 2.8 | 9742.5 | 9742.5 | 5785.7 | 9742.5 | 9742.5 | 0.0 | 0.0 | 0.0 | 40.6 | 1 | 1
30 | 7 | 1 | 272.7 | 15759.0 | 15759.0 | 7366.4 | 15759.0 | 15759.0 | 0.0 | 0.0 | 0.0 | 53.3 | 1 | 3686
30 | 7 | 2 | 270.5 | 17867.0 | 17867.0 | 7335.1 | 17867.0 | 17867.0 | 0.0 | 0.0 | 0.0 | 59.0 | 1 | 3582
30 | 7 | 3 | 194.5 | 15619.6 | 15619.6 | 7474.4 | 15619.6 | 15619.6 | 0.0 | 0.0 | 0.0 | 52.1 | 1 | 5542
30 | 7 | 4 | 454.1 | 18356.9 | 18356.9 | 9136.9 | 18356.9 | 18356.9 | 0.0 | 0.0 | 0.0 | 50.2 | 1 | 10961
30 | 7 | 5 | 1627.6 | 15460.6 | 15460.6 | 6495.7 | 15460.6 | 15460.6 | 0.0 | 0.0 | 0.0 | 58.0 | 1 | 44952
30 | 10 | 1 | 137.4 | 12598.8 | 12598.8 | 6404.5 | 12598.8 | 12598.8 | 0.0 | 0.0 | 0.0 | 49.2 | 1 | 1676
30 | 10 | 2 | 107.1 | 9620.6 | 9620.6 | 5334.9 | 9620.6 | 9620.6 | 0.0 | 0.0 | 0.0 | 44.5 | 1 | 2489
30 | 10 | 3 | 222.7 | 9329.9 | 9329.9 | 5107.6 | 9329.9 | 9329.9 | 0.0 | 0.0 | 0.0 | 45.3 | 1 | 2011
30 | 10 | 4 | 73.8 | 15224.5 | 15224.5 | 7446.2 | 15224.5 | 15224.5 | 0.0 | 0.0 | 0.0 | 51.1 | 1 | 2843
30 | 10 | 5 | 1288.5 | 14665.7 | 14665.7 | 7183.9 | 14665.7 | 14665.7 | 0.0 | 0.0 | 0.0 | 51.0 | 1 | 43768
30 | 15 | 1 | 30.5 | 10085.3 | 10085.3 | 4987.7 | 10085.3 | 10085.3 | 0.0 | 0.0 | 0.0 | 50.5 | 1 | 5685
30 | 15 | 2 | 35.9 | 10658.1 | 10658.1 | 6108.2 | 10658.1 | 10658.1 | 0.0 | 0.0 | 0.0 | 42.7 | 1 | 8781
30 | 15 | 3 | 19.5 | 8466.4 | 8466.4 | 4447.6 | 8466.4 | 8466.4 | 0.0 | 0.0 | 0.0 | 47.5 | 1 | 2377
30 | 15 | 4 | 14.2 | 9980.5 | 9980.2 | 6027.4 | 9980.5 | 9980.5 | 0.0 | 0.0 | 0.0 | 39.6 | 1 | 347
30 | 15 | 5 | 13.7 | 9687.3 | 9687.3 | 5553.1 | 9687.3 | 9687.3 | 0.0 | 0.0 | 0.0 | 42.7 | 1 | 454
40 | 10 | 1 | 3600.7 | 14500.9 | 13814.5 | 6302.4 | 14500.9 | 14500.9 | 4.7 | 4.7 | 0.0 | 56.5 | 0 | 94040
40 | 10 | 2 | 3603.7 | 12213.5 | 11259.1 | 5155.4 | 12213.5 | 12213.5 | 7.8 | 7.8 | 0.0 | 57.8 | 0 | 35736
40 | 10 | 3 | 824.0 | 11071.1 | 11071.1 | 5381.9 | 11071.1 | 11071.1 | 0.0 | 0.0 | 0.0 | 51.4 | 1 | 9141
40 | 10 | 4 | 274.0 | 9502.1 | 9502.1 | 4294.9 | 9502.0 | 9502.1 | 0.0 | 0.0 | 0.0 | 54.8 | 1 | 4495
40 | 10 | 5 | 3600.4 | 10972.0 | 9764.3 | 4805.2 | 10972.0 | 10972.1 | 11.0 | 11.0 | 0.0 | 56.2 | 0 | 40032
40 | 13 | 1 | 3600.6 | 9885.2 | 9750.0 | 5384.9 | 9885.2 | 9885.2 | 1.4 | 1.4 | 0.0 | 45.5 | 0 | 145227
40 | 13 | 2 | 448.1 | 9010.9 | 9010.9 | 5015.9 | 9010.9 | 9010.9 | 0.0 | 0.0 | 0.0 | 44.3 | 1 | 5985
40 | 13 | 3 | 3600.4 | 10645.3 | 10306.0 | 5340.0 | 10645.3 | 10645.3 | 3.2 | 3.2 | 0.0 | 49.8 | 0 | 128506
40 | 13 | 4 | 1447.4 | 8911.8 | 8911.8 | 4340.7 | 8911.8 | 8911.8 | 0.0 | 0.0 | 0.0 | 51.3 | 1 | 21556
40 | 13 | 5 | 3600.3 | 11636.1 | 11161.0 | 5300.9 | 11636.1 | 11636.1 | 4.1 | 4.1 | 0.0 | 54.4 | 0 | 80692
40 | 20 | 1 | 313.4 | 9426.4 | 9426.4 | 4913.9 | 9426.4 | 9426.4 | 0.0 | 0.0 | 0.0 | 47.9 | 1 | 3714
40 | 20 | 2 | 148.2 | 6156.3 | 6156.3 | 3244.3 | 6156.3 | 6156.3 | 0.0 | 0.0 | 0.0 | 47.3 | 1 | 2777
40 | 20 | 3 | 329.4 | 8245.3 | 8245.3 | 4057.7 | 8245.3 | 8245.3 | 0.0 | 0.0 | 0.0 | 50.8 | 1 | 4536
