Chinese Journal of Management Science ›› 2024, Vol. 32 ›› Issue (1): 146-157.doi: 10.16381/j.cnki.issn1003-207x.2021.0203
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Xinyue Zhang1,2,Peng Jin1,2(),Xiaoxuan Hu1,2,Moning Zhu1,2
Received:
2021-01-28
Revised:
2021-11-20
Online:
2024-01-25
Published:
2024-02-08
Contact:
Peng Jin
E-mail:jinpeng@hfut.edu.cn
CLC Number:
Xinyue Zhang,Peng Jin,Xiaoxuan Hu,Moning Zhu. Research on the Time-dependent Multi-depot Open Vehicle Routing Problem with Time Windows[J]. Chinese Journal of Management Science, 2024, 32(1): 146-157.
"
算例 | n | Best known solution | HGA best solution | |||||
---|---|---|---|---|---|---|---|---|
vehicles | Bbest | Btime | vehicles | Rbest | Gap(%) | CPUtime | ||
C101 | 25 | 3 | 191.3 | 0.56 | 3 | 191.81 | 0.27 | 0.28 |
C102 | 25 | 3 | 190.3 | 1.94 | 3 | 190.74 | 0.23 | 0.19 |
C103 | 25 | 3 | 190.3 | 4.03 | 3 | 190.74 | 0.23 | 0.18 |
C104 | 25 | 3 | 186.9 | 8.45 | 3 | 186.90 | 0.00 | 0.65 |
C105 | 25 | 3 | 191.3 | 0.64 | 3 | 191.81 | 0.27 | 0.33 |
C106 | 25 | 3 | 191.3 | 0.62 | 3 | 191.81 | 0.27 | 0.63 |
C107 | 25 | 3 | 191.3 | 0.61 | 3 | 191.81 | 0.27 | 0.39 |
C108 | 25 | 3 | 191.3 | 0.64 | 3 | 191.81 | 0.27 | 0.23 |
C109 | 25 | 3 | 191.3 | 0.87 | 3 | 191.81 | 0.27 | 0.26 |
C101 | 50 | 5 | 362.4 | 2.48 | 5 | 363.25 | 0.23 | 1.85 |
C102 | 50 | 5 | 361.4 | 13.99 | 5 | 361.40 | 0.00 | 2.94 |
C103 | 50 | 5 | 361.4 | 33.78 | 5 | 361.49 | 0.02 | 3.11 |
C104 | 50 | 5 | 358 | 884.46 | 5 | 363.18 | 1.45 | 5.81 |
C105 | 50 | 5 | 362.4 | 5.83 | 5 | 363.25 | 0.23 | 9.89 |
C106 | 50 | 5 | 362.4 | 1.25 | 5 | 363.25 | 0.23 | 70.39 |
C107 | 50 | 5 | 362.4 | 3.85 | 5 | 363.25 | 0.23 | 13.27 |
C108 | 50 | 5 | 362.4 | 8.21 | 5 | 363.25 | 0.23 | 3.93 |
C109 | 50 | 5 | 362.4 | 5.34 | 5 | 363.25 | 0.23 | 1.38 |
C101 | 100 | 10 | 827.3 | 5.86 | 10 | 828.94 | 0.20 | 9.67 |
C102 | 100 | 10 | 827.3 | 111.35 | 10 | 841.36 | 1.70 | 11.45 |
C103 | 100 | 10 | 826.3 | 679.69 | 10 | 838.03 | 1.42 | 7.17 |
C104 | 100 | 10 | 822.9 | 1216.04 | 10 | 824.46 | 0.19 | 12.22 |
C105 | 100 | 10 | 827.3 | 33.21 | 10 | 827.72 | 0.05 | 11.33 |
C106 | 100 | 10 | 827.3 | 23.7 | 10 | 827.45 | 0.02 | 11.45 |
C107 | 100 | 10 | 827.3 | 36.92 | 10 | 828.94 | 0.20 | 12.21 |
C108 | 100 | 10 | 827.3 | 42.2 | 10 | 828.92 | 0.20 | 10.95 |
C109 | 100 | 10 | 827.3 | 72.9 | 10 | 831.56 | 0.51 | 15.28 |
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算例 | n | Best known solution | HGA best solution | ||||
---|---|---|---|---|---|---|---|
