Table 5 Comparative statistical results on CEC-2022 test suite (Dimension = 20).
Function | Metric | HAALO | PSO | PPSO | GA | ALO | RIME | GEO | MSACO | DBO | FPA | SHO | LUS |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
F22-01 | Minimum | 634.09 | 673.85 | 650.86 | 660.19 | 681.5 | 738.33 | 705.11 | 707.47 | 738.65 | 687.94 | 673.72 | 749.66 |
Mean | 657.53 | 692.49 | 669.88 | 671.13 | 700.56 | 768.28 | 732.82 | 720.42 | 766.14 | 715.83 | 687.2 | 764.34 | |
Std Dev | 10.24 | 14.74 | 13.01 | 8.51 | 11.44 | 8.73 | 14.92 | 9.63 | 11.07 | 5.88 | 5.76 | 5.33 | |
Rank | 1.0 | 5.0 | 2.0 | 3.0 | 6.0 | 10.0 | 8.0 | 9.0 | 11.0 | 7.0 | 4.0 | 12.0 | |
F22-02 | Minimum | 606.38 | 702.42 | 714.1 | 704.34 | 690.76 | 694.06 | 707.46 | 733.17 | 749.01 | 697.24 | 708.28 | 697.49 |
Mean | 635.92 | 729.82 | 739.86 | 728.05 | 715.44 | 706.24 | 727.32 | 763.02 | 769.57 | 716.38 | 735.51 | 725.49 | |
Std Dev | 7.98 | 7.1 | 8.44 | 13.99 | 12.03 | 11.08 | 13.27 | 11.87 | 8.75 | 7.31 | 5.49 | 9.51 | |
Rank | 1.0 | 6.0 | 10.0 | 7.0 | 2.0 | 3.0 | 8.0 | 11.0 | 12.0 | 4.0 | 9.0 | 5.0 | |
F22-03 | Minimum | 610.75 | 686.69 | 707.57 | 724.91 | 731.45 | 656.91 | 736.39 | 666.35 | 719.64 | 678.85 | 719.17 | 735.96 |
Mean | 637.82 | 707.63 | 717.75 | 743.62 | 761.3 | 667.83 | 750.35 | 678.62 | 738.37 | 697.64 | 732.27 | 758.57 | |
Std Dev | 12.3 | 7.19 | 14.66 | 10.89 | 7.32 | 10.38 | 11.81 | 13.7 | 14.9 | 9.82 | 7.94 | 5.77 | |
Rank | 1.0 | 5.0 | 6.0 | 9.0 | 10.0 | 2.0 | 12.0 | 3.0 | 8.0 | 4.0 | 7.0 | 11.0 | |
F22-04 | Minimum | 638.4 | 729.41 | 720.95 | 692.96 | 694.37 | 738.71 | 670.06 | 714.08 | 747.91 | 688.26 | 677.21 | 743.5 |
Mean | 667.87 | 757.63 | 731.46 | 711.1 | 715.85 | 765.82 | 681.51 | 743.84 | 777.3 | 713.57 | 699.97 | 769.06 | |
Std Dev | 8.59 | 5.69 | 13.13 | 9.54 | 11.51 | 5.25 | 11.54 | 9.97 | 10.32 | 11.52 | 5.04 | 11.5 | |
Rank | 1.0 | 9.0 | 8.0 | 5.0 | 6.0 | 10.0 | 2.0 | 7.0 | 12.0 | 4.0 | 3.0 | 11.0 | |
F22-05 | Minimum | 635.21 | 680.9 | 668.87 | 735.0 | 702.41 | 678.95 | 716.66 | 657.83 | 670.79 | 723.74 | 702.2 | 685.52 |
Mean | 661.61 | 707.11 | 694.59 | 748.43 | 712.46 | 702.16 | 743.38 | 669.12 | 682.56 | 735.81 | 722.01 | 697.86 | |
Std Dev | 10.83 | 5.92 | 8.79 | 11.73 | 7.4 | 7.7 | 8.28 | 12.1 | 13.15 | 5.61 | 10.37 | 14.0 | |
Rank | 1.0 | 6.0 | 3.0 | 12.0 | 9.0 | 5.0 | 10.0 | 2.0 | 4.0 | 11.0 | 8.0 | 7.0 | |
F22-06 | Minimum | 636.72 | 732.13 | 737.91 | 658.83 | 743.95 | 689.22 | 712.67 | 699.58 | 714.05 | 726.89 | 698.67 | 737.57 |
Mean | 663.12 | 760.47 | 755.98 | 681.54 | 767.14 | 712.07 | 727.37 | 719.18 | 735.65 | 753.0 | 727.49 | 750.34 | |
Std Dev | 6.5 | 10.19 | 9.96 | 5.85 | 13.24 | 14.29 | 6.07 | 14.77 | 9.7 | 10.58 | 13.77 | 11.83 | |
Rank | 1.0 | 9.0 | 11.0 | 2.0 | 12.0 | 3.0 | 6.0 | 5.0 | 7.0 | 8.0 | 4.0 | 10.0 | |