40 | 20 | 4 | 34.5 | 8315.2 | 8315.2 | 4813.6 | 8315.2 | 8315.2 | 0.0 | 0.0 | 0.0 | 42.1 | 1 | 6888
40 | 20 | 5 | 60.7 | 6967.8 | 6967.8 | 3912.2 | 6967.8 | 6967.8 | 0.0 | 0.0 | 0.0 | 43.9 | 1 | 7033
50 | 12 | 1 | 3600.4 | 11063.0 | 9672.4 | 5373.6 | 11063.0 | 10584.5 | 12.6 | 12.6 | 4.3 | 51.4 | 0 | 8175
50 | 12 | 2 | 3600.3 | 10872.5 | 9054.9 | 4343.6 | 10517.5 | 9871.9 | 16.7 | 13.9 | 9.2 | 58.7 | 0 | 9528
50 | 12 | 3 | 3600.3 | 10501.1 | 9665.6 | 5432.0 | 10501.1 | 10501.1 | 8.0 | 8.0 | 0.0 | 48.3 | 0 | 9636
50 | 12 | 4 | 3600.3 | 8682.3 | 7554.9 | 3856.7 | 8653.6 | 8653.6 | 13.0 | 12.7 | 0.3 | 55.4 | 0 | 10552
50 | 12 | 5 | 3600.2 | 9576.8 | 8403.9 | 4455.9 | 9521.1 | 9186.5 | 12.2 | 11.7 | 4.1 | 53.2 | 0 | 13137
50 | 16 | 1 | 2511.1 | 8693.5 | 8693.5 | 4584.7 | 8693.5 | 8693.5 | 0.0 | 0.0 | 0.0 | 47.3 | 1 | 15790
50 | 16 | 2 | 2476.2 | 5966.4 | 5966.4 | 2923.1 | 5966.4 | 5966.4 | 0.0 | 0.0 | 0.0 | 51.0 | 1 | 18136
50 | 16 | 3 | 3600.6 | 9239.6 | 8816.2 | 4706.2 | 9239.6 | 9239.6 | 4.6 | 4.6 | 0.0 | 49.1 | 0 | 11590
50 | 16 | 4 | 3600.2 | 7453.7 | 7048.4 | 3632.3 | 7453.7 | 7453.7 | 5.4 | 5.4 | 0.0 | 51.3 | 0 | 20520
50 | 16 | 5 | 3600.4 | 6961.2 | 6204.4 | 3213.4 | 6924.8 | 6924.8 | 10.9 | 10.4 | 0.5 | 53.6 | 0 | 20968
50 | 25 | 1 | 204.8 | 5561.8 | 5561.8 | 3106.5 | 5561.8 | 5561.8 | 0.0 | 0.0 | 0.0 | 44.1 | 1 | 2501
50 | 25 | 2 | 328.9 | 6891.1 | 6891.1 | 4073.8 | 6891.1 | 6891.1 | 0.0 | 0.0 | 0.0 | 40.9 | 1 | 5674
50 | 25 | 3 | 198.4 | 5582.7 | 5582.7 | 3320.2 | 5582.7 | 5582.7 | 0.0 | 0.0 | 0.0 | 40.5 | 1 | 6625
50 | 25 | 4 | 1414.9 | 5900.7 | 5900.7 | 3237.2 | 5900.7 | 5900.7 | 0.0 | 0.0 | 0.0 | 45.1 | 1 | 40060
50 | 25 | 5 | 251.3 | 6372.0 | 6372.0 | 3536.6 | 6372.0 | 6372.0 | 0.0 | 0.0 | 0.0 | 44.5 | 1 | 2097
Table 102: Summary results table for model $F2_{u}^{flow}$ $|V|$ | p |  $|$#$|$ | cpu |  g$\overline{\text{U}}$R |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ | gUL | nod
---|---|---|---|---|---|---|---|---
20 | 5 | 5 | 29.9 | 53.4 | 0.0 | 0.0 | 0.0 | 5321
20 | 6 | 5 | 42.3 | 52.7 | 0.0 | 0.0 | 0.0 | 2632
20 | 10 | 5 | 10.0 | 44.5 | 0.0 | 0.0 | 0.0 | 1671
30 | 7 | 5 | 563.9 | 54.5 | 0.0 | 0.0 | 0.0 | 13745
30 | 10 | 5 | 365.9 | 48.2 | 0.0 | 0.0 | 0.0 | 10557
30 | 15 | 5 | 22.8 | 44.6 | 0.0 | 0.0 | 0.0 | 3529
40 | 10 | 2 | 2380.6 | 55.3 | 4.7 | 0.0 | 4.7 | 36689
40 | 13 | 2 | 2539.4 | 49.1 | 1.7 | 0.0 | 1.7 | 76393
40 | 20 | 5 | 177.2 | 46.4 | 0.0 | 0.0 | 0.0 | 4990
50 | 12 | 0 | 3600.3 | 53.4 | 11.8 | 3.6 | 12.5 | 10206
50 | 16 | 2 | 3157.7 | 50.5 | 4.1 | 0.1 | 4.2 | 17401
50 | 25 | 5 | 479.7 | 43.0 | 0.0 | 0.0 | 0.0 | 11391

Table 103: Instances results table for model $F2_{u}^{km}$ $|V|$ | p | ins | cpu | objU | objL | objR |  obj$\overline{\text{U}}$ |  obj$\overline{\text{L}}$ | gUL |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ |  g$\overline{\text{U}}$R | opt | nod
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
