Table 6 Performance analysis on multimodal variable-dimension benchmark test functions.
From: Chameleon swarm algorithm with Morlet wavelet mutation for superior optimization performance
F. No. | F52 | F53 | F54 | ||||||
|---|---|---|---|---|---|---|---|---|---|
Metrics | Median | Mean | Std. dev. | Median | Mean | Std. dev. | Median | Mean | Std. dev. |
Proposed | 8.796635 | 37.33597 | 46.83735 | 16.6103 | 15.79659 | 10.26487 | 0.9 | 0.908184 | 0.031144 |
CSA | 238.3937 | 236.7943 | 5.995471 | 33.82992 | 34.46036 | 11.69824 | 1.000004 | 1.000005 | 5.43E-06 |
ABC | 141.4293 | 142.5645 | 12.27796 | 101.5629 | 102.9385 | 9.394156 | 2.130489 | 2.083757 | 0.199241 |
ACO | 268.1623 | 269.0643 | 7.641825 | 261.5707 | 258.3739 | 11.41031 | 7.44305 | 7.42176 | 0.28933 |
EHO | 282.9957 | 283.2481 | 10.05296 | 0.004174 | 0.004197 | 0.000297 | 0.900089 | 0.900088 | 7.01E-06 |
EWA | 308.6437 | 307.3129 | 20.38896 | 9.749386 | 17.30806 | 20.31796 | 1.238955 | 1.533064 | 0.682945 |
KHA | 192.3084 | 189.6491 | 30.76055 | 14.45001 | 14.44976 | 5.087514 | 1.002005 | 1.670184 | 1.639661 |
GSA | 334.164 | 329.096 | 18.884 | 13.929 | 14.725 | 3.8437 | 1 | 1 | 4.12E-17 |
MBO | 120.3378 | 138.4848 | 95.70285 | 153.1993 | 182.8509 | 147.503 | 1.11029 | 1.984482 | 1.425243 |
PSO | 284.885 | 283.941 | 10.731 | 2.403 | 22.051 | 32.595 | 5.352 | 5.187 | 1.932939 |
SCA | 284.328 | 283.5439 | 9.383524 | 4.347903 | 23.4144 | 38.67129 | 5.80416 | 5.250232 | 1.544437 |
F. No. | F55 | F56 | F57 | ||||||
|---|---|---|---|---|---|---|---|---|---|
Metrics | Median | Mean | Std. dev. | Median | Mean | Std. dev. | Median | Mean | Std. dev. |
Proposed | 2.975284 | 82.41973 | 220.0163 | 0.007112 | 0.359627 | 0.527572 | 0.000191 | 0.020201 | 0.059137 |
CSA | 7261.82 | 15884.43 | 26610.79 | 3.889502 | 4.069479 | 2.154352 | 1.494609 | 7.157269 | 16.25589 |
ABC | 2.02E + 08 | 2.57E + 08 | 2.13E + 08 | 8.093523 | 7.72828 | 1.512424 | 1.43E + 07 | 5.90E + 07 | 9.06E + 07 |
ACO | 5.45E + 07 | 6.22E + 07 | 4.93E + 07 | 19.10605 | 19.49763 | 2.515075 | 3.313857 | 4.967021 | 5.238239 |
EHO | 3185.183 | 3115.875 | 348.5288 | 0.003822 | 0.003748 | 0.00021 | 8.76E-08 | 9.38E-08 | 6.00E-08 |
EWA | 8966.783 | 729977.8 | 2,427,104 | 0.149382 | 0.461467 | 0.578919 | 0.000483 | 0.002448 | 0.004004 |
KHA | 62.0103 | 84.86197 | 79.89481 | 0.002959 | 0.007069 | 0.01026 | 39.05739 | 671.1095 | 1634.143 |
GSA | 1.30E + 06 | 3.19E + 06 | 5.46E + 06 | 2.33E-09 | 2.41E-09 | 4.29E-10 | 9.63E-07 | 0.000117 | 0.00061 |
MBO | 1.11E + 10 | 4.49E + 10 | 5.77E + 10 | 5.903644 | 16.86573 | 21.05661 | 9.62E + 09 | 2.31E + 11 | 4.71E + 11 |
