Table 5. Comparison of best, worst, mean, median and standard deviation values for ABC, WOA, BOA PSO, EOSA, DE, GA, HGSO, SOA, and BMO metaheuristic algorithms using the classical benchmark functions over 500 runs and 100 population size.
| ABC | WOA | BOA | PSO | DE | GA | BMO | EOSA | HGSO | SOA | ||
|---|---|---|---|---|---|---|---|---|---|---|---|
| F1 | Best | 2.47E-12 | 2.48E-12 | 2.50E-12 | 2.44E-12 | 1.46E+11 | 4106464761 | 1.04867E+11 | 2.44E-12 | 8.23E-104 | 0 |
| Worst | 2.60168E+11 | 2.48E-12 | 2.50E-12 | 2.44E-12 | 2.58E+11 | 1.35E+11 | 1.26382E+11 | 2.44E-12 | 1.07E+11 | 2.55822E+11 | |
| Mean | 2.04696E+11 | 2.48E-12 | 2.50E-12 | 2.44E-12 | 2.06E+11 | 5647478875 | 1.04953E+11 | 2.44E-12 | 489880801.7 | 9790935384 | |
| F2 | Best | 2.40E-18 | 2.44E-18 | 2.37E-18 | 2.44E-18 | 1.49E+17 | 53323511.38 | 209785.6196 | 2.37E-18 | 44.10261447 | 44.33953792 |
| Worst | 1.45E+17 | 2.44E-18 | 2.37E-18 | 2.44E-18 | 1.49E+17 | 2.52E+16 | 209785.6196 | 2.40E-18 | 1.04E+16 | 1.70E+17 | |
| Mean | 6.40E+16 | 2.44E-18 | 2.37E-18 | 2.44E-18 | 1.49E+17 | 5.83E+13 | 209785.6196 | 2.37E-18 | 3.01E+13 | 2.59E+16 | |
| F3 | Best | 2.86E-12 | 2.82E-12 | 2.76E-12 | 2.86E-12 | 2.71E-146 | 865.7595089 | 260316.6212 | 2.57E-12 | 1.02E-241 | 0 |
| Worst | 100289061.5 | 2.82E-12 | 2.76E-12 | 2.86E-12 | 24647958.47 | 652837.5949 | 260316.6212 | 2.80E-12 | 54779492.97 | 5871510.079 | |
| Mean | 256702.4063 | 2.82E-12 | 2.76E-12 | 2.86E-12 | 85506.69928 | 26635.78996 | 260316.6212 | 2.57E-12 | 114542.9249 | 11743.02016 | |
| F4 | Best | 1.01E-10 | 1.02E-10 | 1.02E-10 | 1.01E-10 | 152250.3059 | 11996.3679 | 210095.2125 | 1.01E-10 | 1.22E-109 | 0 |
| Worst | 2219235.401 | 1.02E-10 | 1.02E-10 | 1.01E-10 | 1083569.996 | 242291.8529 | 210095.2125 | 1.02E-10 | 1472206.755 | 482941.467 | |
| Mean | 260786.7052 | 1.02E-10 | 1.02E-10 | 1.01E-10 | 225703.8591 | 23799.47495 | 210095.2125 | 1.01E-10 | 5060.550052 | 27644.49411 | |
| F5 | Best | 1.08E-19 | 1.16E-19 | 1.13E-19 | 1.04E-19 | 1.00E-24 | 911.4244623 | 209785.6196 | 9.62E-20 | 0.15590465 | 10460.04926 |
| Worst | 18770598227 | 1.16E-19 | 1.13E-19 | 1.04E-19 | 92699584231 | 1419691418 | 209785.6196 | 9.90E-20 | 3.69E+11 | 34961399751 | |
| Mean | 59781217.28 | 1.16E-19 | 1.13E-19 | 1.04E-19 | 238666361.4 | 5408441.124 | 209785.6196 | 9.62E-20 | 745438916.6 | 156886793.6 | |
| F6 | Best | 1.71E-10 | 1.76E-10 | 1.72E-10 | 1.73E-10 | 2394966487 | 4.159217166 | 11210910151 | 1.72E-10 | 1.02650854 | 1.187374865 |
| Worst | 2594482104 | 1.76E-10 | 1.72E-10 | 1.73E-10 | 2567488472 | 678040718.4 | 33979497609 | 1.74E-10 | 429173991.9 | 78169609340 | |
| Mean | 975017964 | 1.76E-10 | 1.72E-10 | 1.73E-10 | 2524020304 | 1702811.703 | 11346936651 | 1.72E-10 | 1632585.894 | 5291097513 | |
| F7 | Best | 0.00537744 | 0.005388969 | 0.005480457 | 0.005391917 | 59.10789733 | 6.976934078 | 14981554900 | 0.003344178 | 9.850801272 | 9.800000008 |
| Worst | 106.5810109 | 0.005388969 | 0.005480457 | 0.005391917 | 107.3461889 | 63.34963883 | 27264639920 | 0.004373574 | 43.96722626 | 1.03559E+11 | |
| Mean | 11.41374051 | 0.005388969 | 0.005480457 | 0.005391917 | 81.28584828 | 8.490634765 | 15100740067 | 0.003346353 | 10.05723641 | 6446484084 | |
