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. 2025 Feb 25;15:6704. doi: 10.1038/s41598-025-86054-3

Table 6.

Comparison of the algorithms for VRPTW.

Instance SA GA PSO ISSA
NV TD NV TD NV TD NV TD
V001 3 175.37 3 175.37 3 175.37 3 175.37
V002 2 167.16 2 167.16 2 167.16 2 167.16
V003 2 161.57 2 161.57 2 161.57 2 161.57
V004 2 159.48 2 159.48 2 159.48 2 159.48
V005 3 175.37 3 175.37 3 175.37 3 175.37
V006 3 175.37 3 175.37 3 175.37 3 175.37
V007 3 175.37 3 175.37 3 175.37 3 175.37
V008 3 175.37 3 175.37 3 175.37 3 175.37
V009 2 169.45 2 160.82 2 160.82 2 160.82
V010 2 211.57 2 199.01 2 199.01 2 199.01
V011 2 199.01 2 199.01 2 199.01 2 199.01
V012 1 193.09 1 193.09 1 193.09 1 193.09
V013 1 187.21 1 187.21 1 187.21 1 187.21
V014 2 199.01 2 199.01 2 199.01 1 265.52
V015 2 211.57 2 199.01 2 199.01 1 247.08
V016 3 222.85 2 198.06 2 198.06 2 198.98
V017 2 198.84 2 198.84 2 198.84 1 204.49
V018 6 516.91 7 513.66 7 511.25 7 514.50
V019 6 439.41 6 434.91 6 434.91 6 434.91
V020 5 376.77 5 371.58 5 371.58 4 380.67
V021 4 351.00 3 331.88 3 331.88 3 331.88
V022 5 434.88 5 432.48 5 432.48 5 432.48
V023 5 395.65 4 384.65 4 384.65 4 384.65
V024 4 356.62 4 352.91 4 350.18 4 356.62
V025 3 314.90 3 314.90 3 314.90 3 314.90
V026 4 373.54 4 379.07 4 373.54 4 376.87
V027 4 364.91 4 364.63 4 361.78 4 364.63
V028 4 352.30 4 360.63 4 353.30 4 353.30
V029 3 310.70 3 310.70 3 310.70 3 310.70
V030 4 389.52 3 388.12 3 388.12 3 388.12
V031 6 428.82 5 363.25 6 422.74 5 363.25
V032 5 392.24 5 362.17 5 362.17 5 362.17
V033 6 424.00 5 362.17 5 398.78 5 362.17
V034 5 390.03 5 358.88 5 382.69 5 358.88
V035 6 428.23 5 363.25 5 363.25 5 363.25
V036 6 433.65 5 363.25 5 363.25 5 363.25
V037 6 429.32 5 363.25 6 429.85 5 363.25
V038 5 363.25 5 363.25 5 363.25 5 363.25
V039 5 363.25 5 363.25 5 397.18 5 363.25
V040 4 417.13 3 361.80 3 361.80 3 361.80
V041 4 417.13 3 361.80 3 361.80 3 361.80
V042 4 466.62 3 361.41 3 361.41 3 361.41
V043 3 383.66 2 351.72 2 351.72 2 351.72
V044 4 446.74 3 361.41 3 361.41 3 361.41
V045 5 470.79 3 361.41 3 361.41 3 361.41
V046 4 392.98 3 361.21 3 378.45 3 361.21
V047 4 405.95 2 352.12 2 352.12 2 352.12
V048 13 1055.48 12 1051.98 13 1135.13 12 1046.70
V049 11 911.44 12 917.89 11 928.72 11 913.60
V050 10 816.30 9 782.09 9 780.77 8 784.56
V051 6 644.25 6 637.05 6 638.31 6 638.31
V052 11 948.63 9 924.02 9 934.75 10 921.60
V053 10 850.75 8 813.96 8 826.96 8 806.77
V054 8 754.19 7 713.50 8 733.48 7 727.15
V055 7 646.24 6 635.92 7 633.60 6 631.40
V056 9 815.07 8 796.02 8 812.70 8 795.70
V057 8 739.90 7 699.38 7 742.77 7 699.38
V058 8 728.95 7 710.03 8 738.61 7 718.98
V059 7 667.52 7 654.63 6 647.21 6 641.31
V060 8 855.55 5 801.77 5 802.07 4 829.91
V061 10 828.94 10 828.94 10 828.94 10 828.94
V062 12 900.77 10 828.94 10 850.99 10 828.94
