Journal of System Simulation ›› 2022, Vol. 34 ›› Issue (8): 1775-1788.doi: 10.16182/j.issn1004731x.joss.21-0244
• Modeling Theory and Methodology • Previous Articles Next Articles
Nan Li1(), Rong Hu1(
), Bin Qian1,2, Huaiping Jin1, Naikang Yu2
Received:
2021-03-23
Revised:
2021-06-06
Online:
2022-08-30
Published:
2022-08-15
Contact:
Rong Hu
E-mail:2235750519@qq.com;ronghu@vip.163.com
CLC Number:
Nan Li, Rong Hu, Bin Qian, Huaiping Jin, Naikang Yu. Research on Time-dependent Vehicle Routing Problem with Multiple Time Windows[J]. Journal of System Simulation, 2022, 34(8): 1775-1788.
Table 1
Comparison results of HDGWO and various deformation algorithms
算例 | GWO_V1 | GWO_V2 | HDGWO_V1 | HDGWO_V2 | HDGWO | |||||
---|---|---|---|---|---|---|---|---|---|---|
BST | AVG | BST | AVG | BST | AVG | BST | AVG | BST | AVG | |
rm101 | 8 752.0 | 9 086.1 | 8 029.8 | 9 065.6 | 7 435.0 | 7 933.7 | 5 357.6 | 5 569.1 | 4 453.5 | 4 529.6 |
rm103 | 9 540.1 | 9 798.1 | 9 174.0 | 9 933.7 | 8 050.3 | 8 602.0 | 6 199.8 | 6 439.5 | 4 912.0 | 5 223.7 |
rm105 | 10 439.7 | 10 873.0 | 9 338.5 | 10 120.5 | 8 845.3 | 9 335.4 | 6 071.8 | 6 347.8 | 5 492.5 | 5 737.2 |
rm201 | 10 613.1 | 11 359.9 | 10 427.9 | 11 762.4 | 8 259.7 | 8 880.0 | 5 277.4 | 5 386.1 | 5 144.5 | 5 276.0 |
rm203 | 16 425.3 | 17 672.8 | 14 695.5 | 16 913.6 | 11 418.2 | 12 858.4 | 7 008.8 | 7 173.6 | 6 369.0 | 6 581.9 |
rm205 | 22 648.9 | 25 069.1 | 18 614.1 | 21 045.3 | 14 166.5 | 17 606.6 | 9 000.5 | 9 234.5 | 6 917.7 | 7 140.3 |
cm101 | 6 641.8 | 7 220.9 | 7 313.1 | 8 205.3 | 6 410.7 | 6 755.8 | 5 518.3 | 5 702.3 | 4 736.3 | 5 077.0 |
cm103 | 7 571.5 | 8 026.2 | 7 820.8 | 8 239.4 | 6 924.7 | 7 337.6 | 5 859.9 | 5 989.7 | 5 467.0 | 5 691.3 |
cm105 | 8 179.0 | 8 585.2 | 8 227.1 | 8 787.2 | 7 476.0 | 7 687.0 | 6 443.4 | 6 718.6 | 5 337.7 | 5 721.0 |
cm201 | 9 043.6 | 9 961.2 | 8 531.9 | 9 694.1 | 7 178.0 | 8 156.2 | 5 557.9 | 5 803.4 | 4 987.9 | 5 216.1 |
cm203 | 11 233.9 | 12 269.9 | 10 844.7 | 12 137.4 | 9 145.2 | 10 028.0 | 6 176.8 | 6 322.5 | 5 499.5 | 5 856.1 |
cm205 | 12 518.8 | 13 821.2 | 11 267.4 | 13 259.4 | 9 985.5 | 10 863.7 | 6 312.4 | 6 987.9 | 5 656.0 | 5 971.8 |
rcm101 | 11 107.8 | 11 616.8 | 10 449.5 | 11 397.3 | 8 981.9 | 10 108.2 | 7 473.5 | 7 807.7 | 5 468.9 | 5 782.7 |
rcm103 | 11 420.4 | 12 010.1 | 10 867.9 | 11 867.7 | 9 711.1 | 10 458.8 | 7 450.3 | 7 604.8 | 5 774.8 | 6 024.5 |
rcm105 | 11 620.9 | 12 470.3 | 11 223.9 | 12 049.4 | 10 213.8 | 10 811.9 | 7 906.0 | 8 180.7 | 5 428.3 | 5 984.5 |
rcm201 | 13 400.6 | 13 763.6 | 12 080.1 | 14 124.6 | 9 825.9 | 10 914.8 | 5 399.0 | 5 906.9 | 5 238.4 | 5 799.6 |
rcm203 | 17 727.4 | 18 722.6 | 16 887.3 | 18 826.4 | 12 809.9 | 14 301.9 | 7 383.0 | 7 642.0 | 6 771.0 | 6 994.2 |