20 | 5 | 1 | 96.8 | 24444.4 | 24444.4 | 11628.1 | 24444.4 | 24444.4 | 0.0 | 0.0 | 0.0 | 52.4 | 1 | 10156
20 | 5 | 2 | 108.0 | 26585.3 | 26585.3 | 13320.5 | 26585.3 | 26585.3 | 0.0 | 0.0 | 0.0 | 49.9 | 1 | 5736
20 | 5 | 3 | 192.7 | 26159.6 | 26159.6 | 11682.6 | 26159.6 | 26159.6 | 0.0 | 0.0 | 0.0 | 55.3 | 1 | 7561
20 | 5 | 4 | 119.1 | 16558.9 | 16558.9 | 6951.0 | 16558.9 | 16558.9 | 0.0 | 0.0 | 0.0 | 58.0 | 1 | 6036
20 | 5 | 5 | 96.3 | 29165.6 | 29165.6 | 14127.3 | 29165.6 | 29165.6 | 0.0 | 0.0 | 0.0 | 51.6 | 1 | 5305
20 | 6 | 1 | 206.1 | 22562.4 | 22562.4 | 10139.9 | 22562.4 | 22562.4 | 0.0 | 0.0 | 0.0 | 55.1 | 1 | 2073
20 | 6 | 2 | 4.2 | 20183.5 | 20183.5 | 10220.2 | 20183.5 | 20183.5 | 0.0 | 0.0 | 0.0 | 49.4 | 1 | 1
20 | 6 | 3 | 146.6 | 25238.2 | 25238.2 | 12124.6 | 25238.2 | 25238.2 | 0.0 | 0.0 | 0.0 | 52.0 | 1 | 2883
20 | 6 | 4 | 159.8 | 20161.1 | 20161.1 | 9580.3 | 20161.1 | 20161.1 | 0.0 | 0.0 | 0.0 | 52.5 | 1 | 2448
20 | 6 | 5 | 266.0 | 27296.4 | 27296.4 | 12384.4 | 27296.4 | 27296.4 | 0.0 | 0.0 | 0.0 | 54.6 | 1 | 1982
20 | 10 | 1 | 18.1 | 15074.8 | 15074.8 | 8445.0 | 15074.8 | 15074.8 | 0.0 | 0.0 | 0.0 | 44.0 | 1 | 172
20 | 10 | 2 | 13.4 | 18092.9 | 18092.9 | 9917.5 | 18092.9 | 18092.9 | 0.0 | 0.0 | 0.0 | 45.2 | 1 | 81
20 | 10 | 3 | 10.3 | 14169.6 | 14169.6 | 7261.8 | 14169.6 | 14169.6 | 0.0 | 0.0 | 0.0 | 48.8 | 1 | 104
20 | 10 | 4 | 5.4 | 19027.0 | 19027.0 | 10680.8 | 19027.0 | 19027.0 | 0.0 | 0.0 | 0.0 | 43.9 | 1 | 1
20 | 10 | 5 | 3.3 | 9742.5 | 9742.5 | 5785.7 | 9742.5 | 9742.5 | 0.0 | 0.0 | 0.0 | 40.6 | 1 | 1
30 | 7 | 1 | 2656.9 | 15759.0 | 15759.0 | 7366.4 | 15759.0 | 15759.0 | 0.0 | 0.0 | 0.0 | 53.3 | 1 | 2950
30 | 7 | 2 | 2262.8 | 17867.0 | 17867.0 | 7335.1 | 17867.0 | 17867.0 | 0.0 | 0.0 | 0.0 | 59.0 | 1 | 3275
30 | 7 | 3 | 1812.7 | 15619.6 | 15619.6 | 7474.4 | 15619.6 | 15619.6 | 0.0 | 0.0 | 0.0 | 52.1 | 1 | 4336
30 | 7 | 4 | 2915.1 | 18356.9 | 18356.9 | 9136.9 | 18356.9 | 18356.9 | 0.0 | 0.0 | 0.0 | 50.2 | 1 | 5770
30 | 7 | 5 | 3600.1 | 15460.6 | 14995.6 | 6495.7 | 15460.6 | 15460.6 | 3.0 | 3.0 | 0.0 | 58.0 | 0 | 4724
30 | 10 | 1 | 767.8 | 12598.8 | 12598.8 | 6404.5 | 12598.8 | 12598.8 | 0.0 | 0.0 | 0.0 | 49.2 | 1 | 2443
30 | 10 | 2 | 818.5 | 9620.6 | 9620.6 | 5334.9 | 9620.6 | 9620.6 | 0.0 | 0.0 | 0.0 | 44.5 | 1 | 2449
30 | 10 | 3 | 1278.7 | 9329.9 | 9329.9 | 5107.6 | 9329.9 | 9329.9 | 0.0 | 0.0 | 0.0 | 45.3 | 1 | 2391
30 | 10 | 4 | 1948.0 | 15224.5 | 15224.5 | 7446.2 | 15224.5 | 15224.5 | 0.0 | 0.0 | 0.0 | 51.1 | 1 | 1965
30 | 10 | 5 | 1569.5 | 14665.7 | 14665.7 | 7183.9 | 14665.7 | 14665.7 | 0.0 | 0.0 | 0.0 | 51.0 | 1 | 4451
30 | 15 | 1 | 53.9 | 10085.3 | 10085.3 | 4987.7 | 10085.3 | 10085.3 | 0.0 | 0.0 | 0.0 | 50.5 | 1 | 395
30 | 15 | 2 | 22.8 | 10658.1 | 10658.1 | 6108.2 | 10658.1 | 10658.1 | 0.0 | 0.0 | 0.0 | 42.7 | 1 | 117
30 | 15 | 3 | 50.7 | 8466.4 | 8466.4 | 4447.6 | 8466.4 | 8466.4 | 0.0 | 0.0 | 0.0 | 47.5 | 1 | 1670
30 | 15 | 4 | 19.2 | 9980.5 | 9979.6 | 6027.4 | 9980.5 | 9980.5 | 0.0 | 0.0 | 0.0 | 39.6 | 1 | 241