vehicles | Tbest | vehicles | Tmin | absolute value | CPUavg | ||
C101 | 25 | 3 | 91.84 | 3 | 79.51 | 12.33 | 0.33 |
C102 | 25 | 3 | 91.36 | 3 | 74.64 | 16.72 | 0.29 |
C103 | 25 | 3 | 91.36 | 3 | 73.12 | 18.24 | 0.28 |
C104 | 25 | 3 | 89.72 | 3 | 79.34 | 10.38 | 3.37 |
C105 | 25 | 3 | 91.84 | 3 | 80.35 | 11.49 | 1.17 |
C106 | 25 | 3 | 91.84 | 3 | 78.89 | 12.95 | 0.44 |
C107 | 25 | 3 | 91.84 | 3 | 84.07 | 7.77 | 0.26 |
C108 | 25 | 3 | 91.84 | 3 | 83.33 | 8.51 | 0.48 |
C109 | 25 | 3 | 91.84 | 3 | 77.99 | 13.85 | 0.50 |
C101 | 50 | 5 | 173.97 | 5 | 149.91 | 24.06 | 1.96 |
C102 | 50 | 5 | 173.49 | 5 | 154.92 | 18.57 | 5.99 |
C103 | 50 | 5 | 173.49 | 5 | 162.81 | 10.68 | 3.12 |
C104 | 50 | 5 | 171.86 | 5 | 159.45 | 12.41 | 2.54 |
C105 | 50 | 5 | 173.97 | 5 | 150.01 | 23.96 | 3.88 |
C106 | 50 | 5 | 173.97 | 5 | 149.50 | 24.47 | 1.29 |
C107 | 50 | 5 | 173.97 | 5 | 166.07 | 7.90 | 1.80 |
C108 | 50 | 5 | 173.97 | 5 | 145.38 | 28.59 | 1.15 |
C109 | 50 | 5 | 173.97 | 5 | 152.88 | 21.09 | 1.63 |
C101 | 100 | 10 | 397.16 | 10 | 383.18 | 13.98 | 3.87 |
C102 | 100 | 10 | 397.15 | 10 | 374.67 | 22.48 | 9.89 |
C103 | 100 | 10 | 396.68 | 10 | 383.23 | 13.45 | 5.99 |
C104 | 100 | 10 | 395.04 | 10 | 353.80 | 41.24 | 4.43 |
C105 | 100 | 10 | 397.16 | 10 | 372.98 | 24.18 | 7.27 |
C106 | 100 | 10 | 397.16 | 10 | 357.47 | 39.69 | 8.15 |
C107 | 100 | 10 | 397.16 | 10 | 374.80 | 22.36 | 6.25 |
C108 | 100 | 10 | 397.16 | 10 | 371.05 | 26.11 | 6.51 |
C109 | 100 | 10 | 397.16 | 10 | 355.95 | 41.21 | 8.22 |
"
Travel time distribution | Best known solution | HGA best solution | Gap1 | Gap2 | ||||
---|---|---|---|---|---|---|---|---|
vehicles | Tavg | Davg | vehicles | T’avg | D’avg | |||
TD1a | 10.00 | 729 | 879 | 10.00 | 650 | 892 | 12.13 | -1.46 |
TD2a | 10.00 | 644 | 864 | 10.00 | 562 | 884 | 14.53 | -2.26 |
TD3a | 10.00 | 608 | 880 | 10.00 | 513 | 882 | 18.46 | -0.23 |
TD1b | 10.00 | 732 | 892 | 10.00 | 650 | 892 | 12.59 | 0.00 |
TD2b | 10.00 | 650 | 883 | 10.00 | 562 | 884 | 15.6 | -0.11 |
TD3b | 10.00 | 584 | 866 | 10.00 | 513 | 882 | 13.79 | -1.81 |
TD1c | 10.00 | 697 | 865 | 10.00 | 650 | 892 | 7.211 | -3.03 |
TD2c | 10.00 | 618 | 863 | 10.00 | 562 | 884 | 9.91 | -2.38 |
TD3c | 10.00 | 565 | 862 | 10.00 | 513 | 882 | 10.08 | -2.27 |
TD1d | 10.00 | 731 | 872 | 10.00 | 650 | 892 | 12.44 | -2.24 |
TD2d | 10.00 | 652 | 856 | 10.00 | 562 | 884 | 15.96 | -3.17 |
TD3d | 10.00 | 612 | 867 | 10.00 | 513 | 882 | 19.24 | -1.70 |
"
算例 | Basic GA | HGA | Gap | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