F22-07 | Minimum | 649.72 | 736.32 | 650.95 | 746.79 | 713.96 | 736.25 | 667.64 | 683.12 | 748.61 | 732.69 | 656.02 | 706.52 |
Mean | 674.85 | 749.77 | 677.68 | 762.8 | 728.61 | 763.1 | 683.89 | 706.21 | 773.15 | 758.24 | 676.83 | 720.76 | |
Std Dev | 8.91 | 11.79 | 6.8 | 10.8 | 15.0 | 6.45 | 13.62 | 14.75 | 14.13 | 9.08 | 14.07 | 10.39 | |
Rank | 1.0 | 10.0 | 2.0 | 11.0 | 7.0 | 9.0 | 4.0 | 5.0 | 12.0 | 8.0 | 3.0 | 6.0 | |
F22-08 | Minimum | 610.0 | 700.4 | 668.33 | 748.4 | 702.76 | 736.43 | 729.69 | 656.69 | 707.99 | 672.69 | 727.28 | 679.85 |
Mean | 625.07 | 719.8 | 686.85 | 766.32 | 728.82 | 752.65 | 741.95 | 684.01 | 723.57 | 684.59 | 755.04 | 709.41 | |
Std Dev | 14.18 | 14.57 | 14.02 | 14.2 | 13.49 | 12.85 | 8.58 | 14.74 | 9.53 | 11.59 | 5.22 | 13.21 | |
Rank | 1.0 | 6.0 | 3.0 | 12.0 | 7.0 | 11.0 | 10.0 | 2.0 | 8.0 | 4.0 | 9.0 | 5.0 | |
F22-09 | Minimum | 645.86 | 676.37 | 726.35 | 704.03 | 662.85 | 697.05 | 689.99 | 651.51 | 694.11 | 714.62 | 706.76 | 743.73 |
Mean | 666.88 | 695.05 | 742.93 | 731.47 | 686.57 | 719.36 | 718.03 | 676.81 | 718.52 | 730.28 | 728.9 | 771.42 | |
Std Dev | 10.33 | 8.51 | 13.11 | 14.79 | 8.23 | 9.91 | 13.11 | 14.06 | 7.21 | 10.81 | 11.03 | 10.17 | |
Rank | 1.0 | 4.0 | 11.0 | 8.0 | 3.0 | 7.0 | 5.0 | 2.0 | 6.0 | 10.0 | 9.0 | 12.0 | |
F22-10 | Minimum | 649.55 | 707.28 | 738.53 | 655.56 | 669.07 | 708.21 | 685.19 | 692.77 | 671.03 | 694.9 | 654.96 | 657.64 |
Mean | 670.43 | 734.6 | 759.11 | 680.91 | 686.65 | 736.31 | 701.81 | 711.69 | 682.19 | 705.22 | 668.49 | 672.08 | |
Std Dev | 10.96 | 11.66 | 8.71 | 6.19 | 11.15 | 13.18 | 14.04 | 12.62 | 12.87 | 14.77 | 7.74 | 5.8 | |
Rank | 1.0 | 10.0 | 12.0 | 3.0 | 5.0 | 11.0 | 7.0 | 8.0 | 6.0 | 9.0 | 2.0 | 4.0 | |
F22-11 | Minimum | 607.63 | 697.55 | 747.22 | 699.96 | 692.97 | 694.04 | 705.95 | 704.95 | 696.05 | 740.48 | 679.2 | 746.57 |
Mean | 624.65 | 717.46 | 768.64 | 725.5 | 715.17 | 718.57 | 728.3 | 726.49 | 711.69 | 769.89 | 704.17 | 771.2 | |
Std Dev | 8.25 | 14.56 | 5.0 | 7.96 | 6.43 | 8.91 | 11.71 | 6.8 | 6.25 | 5.25 | 6.61 | 5.18 | |
Rank | 1.0 | 6.0 | 12.0 | 7.0 | 3.0 | 4.0 | 9.0 | 8.0 | 5.0 | 10.0 | 2.0 | 11.0 | |
F22-12 | Minimum | 637.82 | 650.01 | 749.09 | 706.85 | 711.74 | 661.29 | 662.22 | 684.12 | 652.37 | 668.8 | 718.42 | 717.81 |
Mean | 650.46 | 679.17 | 759.47 | 723.7 | 733.51 | 675.76 | 682.96 | 698.67 | 662.8 | 684.74 | 730.17 | 741.55 | |
Std Dev | 6.87 | 5.74 | 8.58 | 10.12 | 6.5 | 9.91 | 14.81 | 14.41 | 12.28 | 12.47 | 13.71 | 10.15 | |
Rank | 1.0 | 2.0 | 12.0 | 8.0 | 9.0 | 4.0 | 5.0 | 7.0 | 3.0 | 6.0 | 11.0 | 10.0 | |
Friedman rank | Â | 12.0 | 78.0 | 92.0 | 87.0 | 79.0 | 79.0 | 86.0 | 69.0 | 94.0 | 85.0 | 71.0 | 104.0 |
Mean rank | Â | 1.0 | 6.5 | 7.67 | 7.25 | 6.58 | 6.58 | 7.17 | 5.75 | 7.83 | 7.08 | 5.92 | 8.67 |