30 | 15 | 5 | 52.8 | 9687.3 | 9687.3 | 5553.1 | 9687.3 | 9687.3 | 0.0 | 0.0 | 0.0 | 42.7 | 1 | 124
40 | 10 | 1 | 3600.4 | 14500.9 | 11433.4 | 6302.4 | 14500.9 | 14500.9 | 21.1 | 21.1 | 0.0 | 56.5 | 0 | 1476
40 | 10 | 2 | 3600.4 | 12213.5 | 9548.9 | 5155.4 | 12213.5 | 12213.5 | 21.8 | 21.8 | 0.0 | 57.8 | 0 | 1133
40 | 10 | 3 | 3600.4 | 11071.1 | 9674.1 | 5381.9 | 11071.1 | 11071.1 | 12.6 | 12.6 | 0.0 | 51.4 | 0 | 1850
40 | 10 | 4 | 3600.2 | 9502.0 | 8461.5 | 4294.9 | 9502.0 | 9502.1 | 10.9 | 10.9 | 0.0 | 54.8 | 0 | 1954
40 | 10 | 5 | 3600.4 | 10972.1 | 8825.6 | 4805.2 | 10972.0 | 10972.1 | 19.6 | 19.6 | 0.0 | 56.2 | 0 | 1712
40 | 13 | 1 | 3600.4 | 9885.2 | 8713.8 | 5384.9 | 9885.2 | 9885.2 | 11.8 | 11.8 | 0.0 | 45.5 | 0 | 889
40 | 13 | 2 | 3600.2 | 9010.9 | 8511.7 | 5015.9 | 9010.9 | 9010.9 | 5.5 | 5.5 | 0.0 | 44.3 | 0 | 1966
40 | 13 | 3 | 3600.4 | 10645.3 | 9376.4 | 5340.0 | 10645.3 | 10645.3 | 11.9 | 11.9 | 0.0 | 49.8 | 0 | 968
40 | 13 | 4 | 3600.2 | 8911.8 | 7656.7 | 4340.7 | 8911.8 | 8911.8 | 14.1 | 14.1 | 0.0 | 51.3 | 0 | 1816
40 | 13 | 5 | 3600.3 | 11636.1 | 10140.5 | 5300.9 | 11636.1 | 11636.1 | 12.8 | 12.8 | 0.0 | 54.4 | 0 | 1793
40 | 20 | 1 | 2388.5 | 9426.4 | 9426.4 | 4913.9 | 9426.4 | 9426.4 | 0.0 | 0.0 | 0.0 | 47.9 | 1 | 2371
40 | 20 | 2 | 2356.1 | 6156.3 | 6156.3 | 3244.3 | 6156.3 | 6156.3 | 0.0 | 0.0 | 0.0 | 47.3 | 1 | 3130
40 | 20 | 3 | 2640.2 | 8245.3 | 8245.3 | 4057.7 | 8245.3 | 8245.3 | 0.0 | 0.0 | 0.0 | 50.8 | 1 | 2174
40 | 20 | 4 | 1356.7 | 8315.2 | 8315.2 | 4813.6 | 8315.2 | 8315.2 | 0.0 | 0.0 | 0.0 | 42.1 | 1 | 2032
40 | 20 | 5 | 1195.0 | 6967.8 | 6967.8 | 3912.2 | 6967.8 | 6967.8 | 0.0 | 0.0 | 0.0 | 43.9 | 1 | 2090
50 | 12 | 1 | 3600.2 | 11063.0 | 8920.4 | 5373.6 | 11063.0 | 10584.5 | 19.4 | 19.4 | 4.3 | 51.4 | 0 | 18
50 | 12 | 2 | 3600.5 | 11005.2 | 7957.2 | 4343.6 | 10517.5 | 9871.9 | 27.7 | 24.3 | 10.3 | 58.7 | 0 | 15
50 | 12 | 3 | 3600.1 | 10501.1 | 8754.9 | 5432.0 | 10501.1 | 10501.1 | 16.6 | 16.6 | 0.0 | 48.3 | 0 | 1
50 | 12 | 4 | 3600.2 | 8682.3 | 6939.6 | 3856.7 | 8653.6 | 8653.6 | 20.1 | 19.8 | 0.3 | 55.4 | 0 | 16
50 | 12 | 5 | 3600.2 | 9521.1 | 7673.6 | 4455.9 | 9521.1 | 9186.5 | 19.4 | 19.4 | 3.5 | 53.2 | 0 | 1
50 | 16 | 1 | 3600.3 | 8693.5 | 7564.6 | 4584.7 | 8693.5 | 8693.5 | 13.0 | 13.0 | 0.0 | 47.3 | 0 | 218
50 | 16 | 2 | 3600.2 | 5980.2 | 5061.9 | 2923.1 | 5966.4 | 5966.4 | 15.4 | 15.2 | 0.2 | 51.0 | 0 | 34
50 | 16 | 3 | 3600.6 | 9239.6 | 7950.6 | 4706.2 | 9239.6 | 9239.6 | 13.9 | 13.9 | 0.0 | 49.1 | 0 | 15
50 | 16 | 4 | 3600.2 | 7453.7 | 6485.4 | 3632.3 | 7453.7 | 7453.7 | 13.0 | 13.0 | 0.0 | 51.3 | 0 | 144
50 | 16 | 5 | 3600.2 | 6961.2 | 5813.1 | 3213.4 | 6924.8 | 6924.8 | 16.5 | 16.0 | 0.5 | 53.6 | 0 | 184
50 | 25 | 1 | 3533.5 | 5561.8 | 5561.8 | 3106.5 | 5561.8 | 5561.8 | 0.0 | 0.0 | 0.0 | 44.1 | 1 | 1908
50 | 25 | 2 | 2672.8 | 6891.1 | 6891.1 | 4073.8 | 6891.1 | 6891.1 | 0.0 | 0.0 | 0.0 | 40.9 | 1 | 2534