| F8 | Best | 3.65E-10 | 3.74E-10 | 3.66E-10 | 3.73E-10 | 985634985.2 | 17956.26097 | 354906921.5 | 3.74E-10 | 4950 | 4950 |
| Worst | 1384897512 | 3.74E-10 | 3.66E-10 | 3.73E-10 | 1361818654 | 464120523.3 | 554301224 | 3.75E-10 | 340835146.7 | 1457114306 | |
| Mean | 889078912.1 | 3.74E-10 | 3.66E-10 | 3.73E-10 | 1254140695 | 1772015.04 | 355869483 | 3.74E-10 | 1336939.589 | 24765556.99 | |
| F9 | Best | 2.45E-06 | 2.45E-06 | 2.44E-06 | 2.42E-06 | 150745.5792 | 4173.394244 | 123695.6791 | 2.43E-06 | 0.5 | 0.5 |
| Wworst | 263287.4203 | 2.45E-06 | 2.44E-06 | 2.42E-06 | 262848.6996 | 139559.2807 | 140863.5674 | 2.44E-06 | 75064.78913 | 264461.4534 | |
| Mean | 205450.4186 | 2.45E-06 | 2.44E-06 | 2.42E-06 | 207583.4194 | 5816.112605 | 123809.6376 | 2.43E-06 | 366.1429711 | 7460.348419 | |
| F10 | Best | 0.065264947 | 0.055534741 | 0.065630095 | 0.065272135 | 11.29812226 | 4.736804364 | 9702.905179 | 0.046648475 | 0 | 0 |
| Worst | 11.507642 | 0.065329978 | 0.065630095 | 0.065272135 | 11.44580276 | 10.09038934 | 13005.22209 | 0.058911739 | 8.480262936 | 26494.77467 | |
| Mean | 2.862967765 | 0.057169632 | 0.065630095 | 0.065272135 | 11.40128365 | 5.190692848 | 9721.634657 | 0.046680024 | 0.114397103 | 1112.80629 | |
| F11 | Best | 0.000250786 | 0.000246696 | 0.000249866 | 0.000252195 | 13.25336872 | 40.41662168 | 1985.011032 | 0.000246298 | 11.51810893 | 100 |
| Worst | 1477.956124 | 0.000246696 | 0.000249866 | 0.000252195 | 1437.269586 | 820.6332779 | 58896.95022 | 0.000247986 | 669.1654077 | 9900 | |
| Mean | 106.6199225 | 0.000246696 | 0.000249866 | 0.000252195 | 225.3094727 | 57.42482498 | 3143.086142 | 0.000246305 | 29.56622817 | 3803.34477 | |
| F12 | Best | 4.59E-10 | 4.56E-10 | 4.50E-10 | 4.62E-10 | 921421360.4 | 16533.59328 | 23577837147 | 4.51E-10 | 98.86771563 | 98.97310275 |
| Worst | 1085749209 | 4.56E-10 | 4.50E-10 | 4.62E-10 | 1105359990 | 365586773.6 | 48156845615 | 4.57E-10 | 237130959.5 | 1.37169E+11 | |
| Mean | 391773892 | 4.56E-10 | 4.50E-10 | 4.62E-10 | 1041990575 | 1472601.153 | 23631867107 | 4.51E-10 | 746936.1114 | 13444857087 | |
| F13 | Best | 2.47E-06 | 2.43E-06 | 2.45E-06 | 2.44E-06 | 149354.2611 | 4296.604798 | 105811.7963 | 2.43E-06 | 19.93229264 | 23.75105029 |
| Worst | 257643.1306 | 2.43E-06 | 2.45E-06 | 2.44E-06 | 261762.2494 | 138652.6906 | 142526.1384 | 2.44E-06 | 91297.1041 | 275194.0507 | |
| Mean | 205778.2306 | 2.43E-06 | 2.45E-06 | 2.44E-06 | 204473.9907 | 5798.078168 | 106135.334 | 2.43E-06 | 401.736332 | 18094.64593 | |
| F14 | Best | 3.01E-70 | 3.60E-70 | 2.93E-70 | 2.61E-70 | 8.61E+48 | 1200.2428 | 5490765292 | 2.02E-70 | 1200.00029 | 36750667194 |
| Worst | 4.50E+54 | 3.60E-70 | 2.93E-70 | 2.61E-70 | 7.42E+54 | 1.37E+51 | 5.41E+39 | 2.53E-70 | 2.72E+54 | 1200.052508 | |
| Mean | 1.09E+52 | 3.60E-70 | 2.93E-70 | 2.61E-70 | 5.52E+53 | 5.37E+48 | 2.73E+48 | 2.02E-70 | 1.08E+52 | 9.95E+52 | |
| F15 | Best | 2.09E-29 | 1.78E-29 | 1.89E-29 | 2.03E-29 | 438320.8487 | 110941.4238 | 10.88064761 | 1.79E-29 | 592240.2576 | 248.3259763 |
| Worst | 2.76E+24 | 1.78E-29 | 1.89E-29 | 2.03E-29 | 1.10E+24 | 1.04E+24 | 1.10E+24 | 1.93E-29 | 1.92E+23 | 1.06326E+12 | |
| Mean | 1.43E+22 | 1.78E-29 | 1.89E-29 | 2.03E-29 | 3.47E+21 | 3.14E+21 | 1.10E+24 | 1.79E-29 | 6.82E+20 | 8.71E+18 | |
| Total Count | 2 | 2 | 2 | 1 | 1 | 0 | 0 | 6 | 1 | 4 | |