PSO | 5648.34 | 24108.2 | 74191.49 | 0.00263 | 0.36883 | 1.91746 | 1.61E-05 | 0.068383 | 0.235971 |
SCA | 5467.49 | 155527.1 | 663171.5 | 0.012907 | 0.2607 | 1.027096 | 2.92E-06 | 0.00044 | 0.001596 |
F. No. | F58 | F59 | F60 | ||||||
|---|---|---|---|---|---|---|---|---|---|
Metrics | Median | Mean | Std. dev. | Median | Mean | Std. dev. | Median | Mean | Std. dev. |
Proposed | 0.00053 | 0.426366 | 0.796014 | 167.3204 | 187.7189 | 101.2445 | 0.649873 | 0.789873 | 0.430997 |
CSA | 19.96677 | 19.96677 | 2.50E-13 | 559.5002 | 551.3081 | 126.7834 | 2.199873 | 2.229873 | 0.453454 |
ABC | 11.37484 | 11.44861 | 1.135508 | 34930.49 | 37092.29 | 17430.46 | 10.55882 | 10.48822 | 1.535124 |
ACO | 20.1862 | 17.82319 | 6.144791 | 537.5839 | 544.264 | 115.8048 | 2.437575 | 2.430375 | 0.162851 |
EHO | 0.020634 | 0.020484 | 0.000879 | 91.22564 | 89.54167 | 7.977985 | 0.003621 | 0.003589 | 0.00068 |
EWA | 2.143827 | 2.272101 | 1.256036 | 240.376 | 642.5243 | 941.1934 | 0.703339 | 0.708207 | 0.403842 |
KHA | 0.015684 | 0.593088 | 0.773717 | 26.23202 | 28.17637 | 11.21959 | 0.399873 | 0.37654 | 0.067891 |
GSA | 3.60E-09 | 3.63E-09 | 5.96E-10 | 6938.763 | 7228.061 | 3661.526 | 1.10053 | 1.23176 | 0.37839 |
MBO | 18.79768 | 14.48087 | 6.868299 | 320131.8 | 523060.6 | 580796.7 | 11.55212 | 12.37401 | 9.481711 |
PSO | 20.03872 | 11.22343 | 9.946171 | 98.94225 | 108.0212 | 33.63604 | 0.19989 | 0.257741 | 0.127403 |
SCA | 18.40507 | 12.60029 | 8.840296 | 98.17692 | 106.4712 | 22.18569 | 0.199893 | 0.234155 | 0.090015 |
F. No. | F61 | F62 | F63 | ||||||
|---|---|---|---|---|---|---|---|---|---|
Metrics | Median | Mean | Std. dev. | Median | Mean | Std. dev. | Median | Mean | Std. dev. |
Proposed | -1174.94 | -1174.94 | 0.005321 | 9.81E-07 | 0.008174 | 0.011995 | -0.99962 | -0.99963 | 0.000156 |
CSA | -1033.61 | -1029.02 | 38.97252 | 0.063872 | 0.072718 | 0.036005 | 3.70E-16 | 2.19E-15 | 6.89E-15 |
ABC | -1017.71 | -1021.8 | 22.05166 | 1.485707 | 1.470638 | 0.194775 | 1.52E-12 | 1.58E-12 | 5.04E-13 |
ACO | -671.582 | -668.226 | 49.94495 | 0.825488 | 0.802076 | 0.081675 | 1.65E-10 | 1.71E-10 | 6.44E-11 |
EHO | -684.502 | -688.633 | 23.95882 | 0.000323 | 0.000314 | 4.65E-05 | -0.39712 | -0.42138 | 0.108902 |
EWA | -697.45 | -689.519 | 40.91739 | 0.241972 | 0.373633 | 0.371149 | 5.51E-11 | -0.04825 | 0.126594 |
KHA | -1017.27 | -1006.15 | 31.37359 | 0.010242 | 0.012663 | 0.011143 | 1.20E-14 | 4.00E-13 | 1.88E-12 |
GSA | -1111.37 | -1109.95 | 26.92511 | 0 | 0 | 0 | 5.52E-30 | 5.98E-30 | 2.03E-30 |