50 | 25 | 3 | 2063.5 | 5582.7 | 5582.7 | 3320.2 | 5582.7 | 5582.7 | 0.0 | 0.0 | 0.0 | 40.5 | 1 | 1421
50 | 25 | 4 | 3600.5 | 5900.7 | 5489.4 | 3237.2 | 5900.7 | 5900.7 | 7.0 | 7.0 | 0.0 | 45.1 | 0 | 749
50 | 25 | 5 | 3600.7 | 6372.0 | 5968.5 | 3536.6 | 6372.0 | 6372.0 | 6.3 | 6.3 | 0.0 | 44.5 | 0 | 1067
Table 104: Summary results table for model $F2_{u}^{km}$ $|V|$ | p |  $|$#$|$ | cpu |  g$\overline{\text{U}}$R |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ | gUL | nod
---|---|---|---|---|---|---|---|---
20 | 5 | 5 | 122.6 | 53.4 | 0.0 | 0.0 | 0.0 | 6959
20 | 6 | 5 | 156.5 | 52.7 | 0.0 | 0.0 | 0.0 | 1877
20 | 10 | 5 | 10.1 | 44.5 | 0.0 | 0.0 | 0.0 | 72
30 | 7 | 4 | 2649.5 | 54.5 | 0.6 | 0.0 | 0.6 | 4211
30 | 10 | 5 | 1276.5 | 48.2 | 0.0 | 0.0 | 0.0 | 2740
30 | 15 | 5 | 39.9 | 44.6 | 0.0 | 0.0 | 0.0 | 509
40 | 10 | 0 | 3600.4 | 55.3 | 17.2 | 0.0 | 17.2 | 1625
40 | 13 | 0 | 3600.3 | 49.1 | 11.2 | 0.0 | 11.2 | 1486
40 | 20 | 5 | 1987.3 | 46.4 | 0.0 | 0.0 | 0.0 | 2359
50 | 12 | 0 | 3600.2 | 53.4 | 19.9 | 3.7 | 20.6 | 10
50 | 16 | 0 | 3600.3 | 50.5 | 14.2 | 0.1 | 14.4 | 119
50 | 25 | 3 | 3094.2 | 43.0 | 2.7 | 0.0 | 2.7 | 1536

Table 105: Instances results table for model $F2_{u}^{sub}$ $|V|$ | p | ins | cpu | objU | objL | objR |  obj$\overline{\text{U}}$ |  obj$\overline{\text{L}}$ | gUL |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ |  g$\overline{\text{U}}$R | opt | nod
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
20 | 5 | 1 | 22.0 | 24444.4 | 24444.4 | 11628.1 | 24444.4 | 24444.4 | 0.0 | 0.0 | 0.0 | 52.4 | 1 | 6182
20 | 5 | 2 | 20.5 | 26585.3 | 26585.3 | 13320.5 | 26585.3 | 26585.3 | 0.0 | 0.0 | 0.0 | 49.9 | 1 | 10858
20 | 5 | 3 | 33.5 | 26159.6 | 26159.6 | 11682.6 | 26159.6 | 26159.6 | 0.0 | 0.0 | 0.0 | 55.3 | 1 | 14106
20 | 5 | 4 | 14.5 | 16558.9 | 16558.9 | 6951.0 | 16558.9 | 16558.9 | 0.0 | 0.0 | 0.0 | 58.0 | 1 | 5909
20 | 5 | 5 | 27.6 | 29165.6 | 29165.6 | 14127.3 | 29165.6 | 29165.6 | 0.0 | 0.0 | 0.0 | 51.6 | 1 | 3050
20 | 6 | 1 | 57.9 | 22562.4 | 22562.4 | 10139.9 | 22562.4 | 22562.4 | 0.0 | 0.0 | 0.0 | 55.1 | 1 | 3848
20 | 6 | 2 | 3.0 | 20183.5 | 20183.5 | 10220.2 | 20183.5 | 20183.5 | 0.0 | 0.0 | 0.0 | 49.4 | 1 | 1
20 | 6 | 3 | 36.0 | 25238.2 | 25238.2 | 12124.6 | 25238.2 | 25238.2 | 0.0 | 0.0 | 0.0 | 52.0 | 1 | 3335
20 | 6 | 4 | 19.3 | 20161.1 | 20161.1 | 9580.3 | 20161.1 | 20161.1 | 0.0 | 0.0 | 0.0 | 52.5 | 1 | 2625
20 | 6 | 5 | 30.7 | 27296.4 | 27296.4 | 12384.4 | 27296.4 | 27296.4 | 0.0 | 0.0 | 0.0 | 54.6 | 1 | 2916
20 | 10 | 1 | 5.4 | 15074.8 | 15074.8 | 8445.0 | 15074.8 | 15074.8 | 0.0 | 0.0 | 0.0 | 44.0 | 1 | 2542
20 | 10 | 2 | 17.2 | 18092.9 | 18092.9 | 9917.5 | 18092.9 | 18092.9 | 0.0 | 0.0 | 0.0 | 45.2 | 1 | 3703
20 | 10 | 3 | 4.8 | 14169.6 | 14169.6 | 7261.8 | 14169.6 | 14169.6 | 0.0 | 0.0 | 0.0 | 48.8 | 1 | 916
20 | 10 | 4 | 3.9 | 19027.0 | 19027.0 | 10680.8 | 19027.0 | 19027.0 | 0.0 | 0.0 | 0.0 | 43.9 | 1 | 111
20 | 10 | 5 | 1.9 | 9742.5 | 9742.5 | 5785.7 | 9742.5 | 9742.5 | 0.0 | 0.0 | 0.0 | 40.6 | 1 | 1