V063 11 942.79 10 853.83 10 886.58 10 828.06
V064 10 902.95 10 824.78 10 957.25 10 824.78
V065 13 1043.82 10 828.94 10 828.94 10 828.94
V066 11 861.70 10 828.94 10 828.94 10 828.94
V067 11 887.15 10 828.94 10 828.94 10 828.94
V068 12 1007.06 10 828.94 11 929.68 10 828.94
V069 10 857.70 10 828.94 10 1004.01 10 828.94
V070 8 841.73 3 591.56 3 591.56 3 591.56
V071 7 770.52 3 591.56 3 591.56 3 591.56
V072 7 882.13 4 604.87 3 607.55 3 591.17
V073 4 691.14 4 619.72 4 619.72 3 590.60
V074 7 778.00 3 588.88 3 588.88 3 588.88
V075 6 723.07 3 588.49 3 588.49 3 588.49
V076 7 735.96 3 588.29 3 588.29 3 588.29
V077 6 747.06 3 588.32 3 588.32 3 588.32
V078 22 1739.39 20 1661.62 20 1666.38 19 1651.10
V079 20 1552.53 18 1479.89 18 1490.95 18 1473.62
V080 16 1292.23 14 1228.13 14 1240.78 14 1220.83
V081 13 1098.94 11 1004.13 11 1050.90 10 998.55
V082 18 1490.12 16 1415.67 15 1430.77 15 1387.27
V083 15 1289.28 14 1299.46 13 1300.65 13 1254.35
V084 14 1175.85 12 1109.57 12 1157.85 11 1085.49
V085 12 1028.78 11 1023.39 11 1022.22 10 959.41
V086 16 1263.15 14 1236.92 13 1250.02 13 1170.82
V087 14 1198.12 12 1166.70 12 1141.15 12 1098.27
V088 13 1116.39 12 1102.00 12 1108.97 11 1067.20
V089 12 1070.40 11 1040.84 11 1036.70 10 996.43
V090 10 1198.86 7 1189.34 7 1175.23 5 1203.62
V091 24 3272.67 20 2704.57 20 2806.19 20 2704.57
V092 24 3288.13 20 2700.65 20 2809.79 20 2700.65
V093 24 3387.46 20 2683.28 20 3289.11 19 2748.07
V094 23 3279.25 19 2682.45 19 3650.64 18 2752.97
V095 24 3298.38 20 2702.05 21 3099.08 20 2702.05
V096 26 3527.01 20 2701.04 23 3421.09 20 2701.04
V097 24 3345.68 20 2731.25 21 3594.87 20 2709.37
V098 24 3254.30 20 2690.27 21 3700.51 20 2690.28
V099 23 3214.45 20 2747.30 20 3822.84 19 2715.71
V100 23 3497.34 20 2740.26 20 4040.52 19 2762.32
V101 14 2029.16 7 1984.01 7 2015.82 7 1985.24
V102 15 2455.46 8 1959.74 7 1948.31 7 1858.65
V103 14 2519.10 8 1835.97 7 1919.23 8 1846.10
V104 11 2046.21 8 1801.53 7 1887.02 7 1820.95
V105 15 2346.39 6 1904.36 7 1965.48 7 1998.41
V106 12 2177.58 8 1990.58 7 1935.20 7 1868.78
V107 13 2374.65 7 1870.65 7 2052.80 7 1993.23
V108 11 2128.22 9 1956.92 7 1883.45 7 1958.15
V109 13 2244.06 8 1864.45 8 1922.70 7 1847.28
V110 12 2158.28 7 1805.33 8 1910.66 7 1828.30
V111 73 17,876.57 59 14,198.43 66 20,173.71 60 13,940.77
V112 65 16,260.82 56 13,572.86 60 19,185.98 55 13,373.04
V113 61 15,845.44 50 13,812.26 52 18,992.69 49 12,776.23
V114 53 13,961.63 47 13,221.43 48 19,841.14 47 12,698.50
V115 68 17,416.29 57 13,815.20 65 20,864.66 57 13,753.12
V116 66 16,562.71 58 13,907.92 66 22,066.91 56 13,650.83
V117 67 17,074.79 55 13,820.07 62 22,653.31 55 13,702.45
V118 66 16,950.98 54 13,881.50 63 23,500.70 53 13,668.19
V119 61 16,180.71 51 13,469.27 56 20,551.42 50 13,102.00
V120 56 14,896.15 49 13,846.39 56 21,457.53 49 13,607.89