rcm205 | 17 036.2 | 18 507.4 | 15 402.5 | 17 651.3 | 11 831.9 | 13 416.0 | 7 259.9 | 7 487.3 | 6 442.8 | 6 591.7 |
Table 2
Experimental comparison results of HAVNTS, AVNS and HDGWO under time dependent functions TD3a and TD3b
算例 | TD3a | TD3b | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
HAVNTS | AVNS | HDGWO | HAVNTS | AVNS | HDGWO | |||||||
BST | AVG | BST | AVG | BST | AVG | BST | AVG | BST | AVG | BST | AVG | |
rm101 | 5 063.5 | 5 479.8 | 4 890.2 | 5 187.2 | 4 713.4 | 4 952.0 | 4 904.3 | 5 513.1 | 4 535.7 | 4 939.3 | 4 439.0 | 4 572.1 |
rm103 | 5 616.2 | 5 804.5 | 4 983.8 | 5 475.2 | 5 035.0 | 5 367.6 | 5 595.1 | 5 969.4 | 5 106.6 | 5 428.3 | 4 855.9 | 5 300.8 |
rm105 | 5 716.4 | 5 999.8 | 5 403.4 | 5 885.0 | 5 502.9 | 5 690.3 | 6 123.3 | 6 455.7 | 5 470.4 | 6 017.7 | 5 541.2 | 5 930.9 |
rm201 | 7 189.5 | 7 371.9 | 6 024.2 | 7 054.0 | 4 862.6 | 5 091.2 | 7 581.0 | 7 893.3 | 6 395.5 | 7 439.5 | 5 236.5 | 5 305.1 |
rm203 | 7 541.9 | 8 067.7 | 7 306.9 | 7 719.3 | 5 219.5 | 6 430.3 | 7 851.8 | 8 496.3 | 7 443.4 | 7 876.1 | 6 507.9 | 6 654.3 |
rm205 | 8 272.7 | 9 560.2 | 9 072.1 | 9 393.7 | 8 031.8 | 8 346.6 | 8 184.6 | 9 161.8 | 8 016.9 | 9 066.1 | 7 055.8 | 7 267.8 |
cm101 | 5 059.9 | 5 276.8 | 4 947.6 | 5 093.3 | 4 887.6 | 5 119.5 | 5 237.1 | 5 513.8 | 4 881.2 | 5 099.2 | 4 810.5 | 5 157.4 |
cm103 | 5 434.7 | 5 702.4 | 5 241.8 | 5 458.3 | 5 159.7 | 5 414.5 | 5 893.3 | 6 149.7 | 5 630.9 | 5 873.2 | 5 520.5 | 5 687.7 |
cm105 | 5 547.7 | 5 739.8 | 5 273.8 | 5 563.5 | 5 383.5 | 5 560.1 | 5 933.8 | 6 197.8 | 5 339.7 | 5 752.7 | 5 458.2 | 5 645.5 |
cm201 | 4 778.8 | 5 032.9 | 4 379.5 | 4 647.0 | 4 718.7 | 4 937.1 | 5 447.8 | 5 694.8 | 4 920.3 | 5 245.1 | 5 133.6 | 5 336.6 |
cm203 | 5 063.6 | 5 505.1 | 4 714.5 | 5 209.0 | 4 966.1 | 5 111.9 | 5 715.1 | 6 367.3 | 5 282.6 | 5 754.8 | 5 716.9 | 5 954.6 |
cm205 | 5 228.5 | 5 686.5 | 4 907.6 | 5 337.1 | 5 051.9 | 5 665.2 | 5 819.4 | 6 259.7 | 5 332.1 | 5 818.4 | 5 776.4 | 6 067.1 |
rcm101 | 6 078.8 | 6 505.6 | 5 982.3 | 6 422.0 | 5 788.2 | 6 209.8 | 6 193.9 | 6 504.5 | 5 675.2 | 6 046.6 | 5 378.6 | 5 752.3 |
rcm103 | 6 014.7 | 6 566.7 | 6 007.0 | 6 597.4 | 5 820.4 | 6 225.9 | 6 207.4 | 6 702.6 | 5 856.1 | 6 320.4 | 5 830.2 | 6 106.2 |
rcm105 | 6 358.1 | 6 876.3 | 6 387.4 | 6 806.1 | 6 163.5 | 6 483.5 | 5 857.2 | 6 633.7 | 5 784.1 | 6 306.6 | 5 762.6 | 6 078.1 |
rcm201 | 7 288.1 | 8 641.2 | 7 177.7 | 8 199.1 | 4 869.9 | 5 099.9 | 8 078.6 | 9 401.7 | 7 683.4 | 8 629.0 | 5 375.2 | 5 673.9 |
rcm203 | 8 669.9 | 9 340.7 | 8 395.6 | 9 214.8 | 6 497.2 | 6 799.4 | 9 110.5 | 9 713.5 | 7 549.7 | 9 205.5 | 6 922.2 | 7 071.0 |
rcm205 | 8 887.1 | 9 586.2 | 8 576.6 | 9 018.9 | 6 400.6 | 6 736.9 | 8 916.2 | 9 579.6 | 7 501.8 | 8 938.1 | 6 496.8 | 6 676.1 |