30 | 7 | 1 | 169.1 | 15759.0 | 15759.0 | 7366.4 | 15759.0 | 15759.0 | 0.0 | 0.0 | 0.0 | 53.3 | 1 | 4207
30 | 7 | 2 | 170.2 | 17867.0 | 17867.0 | 7335.1 | 17867.0 | 17867.0 | 0.0 | 0.0 | 0.0 | 59.0 | 1 | 4067
30 | 7 | 3 | 122.8 | 15619.6 | 15619.6 | 7474.4 | 15619.6 | 15619.6 | 0.0 | 0.0 | 0.0 | 52.1 | 1 | 5135
30 | 7 | 4 | 372.1 | 18356.9 | 18356.9 | 9136.9 | 18356.9 | 18356.9 | 0.0 | 0.0 | 0.0 | 50.2 | 1 | 16340
30 | 7 | 5 | 802.2 | 15460.6 | 15460.6 | 6495.7 | 15460.6 | 15460.6 | 0.0 | 0.0 | 0.0 | 58.0 | 1 | 44097
30 | 10 | 1 | 25.3 | 12598.8 | 12598.8 | 6404.5 | 12598.8 | 12598.8 | 0.0 | 0.0 | 0.0 | 49.2 | 1 | 3245
30 | 10 | 2 | 47.8 | 9620.6 | 9620.6 | 5334.9 | 9620.6 | 9620.6 | 0.0 | 0.0 | 0.0 | 44.5 | 1 | 2879
30 | 10 | 3 | 87.7 | 9329.9 | 9329.9 | 5107.6 | 9329.9 | 9329.9 | 0.0 | 0.0 | 0.0 | 45.3 | 1 | 2996
30 | 10 | 4 | 118.6 | 15224.5 | 15224.5 | 7446.2 | 15224.5 | 15224.5 | 0.0 | 0.0 | 0.0 | 51.1 | 1 | 3378
30 | 10 | 5 | 517.0 | 14665.7 | 14665.7 | 7183.9 | 14665.7 | 14665.7 | 0.0 | 0.0 | 0.0 | 51.0 | 1 | 54578
30 | 15 | 1 | 77.5 | 10085.3 | 10085.3 | 4987.7 | 10085.3 | 10085.3 | 0.0 | 0.0 | 0.0 | 50.5 | 1 | 2415
30 | 15 | 2 | 89.3 | 10658.1 | 10658.1 | 6108.2 | 10658.1 | 10658.1 | 0.0 | 0.0 | 0.0 | 42.7 | 1 | 5470
30 | 15 | 3 | 16.7 | 8466.4 | 8466.4 | 4447.6 | 8466.4 | 8466.4 | 0.0 | 0.0 | 0.0 | 47.5 | 1 | 3613
30 | 15 | 4 | 20.8 | 9980.5 | 9980.5 | 6027.4 | 9980.5 | 9980.5 | 0.0 | 0.0 | 0.0 | 39.6 | 1 | 1637
30 | 15 | 5 | 10.6 | 9687.3 | 9687.3 | 5553.1 | 9687.3 | 9687.3 | 0.0 | 0.0 | 0.0 | 42.7 | 1 | 589
40 | 10 | 1 | 3600.3 | 14500.9 | 13876.5 | 6302.4 | 14500.9 | 14500.9 | 4.3 | 4.3 | 0.0 | 56.5 | 0 | 134757
40 | 10 | 2 | 3600.6 | 12213.5 | 12075.0 | 5155.4 | 12213.5 | 12213.5 | 1.1 | 1.1 | 0.0 | 57.8 | 0 | 111338
40 | 10 | 3 | 595.6 | 11071.1 | 11071.1 | 5381.9 | 11071.1 | 11071.1 | 0.0 | 0.0 | 0.0 | 51.4 | 1 | 14902
40 | 10 | 4 | 441.9 | 9502.1 | 9502.1 | 4294.9 | 9502.0 | 9502.1 | 0.0 | 0.0 | 0.0 | 54.8 | 1 | 3734
40 | 10 | 5 | 3600.4 | 10972.1 | 10498.4 | 4805.2 | 10972.0 | 10972.1 | 4.3 | 4.3 | 0.0 | 56.2 | 0 | 106148
40 | 13 | 1 | 2947.1 | 9885.2 | 9885.2 | 5384.9 | 9885.2 | 9885.2 | 0.0 | 0.0 | 0.0 | 45.5 | 1 | 92788
40 | 13 | 2 | 382.4 | 9010.9 | 9010.9 | 5015.9 | 9010.9 | 9010.9 | 0.0 | 0.0 | 0.0 | 44.3 | 1 | 8480
40 | 13 | 3 | 3600.5 | 10645.3 | 10520.1 | 5340.0 | 10645.3 | 10645.3 | 1.2 | 1.2 | 0.0 | 49.8 | 0 | 108946
40 | 13 | 4 | 1041.4 | 8911.8 | 8911.8 | 4340.7 | 8911.8 | 8911.8 | 0.0 | 0.0 | 0.0 | 51.3 | 1 | 27629
40 | 13 | 5 | 3600.4 | 11636.1 | 11037.9 | 5300.9 | 11636.1 | 11636.1 | 5.1 | 5.1 | 0.0 | 54.4 | 0 | 92423
40 | 20 | 1 | 225.3 | 9426.4 | 9426.4 | 4913.9 | 9426.4 | 9426.4 | 0.0 | 0.0 | 0.0 | 47.9 | 1 | 6134
40 | 20 | 2 | 117.3 | 6156.3 | 6156.3 | 3244.3 | 6156.3 | 6156.3 | 0.0 | 0.0 | 0.0 | 47.3 | 1 | 3425
40 | 20 | 3 | 226.0 | 8245.3 | 8245.3 | 4057.7 | 8245.3 | 8245.3 | 0.0 | 0.0 | 0.0 | 50.8 | 1 | 9306
40 | 20 | 4 | 100.3 | 8315.2 | 8315.2 | 4813.6 | 8315.2 | 8315.2 | 0.0 | 0.0 | 0.0 | 42.1 | 1 | 1342