MBO | -1076.01 | -944.27 | 260.2547 | 4.011049 | 7.176058 | 6.325458 | 9.28E-12 | 1.46E-08 | 3.57E-08 |
PSO | -619.056 | -613.96 | 43.5838 | 0.000387 | 0.103111 | 0.178225 | 1.52E-10 | 1.80E-10 | 1.31E-10 |
SCA | -623.941 | -626.155 | 52.84877 | 0.003898 | 0.092368 | 0.157481 | 1.16E-10 | 1.56E-10 | 1.11E-10 |
F. No. | F64 | F65 | F66 | ||||||
|---|---|---|---|---|---|---|---|---|---|
Metrics | Median | Mean | Std. dev. | Median | Mean | Std. dev. | Median | Mean | Std. dev. |
Proposed | 3.52E-12 | 3.52E-12 | 9.53E-16 | 8.70E-05 | 0.021863 | 0.055795 | 3.96E-06 | 0.007619 | 0.028974 |
CSA | 1.76E-11 | 1.76E-11 | 3.69E-18 | 45.57699 | 41.77412 | 25.13016 | 6.2805 | 5.935862 | 2.325529 |
ABC | 2.71E-11 | 2.64E-11 | 4.61E-12 | 53026.77 | 102341.9 | 125225.6 | 9.173057 | 5612.849 | 29411.94 |
ACO | 3.12E-10 | 3.15E-10 | 1.67E-10 | 1.34E + 05 | 1.91E + 05 | 2.14E + 05 | 2.29E + 04 | 5.32E + 04 | 7.41E + 04 |
EHO | 3.87E-07 | 4.23E-07 | 2.03E-07 | 2.473693 | 2.46669 | 0.132225 | 0.460823 | 0.45868 | 0.044851 |
EWA | 9.86E-08 | 4.95E-07 | 1.09E-06 | 4.878637 | 5.158461 | 1.260947 | 1.82917 | 2.078248 | 0.963983 |
KHA | 1.25E-10 | 2.32E-07 | 7.78E-07 | 0.000167 | 0.002012 | 0.004889 | 0.27899 | 0.467207 | 0.567746 |
GSA | 3.65E-12 | 3.64E-12 | 5.52E-14 | 2.16E-18 | 2.26E-18 | 6.19E-19 | 1.47E-19 | 0.035409 | 0.103724 |
MBO | 1.71E-11 | 1.50E-11 | 4.94E-12 | 1,410,627 | 1.72E + 08 | 3.03E + 08 | 65.10721 | 66,255,921 | 1.56E + 08 |
PSO | 2.93E-10 | 3.30E-10 | 2.02E-10 | 2.438557 | 5.188774 | 11.15144 | 0.681527 | 1.258365 | 1.435293 |
SCA | 4.15E-10 | 4.08E-10 | 1.79E-10 | 2.687764 | 3.719848 | 3.361161 | 0.669408 | 0.865804 | 0.520371 |
F. No. | F67 | F68 | |||||||
|---|---|---|---|---|---|---|---|---|---|
Metrics | Median | Mean | Std. dev. | Median | Mean | Std. dev. | |||
Proposed | -24.2097 | -23.9244 | 1.192935 | 0.555545 | 0.55615 | 0.258694 | |||
CSA | -18.4328 | -18.5526 | 1.970272 | 0.576142 | 0.646125 | 0.268376 | |||
ABC | -19.5097 | -19.6271 | 1.195944 | 2.051203 | 2.155658 | 0.618281 | |||
ACO | -9.60851 | -9.58506 | 0.368916 | 0.212721 | 0.219866 | 0.053785 | |||
EHO | -11.6481 | -11.5874 | 0.593605 | 2.91E-05 | 3.09E-05 | 2.31E-05 | |||
EWA | -11.0755 | -11.3069 | 0.87826 | 0.037217 | 0.044023 | 0.031715 | |||
KHA | -22.3215 | -22.3038 | 1.537473 | 0.037357 | 0.040049 | 0.016935 | |||
GSA | -27.4414 | -27.4173 | 0.739022 | 0.018441 | 0.020708 | 0.009074 | |||
MBO | -16.5023 | -15.9714 | 3.072747 | 82.25565 | 64.20257 | 42.81425 | |||
PSO | -7.79848 | -7.8029 | 0.748354 | 0.0117 | 0.015809 | 0.016752 | |||
SCA | -7.5375 | -7.60054 | 0.845505 | 0.01594 | 0.026684 | 0.03207 | |||