Table 3
Experimental comparison results of HAVNTS, AVNS and HDGWO under time dependent functions TD3c and TD3d
算例 | TD3c | TD3d | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
HAVNTS | AVNS | HDGWO | HAVNTS | AVNS | HDGWO | |||||||
BST | AVG | BST | AVG | BST | AVG | BST | AVG | BST | AVG | BST | AVG | |
rm101 | 5 302.8 | 5 552.0 | 5 130.8 | 5 354.9 | 4 540.7 | 4 767.5 | 4 884.3 | 5 318.2 | 4 476.1 | 5 007.6 | 4 521.8 | 4 759.4 |
rm103 | 5 435.8 | 6 011.0 | 5 300.6 | 5 756.8 | 4 944.7 | 5 256.1 | 5 257.1 | 5 887.5 | 5 157.0 | 5 534.0 | 4 879.9 | 5 241.4 |
rm105 | 5 625.6 | 5 995.9 | 5 259.2 | 5 820.4 | 5 375.0 | 5 572.0 | 6 000.7 | 6 314.2 | 5 676.5 | 6 120.0 | 5 636.7 | 5 909.4 |
rm201 | 6 056.5 | 7 112.1 | 6 563.6 | 6 752.9 | 4 741.5 | 4 945.6 | 6 446.5 | 7 618.0 | 6 248.2 | 7 248.2 | 4 059.9 | 5 095.6 |
rm203 | 7 034.6 | 7 487.4 | 6 887.3 | 7 266.0 | 6 099.4 | 6 314.3 | 7 841.5 | 8 482.7 | 7 797.0 | 8 401.4 | 5 735.7 | 6 687.2 |
rm205 | 7 786.6 | 8 740.1 | 7 645.2 | 8 452.4 | 6 925.0 | 7 787.7 | 9 544.9 | 10 149.9 | 8 327.3 | 9 615.0 | 8 349.7 | 9 136.3 |
cm101 | 4 549.1 | 4 739.3 | 4 403.9 | 4 566.7 | 4 381.1 | 4 600.5 | 5 737.2 | 5 993.5 | 5 531.4 | 5 835.3 | 5 449.4 | 5 790.3 |
cm103 | 5 336.0 | 5 521.1 | 5 158.1 | 5 402.9 | 5 090.4 | 5 358.4 | 5 941.0 | 6 192.0 | 5 781.9 | 6 039.7 | 5 706.3 | 5 872.2 |
cm105 | 5 176.8 | 5 355.6 | 5 012.4 | 5 160.6 | 5 001.7 | 5 186.0 | 6 202.2 | 6 412.2 | 5 997.4 | 6 280.9 | 5 929.2 | 6 196.2 |
cm201 | 4 343.6 | 4 530.1 | 4 184.1 | 4 307.0 | 4 287.1 | 4 507.2 | 6 048.1 | 6 974.5 | 5 481.4 | 6 543.3 | 5 432.9 | 5 642.3 |
cm203 | 4 849.2 | 5 038.3 | 4 568.5 | 4 808.2 | 4 670.1 | 4 825.2 | 7 060.4 | 7 469.0 | 6 924.4 | 7 203.8 | 6 283.7 | 7 129.0 |
cm205 | 4 726.3 | 5 043.1 | 4 703.0 | 4 847.0 | 4 740.3 | 4 825.9 | 6 465.7 | 7 534.3 | 6 134.6 | 7 411.1 | 6 364.6 | 7 398.3 |
rcm101 | 6 226.8 | 6 552.2 | 5 948.1 | 6 407.6 | 5 688.1 | 6 094.1 | 6 014.0 | 6 511.0 | 6 014.3 | 6 357.5 | 5 688.2 | 6 018.0 |
rcm103 | 6 320.6 | 6 793.5 | 6 161.1 | 6 617.0 | 5 843.5 | 6 078.4 | 6 403.9 | 6 601.8 | 6 070.7 | 6 608.0 | 6 014.9 | 6 187.0 |
rcm105 | 6 489.1 | 6 939.3 | 6 485.7 | 6 851.5 | 6 287.4 | 6 518.2 | 6 051.7 | 6 537.8 | 6 029.9 | 6 427.2 | 6 049.5 | 6 327.9 |
rcm201 | 7 357.8 | 8 425.3 | 6 899.9 | 8 176.6 | 5 005.0 | 5 141.2 | 7 879.1 | 9 253.9 | 7 684.7 | 8 859.0 | 5 314.5 | 6 263.9 |
rcm203 | 8 207.1 | 9 098.1 | 7 914.7 | 8 433.2 | 6 310.0 | 6 458.3 | 8 235.5 | 9 823.0 | 9 042.6 | 9 548.2 | 7 044.3 | 7 164.2 |
rcm205 | 8 192.1 | 8 558.9 | 6 845.0 | 8 190.9 | 6 177.4 | 6 332.5 | 9 120.1 | 9 779.9 | 6 594.1 | 9 001.6 | 5 371.0 | 6 526.8 |
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