40 | 20 | 5 | 118.8 | 6967.8 | 6967.8 | 3912.2 | 6967.8 | 6967.8 | 0.0 | 0.0 | 0.0 | 43.9 | 1 | 3167
50 | 12 | 1 | 3600.3 | 11117.1 | 10204.2 | 5373.6 | 11063.0 | 10584.5 | 8.2 | 7.8 | 4.8 | 51.4 | 0 | 27041
50 | 12 | 2 | 3600.4 | 10933.4 | 9561.8 | 4343.6 | 10517.5 | 9871.9 | 12.6 | 9.1 | 9.7 | 58.7 | 0 | 32640
50 | 12 | 3 | 3600.3 | 11222.7 | 9538.9 | 5432.0 | 10501.1 | 10501.1 | 15.0 | 9.2 | 6.4 | 48.3 | 0 | 22088
50 | 12 | 4 | 3600.2 | 8682.3 | 7770.4 | 3856.7 | 8653.6 | 8653.6 | 10.5 | 10.2 | 0.3 | 55.4 | 0 | 29787
50 | 12 | 5 | 3600.4 | 9576.8 | 8666.3 | 4455.9 | 9521.1 | 9186.5 | 9.5 | 9.0 | 4.1 | 53.2 | 0 | 37287
50 | 16 | 1 | 3600.3 | 8697.4 | 8337.3 | 4584.7 | 8693.5 | 8693.5 | 4.1 | 4.1 | 0.0 | 47.3 | 0 | 31096
50 | 16 | 2 | 3600.2 | 5966.4 | 5803.3 | 2923.1 | 5966.4 | 5966.4 | 2.7 | 2.7 | 0.0 | 51.0 | 0 | 34788
50 | 16 | 3 | 3600.2 | 9239.6 | 8969.1 | 4706.2 | 9239.6 | 9239.6 | 2.9 | 2.9 | 0.0 | 49.1 | 0 | 25732
50 | 16 | 4 | 3600.2 | 8422.4 | 6796.9 | 3632.3 | 7453.7 | 7453.7 | 19.3 | 8.8 | 11.5 | 51.3 | 0 | 31306
50 | 16 | 5 | 3600.1 | 8893.5 | 6097.1 | 3213.4 | 6924.8 | 6924.8 | 31.4 | 11.9 | 22.1 | 53.6 | 0 | 40862
50 | 25 | 1 | 426.3 | 5561.8 | 5561.8 | 3106.5 | 5561.8 | 5561.8 | 0.0 | 0.0 | 0.0 | 44.1 | 1 | 2567
50 | 25 | 2 | 944.6 | 6891.1 | 6891.1 | 4073.8 | 6891.1 | 6891.1 | 0.0 | 0.0 | 0.0 | 40.9 | 1 | 12392
50 | 25 | 3 | 410.1 | 5582.7 | 5582.7 | 3320.2 | 5582.7 | 5582.7 | 0.0 | 0.0 | 0.0 | 40.5 | 1 | 3755
50 | 25 | 4 | 924.3 | 5900.7 | 5900.7 | 3237.2 | 5900.7 | 5900.7 | 0.0 | 0.0 | 0.0 | 45.1 | 1 | 21798
50 | 25 | 5 | 258.8 | 6372.0 | 6372.0 | 3536.6 | 6372.0 | 6372.0 | 0.0 | 0.0 | 0.0 | 44.5 | 1 | 1834
Table 106: Summary results table for model $F2_{u}^{sub}$ $|V|$ | p |  $|$#$|$ | cpu |  g$\overline{\text{U}}$R |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ | gUL | nod
---|---|---|---|---|---|---|---|---
20 | 5 | 5 | 23.6 | 53.4 | 0.0 | 0.0 | 0.0 | 8021
20 | 6 | 5 | 29.4 | 52.7 | 0.0 | 0.0 | 0.0 | 2545
20 | 10 | 5 | 6.6 | 44.5 | 0.0 | 0.0 | 0.0 | 1455
30 | 7 | 5 | 327.3 | 54.5 | 0.0 | 0.0 | 0.0 | 14769
30 | 10 | 5 | 159.3 | 48.2 | 0.0 | 0.0 | 0.0 | 13415
30 | 15 | 5 | 43.0 | 44.6 | 0.0 | 0.0 | 0.0 | 2745
40 | 10 | 2 | 2367.8 | 55.3 | 1.9 | 0.0 | 1.9 | 74176
40 | 13 | 3 | 2314.4 | 49.1 | 1.3 | 0.0 | 1.3 | 66053
40 | 20 | 5 | 157.5 | 46.4 | 0.0 | 0.0 | 0.0 | 4675
50 | 12 | 0 | 3600.3 | 53.4 | 9.1 | 5.1 | 11.2 | 29769
50 | 16 | 0 | 3600.2 | 50.5 | 6.1 | 6.7 | 12.1 | 32757
50 | 25 | 5 | 592.8 | 43.0 | 0.0 | 0.0 | 0.0 | 8469

Table 107: Instances results table for model OMT Benders modern Kruskal for covering $|V|$ | p | ins | cpu | objU | objL | objR |  obj$\overline{\text{U}}$ |  obj$\overline{\text{L}}$ | gUL |  g$\overline{\text{U}}$L |  gU$\overline{\text{L}}$ |  g$\overline{\text{U}}$R | opt | nod
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
20 | 5 | 1 | 504.6 | 24444.4 | 24444.4 | 5459.2 | 24444.4 | 24444.4 | 0.0 | 0.0 | 0.0 | 77.7 | 1 | 465124