vehicles | Sbasic | CPUtime | vehicles | Smax | Savg | Smin | Gap1 | Gap2 | CPUavg | B~H(%) | |
C3-101 | 6 | 101.14 | 0.32 | 3 | 86.33 | 84.85 | 82.45 | 1.74 | -2.83 | 0.34 | 22.67 |
C3-102 | 5 | 117.42 | 0.31 | 5 | 107.78 | 106.83 | 105.68 | 0.89 | -1.08 | 0.32 | 11.11 |
C3-103 | 5 | 113.3 | 0.30 | 5 | 108.57 | 105.96 | 101.39 | 2.46 | -4.31 | 0.32 | 11.75 |
C3-104 | 6 | 108.63 | 0.31 | 4 | 94.04 | 93.33 | 92.56 | 0.76 | -0.83 | 0.35 | 17.36 |
C3-105 | 4 | 126.36 | 0.32 | 6 | 121.61 | 119.26 | 114.89 | 1.97 | -3.66 | 0.33 | 9.97 |
C3-106 | 6 | 121.31 | 0.31 | 5 | 104.84 | 103.96 | 102.9 | 0.85 | -1.02 | 0.32 | 17.89 |
C3-107 | 4 | 109.47 | 0.31 | 5 | 114.28 | 111.86 | 106.9 | 2.16 | -4.44 | 0.35 | 2.41 |
C3-108 | 6 | 120.83 | 0.31 | 6 | 117.61 | 114.71 | 110.11 | 2.53 | -4.01 | 0.35 | 9.73 |
C3-109 | 5 | 117.14 | 0.42 | 4 | 106.17 | 102.72 | 98.24 | 3.35 | -4.37 | 0.47 | 19.24 |
C5-101 | 10 | 238.95 | 2.05 | 8 | 211.12 | 207.24 | 201.28 | 1.87 | -2.88 | 2.28 | 18.72 |
C5-102 | 10 | 280.61 | 6.05 | 10 | 254.4 | 250.16 | 245.91 | 1.7 | -1.7 | 6.75 | 14.11 |
C5-103 | 10 | 280.55 | 3.11 | 9 | 242.82 | 237.73 | 235.73 | 2.14 | -0.84 | 3.71 | 19.01 |
C5-104 | 10 | 250.1 | 1.04 | 9 | 223.81 | 220.99 | 216.31 | 1.28 | -2.12 | 1.25 | 15.62 |
C5-105 | 9 | 218.99 | 2.10 | 8 | 201.04 | 197.82 | 191.84 | 1.63 | -3.02 | 2.71 | 14.15 |
C5-106 | 10 | 237.57 | 10.51 | 9 | 210.94 | 207.46 | 202.55 | 1.68 | -2.37 | 11.21 | 17.29 |
C5-107 | 10 | 256.02 | 2.19 | 10 | 234.79 | 231.13 | 225.09 | 1.58 | -2.61 | 2.14 | 13.74 |
C5-108 | 9 | 236.7 | 1.86 | 7 | 196.38 | 193.45 | 188.59 | 1.51 | -2.51 | 2.06 | 25.51 |
C5-109 | 10 | 249.41 | 1.38 | 10 | 233.33 | 230.58 | 222.08 | 1.19 | -3.69 | 1.68 | 12.31 |
C7-101 | 17 | 478.8 | 60.18 | 17 | 449.72 | 449.15 | 448.8 | 0.13 | -0.08 | 62.18 | 6.68 |
C7-102 | 17 | 580.43 | 50.28 | 17 | 567.52 | 564.21 | 560.43 | 0.59 | -0.67 | 51.48 | 3.57 |
C7-103 | 18 | 595.45 | 20.10 | 18 | 574.71 | 570.08 | 575.45 | 0.81 | 0.94 | 21.3 | 3.48 |
C7-104 | 13 | 529.35 | 7.23 | 18 | 520.82 | 517.26 | 512.41 | 0.69 | -0.94 | 7.83 | 3.30 |
C7-105 | 10 | 399.12 | 74.51 | 11 | 388.34 | 388.34 | 388.34 | 0.00 | 0.00 | 75.51 | 2.78 |
C7-106 | 15 | 534.71 | 66.00 | 20 | 526.49 | 521.19 | 515.44 | 1.02 | -1.1 | 66.66 | 3.74 |
C7-107 | 10 | 428.9 | 79.95 | 12 | 416.26 | 414.36 | 413.42 | 0.46 | -0.23 | 74.56 | 3.74 |
C7-108 | 10 | 391.28 | 58.13 | 10 | 380.75 | 376.53 | 373.22 | 1.12 | -0.88 | 60.13 | 4.84 |
C7-109 | 10 | 473.55 | 47.64 | 11 | 465.13 | 463.4 | 461.14 | 0.37 | -0.49 | 46.28 | 2.69 |
