Skip to main content
. 2024 Dec 30;14:31553. doi: 10.1038/s41598-024-82918-2

Table 4.

The Generational Distance (GD) metric obtained for the eight trusses.

GD MOSCA MODA MOWHO MOMFO MOMPA NSGA-II DEMO MOCS MOCS2arc
10-bar Average 81.22 88.46 67.32 70.42 102.94 87.36 264.55 52.23 58.32
Max 131.02 145.26 110.45 98.19 208.99 147.97 336.37 60.21 66.12
Min 38.58 53.66 34.67 46.91 58.49 52.90 205.65 35.34 53.20
Std 19.19 21.75 18.56 13.26 38.38 23.48 34.07 5.26 2.96
Friedman 5 6 4 4 7 6 9 2 3
25-bar Average 33.82 54.73 25.23 33.09 75.30 38.56 105.88 16.80 20.32
Max 96.72 75.76 39.69 51.33 112.74 61.37 144.86 21.34 22.09
Min 12.45 31.21 18.12 26.03 36.71 19.56 62.51 5.77 18.31
Std 16.23 11.65 4.98 6.19 19.20 9.97 20.13 4.04 0.93
Friedman 4 7 3 5 8 5 9 1 2
37-bar Average 17.53 34.61 18.84 15.60 27.33 25.97 75.05 9.76 11.03
Max 26.29 46.16 33.93 21.66 54.01 34.73 129.49 11.06 12.43
Min 10.76 21.30 12.36 8.89 14.41 13.82 38.49 8.48 9.56
Std 3.76 6.83 5.77 2.71 9.26 5.58 26.15 0.58 0.59
Friedman 4 7 5 4 7 6 9 1 2
60-bar Average 43.13 87.57 51.96 34.08 61.22 56.56 191.35 23.81 23.22
Max 67.40 116.06 85.68 42.82 90.43 73.80 231.66 56.17 26.57
Min 27.58 67.91 31.77 27.42 39.98 37.56 130.02 16.41 19.92
Std 9.44 13.07 12.58 4.02 13.32 9.74 23.34 7.88 1.39
Friedman 4 8 5 3 6 6 9 2 2
72-bar Average 113.43 239.32 115.56 71.41 197.95 122.09 465.80 41.01 42.93
Max 181.92 402.59 190.85 114.02 277.33 235.73 689.13 56.67 48.08
Min 52.52 114.58 69.01 55.93 125.12 58.43 269.63 34.09 38.91
Std 33.63 64.64 29.88 12.57 44.05 35.74 90.51 5.05 2.68
Friedman 5 8 5 3 7 5 9 1 2
120-bar Average 557.51 441.84 395.32 443.24 608.57 395.01 908.62 367.42 404.56
Max 730.24 605.87 633.89 606.89 929.99 579.63 1297.79 435.26 444.86
Min 321.92 320.36 215.09 329.61 409.49 231.97 576.24 291.15 349.28
Std 102.68 72.50 106.16 71.88 129.89 86.01 155.70 27.75 23.46
Friedman 7 5 3 5 7 3 9 2 4
200-bar Average 521.89 1120.15 542.69 224.99 565.73 470.48 1967.71 104.30 111.82
Max 1010.81 1612.03 912.99 299.73 887.45 725.87 2682.24 217.77 125.08
Min 166.17 409.60 247.78 147.42 400.14 217.52 1234.84 92.27 101.85
Std 217.10 295.61 160.88 45.73 117.95 127.75 374.15 22.20 4.74
Friedman 5 8 6 3 6 5 9 1 2
942-bar Average 92,707.63 58,690.98 46,049.22 37,420.07 41,414.17 37,999.36 68,877.23 11,223.40 13,120.63
Max 143,318.56 103,360.16 82,501.98 46,643.30 78,357.72 80,304.43 106,358.25 13,879.34 16,739.39
Min 66,320.25 32,922.23 23,724.33 26,637.04 21,620.65 17,216.42 43,963.51 8612.12 11,284.82
Std 16,199.47 18,591.74 15,467.51 4062.99 14,883.13 12,510.65 16,885.92 1061.14 1099.50
Friedman 9 7 5 5 5 4 7 1 2
Average Friedman 44.00 55.00 36.67 31.73 52.07 41.17 70.17 11.50 17.70
Overall Friedman rank 6 7 5 4 7 5 9 1 2