20 | 5 | 2 | 406.8 | 26585.3 | 26585.3 | 6947.0 | 26585.3 | 26585.3 | 0.0 | 0.0 | 0.0 | 73.9 | 1 | 402179
20 | 5 | 3 | 755.5 | 26159.6 | 26159.6 | 5859.3 | 26159.6 | 26159.6 | 0.0 | 0.0 | 0.0 | 77.6 | 1 | 547956
20 | 5 | 4 | 507.7 | 16558.9 | 16558.9 | 3801.4 | 16558.9 | 16558.9 | 0.0 | 0.0 | 0.0 | 77.0 | 1 | 376109
20 | 5 | 5 | 1114.9 | 29165.6 | 29165.6 | 7835.4 | 29165.6 | 29165.6 | 0.0 | 0.0 | 0.0 | 73.1 | 1 | 799871
20 | 6 | 1 | 3600.2 | 22562.4 | 17182.0 | 4648.1 | 22562.4 | 22562.4 | 23.9 | 23.9 | 0.0 | 79.4 | 0 | 1376894
20 | 6 | 2 | 556.8 | 20183.5 | 20183.5 | 6014.2 | 20183.5 | 20183.5 | 0.0 | 0.0 | 0.0 | 70.2 | 1 | 538047
20 | 6 | 3 | 3600.1 | 25238.2 | 19958.2 | 5204.0 | 25238.2 | 25238.2 | 20.9 | 20.9 | 0.0 | 79.4 | 0 | 1503086
20 | 6 | 4 | 3600.1 | 20161.1 | 16480.8 | 4394.6 | 20161.1 | 20161.1 | 18.2 | 18.2 | 0.0 | 78.2 | 0 | 1621543
20 | 6 | 5 | 3600.1 | 27308.9 | 19276.1 | 5184.1 | 27296.4 | 27296.4 | 29.4 | 29.4 | 0.0 | 81.0 | 0 | 1784615
20 | 10 | 1 | 3600.2 | 15238.6 | 7763.9 | 2419.6 | 15074.8 | 15074.8 | 49.0 | 48.5 | 1.1 | 84.0 | 0 | 564542
20 | 10 | 2 | 3600.3 | 18422.2 | 9521.8 | 2372.4 | 18092.9 | 18092.9 | 48.3 | 47.4 | 1.8 | 86.9 | 0 | 669852
20 | 10 | 3 | 3600.1 | 14428.7 | 7399.6 | 1828.8 | 14169.6 | 14169.6 | 48.7 | 47.8 | 1.8 | 87.1 | 0 | 618889
20 | 10 | 4 | 3600.2 | 20029.0 | 10057.3 | 2316.8 | 19027.0 | 19027.0 | 49.8 | 47.1 | 5.0 | 87.8 | 0 | 535104
20 | 10 | 5 | 3600.2 | 9742.5 | 5256.0 | 806.2 | 9742.5 | 9742.5 | 46.0 | 46.0 | 0.0 | 91.7 | 0 | 695516
30 | 7 | 1 | 3600.1 | 17431.5 | 10498.1 | 3461.6 | 15759.0 | 15759.0 | 39.8 | 33.4 | 9.6 | 78.0 | 0 | 454275
30 | 7 | 2 | 3600.2 | 20822.8 | 11568.3 | 4139.3 | 17867.0 | 17867.0 | 44.4 | 35.2 | 14.2 | 76.8 | 0 | 389155
30 | 7 | 3 | 3600.2 | 17202.8 | 10798.1 | 4202.6 | 15619.6 | 15619.6 | 37.2 | 30.9 | 9.2 | 73.1 | 0 | 398114
30 | 7 | 4 | 3600.1 | 20464.5 | 11429.0 | 4464.4 | 18356.9 | 18356.9 | 44.1 | 37.7 | 10.3 | 75.7 | 0 | 409351
30 | 7 | 5 | 3600.2 | 16136.4 | 9465.5 | 3479.7 | 15460.6 | 15460.6 | 41.3 | 38.8 | 4.2 | 77.5 | 0 | 468779
30 | 10 | 1 | 3600.4 | 15351.4 | 8045.0 | 2800.6 | 12598.8 | 12598.8 | 47.6 | 36.1 | 17.9 | 77.8 | 0 | 375580
30 | 10 | 2 | 3600.2 | 11688.7 | 4992.1 | 1911.3 | 9620.6 | 9620.6 | 57.3 | 48.1 | 17.7 | 80.1 | 0 | 547219
30 | 10 | 3 | 3600.2 | 10581.4 | 5170.6 | 1887.8 | 9329.9 | 9329.9 | 51.1 | 44.6 | 11.8 | 79.8 | 0 | 332561
30 | 10 | 4 | 3600.3 | 17639.1 | 9385.9 | 3146.7 | 15224.5 | 15224.5 | 46.8 | 38.4 | 13.7 | 79.3 | 0 | 355617
30 | 10 | 5 | 3600.7 | 15955.8 | 7664.7 | 2907.3 | 14665.7 | 14665.7 | 52.0 | 47.7 | 8.1 | 80.2 | 0 | 357914
30 | 15 | 1 | 3600.3 | 12584.3 | 3246.5 | 912.7 | 10085.3 | 10085.3 | 74.2 | 67.8 | 19.9 | 91.0 | 0 | 458908
30 | 15 | 2 | 3600.8 | 11289.2 | 3526.3 | 1018.6 | 10658.1 | 10658.1 | 68.8 | 66.9 | 5.6 | 90.4 | 0 | 387267
30 | 15 | 3 | 3600.5 | 9565.3 | 2775.1 | 709.7 | 8466.4 | 8466.4 | 71.0 | 67.2 | 11.5 | 91.6 | 0 | 419922