Avg | 1.35 | -1.92 | 11.39 |
"
算例 | TDMDVRPTW | TDMDOVRPTW | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
vehicles | Rbest | Cbest | CPUtime | vehicles | R'best | C'best | CPUtime | Gap1 | Gap2 | |
C3-101 | 3 | 60.05 | 90.05 | 0.33 | 3 | 52.45 | 82.45 | 0.34 | 14.49 | 9.22 |
C3-102 | 5 | 69.84 | 119.84 | 0.28 | 5 | 55.68 | 105.68 | 0.32 | 25.43 | 13.40 |
C3-103 | 5 | 61.39 | 111.39 | 0.29 | 5 | 51.39 | 101.39 | 0.32 | 19.46 | 9.86 |
C3-104 | 4 | 59.32 | 99.32 | 0.23 | 4 | 52.56 | 92.56 | 0.35 | 12.86 | 7.30 |
C3-105 | 6 | 58.25 | 118.25 | 0.74 | 6 | 54.89 | 114.89 | 0.33 | 6.11 | 2.92 |
C3-106 | 6 | 56.63 | 116.63 | 0.76 | 5 | 52.90 | 102.90 | 0.32 | 7.05 | 13.34 |
C3-107 | 5 | 64.02 | 114.02 | 0.76 | 5 | 56.90 | 106.90 | 0.35 | 12.52 | 6.66 |
C3-108 | 6 | 51.14 | 111.14 | 0.43 | 6 | 50.11 | 110.11 | 0.35 | 2.05 | 0.93 |
C3-109 | 4 | 60.59 | 100.59 | 0.48 | 4 | 58.24 | 98.24 | 0.47 | 4.04 | 2.39 |
C5-101 | 8 | 133.67 | 213.67 | 2.92 | 8 | 121.28 | 201.28 | 2.28 | 10.22 | 6.16 |
C5-102 | 10 | 159.06 | 259.06 | 1.61 | 10 | 145.91 | 245.91 | 6.75 | 9.01 | 5.35 |
C5-103 | 10 | 150.06 | 250.06 | 1.16 | 9 | 145.73 | 235.73 | 3.71 | 2.97 | 6.08 |
C5-104 | 10 | 137.23 | 237.23 | 0.78 | 9 | 126.31 | 216.31 | 1.25 | 8.65 | 9.67 |
C5-105 | 8 | 115.03 | 195.03 | 3.42 | 8 | 111.84 | 191.84 | 2.71 | 2.85 | 1.66 |
C5-106 | 9 | 118.31 | 208.31 | 4.56 | 9 | 112.55 | 202.55 | 11.21 | 5.12 | 2.84 |
C5-107 | 10 | 140.64 | 240.67 | 4.29 | 10 | 125.09 | 225.09 | 2.14 | 12.43 | 6.92 |
C5-108 | 8 | 128.38 | 208.38 | 3.02 | 7 | 118.59 | 188.59 | 2.06 | 8.25 | 10.49 |
C5-109 | 10 | 139.54 | 239.54 | 2.16 | 10 | 122.08 | 222.08 | 1.68 | 14.30 | 7.86 |
C7-101 | 17 | 291.01 | 461.01 | 28.21 | 17 | 278.80 | 448.80 | 62.18 | 4.38 | 2.72 |
C7-102 | 17 | 396.67 | 566.67 | 24.72 | 17 | 390.43 | 560.43 | 51.48 | 1.60 | 1.11 |
C7-103 | 19 | 390.53 | 580.16 | 19.61 | 18 | 385.45 | 575.45 | 21.30 | 1.32 | 0.82 |
C7-104 | 19 | 341.71 | 531.71 | 7.36 | 18 | 332.41 | 512.41 | 7.83 | 2.80 | 3.77 |
C7-105 | 13 | 309.93 | 439.93 | 49.22 | 11 | 278.34 | 388.34 | 75.51 | 11.35 | 13.28 |
C7-106 | 20 | 333.19 | 533.19 | 65.85 | 20 | 315.44 | 515.44 | 66.66 | 5.63 | 3.44 |
C7-107 | 15 | 303.86 | 453.86 | 56.02 | 12 | 293.42 | 413.42 | 74.56 | 3.56 | 9.78 |
C7-108 | 12 | 300.79 | 420.79 | 40.91 | 10 | 273.22 | 373.22 | 60.13 | 10.09 | 12.75 |
C7-109 | 12 | 356.29 | 476.29 | 29.73 | 11 | 351.14 | 461.14 | 46.28 | 1.47 | 3.29 |
Avg | 8.15 | 6.45 |
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