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. 2021 Sep 7;2021:6379469. doi: 10.1155/2021/6379469

Table 5.

Results of algorithms on 23 benchmark functions.

Function HSMSSA SMA SSA AO AOA WOA SCA MVO
F1 Mean 0.0000E + 00 3.3100E − 303 2.1200E − 07 3.4900E − 113 4.9600E − 06 3.0200E − 74 2.2039E + 01 1.2581E + 00
Std 0.0000E + 00 0.0000E + 00 2.3600E − 07 1.9100E − 112 2.1600E − 06 1.6500E − 73 3.4334E + 01 4.4824E − 01
F2 Mean 0.0000E + 00 8.7800E − 161 1.9590E + 00 5.0900E − 59 1.9805E − 03 3.1700E − 50 2.6402E − 02 1.2927E + 00
Std 0.0000E + 00 4.8000E − 160 1.4157E + 00 2.7900E − 58 1.9063E − 03 1.5800E − 49 2.9329E − 02 1.1310E + 00
F3 Mean 0.0000E + 00 1.4159e − 313 2.1110E + 03 3.7000E − 101 9.6539E − 04 4.3306E + 04 8.0776E + 03 2.3785E + 02
Std 0.0000E + 00 0.0000E + 00 1.5514E + 03 2.0200E − 100 8.1952E − 04 1.6945E + 04 4.7486E + 03 1.2902E + 02
F4 Mean 0.0000E + 00 1.4800E − 150 1.1761E + 01 1.7300E − 55 1.7772E − 02 5.2341E + 01 3.4937E + 01 1.9521E + 00
Std 0.0000E + 00 8.1300E − 150 4.0647E + 00 9.5000E − 55 1.1446E − 02 2.8502E + 01 1.3547E + 01 7.5824E − 01
F5 Mean 8.0753E − 02 5.0378E + 00 1.0827E + 02 5.2141E − 03 2.8034E + 01 2.8032E + 01 7.1843E + 04 4.7661E + 02
Std 2.7660E − 01 9.1628E + 00 1.4901E + 02 7.2117E − 03 2.0336E − 01 4.1099E − 01 1.2854E + 05 7.8524E + 02
F6 Mean 8.2900E − 07 5.8093E − 03 1.3800E − 07 1.3859E − 04 3.1018E + 00 3.6069E − 01 1.1633E + 01 1.1004E + 00
Std 4.9600E − 07 2.4730E − 03 1.5300E − 07 2.1774E − 04 2.2067E − 01 2.2358E − 01 9.7843E + 00 3.6012E − 01
F7 Mean 6.4400E − 05 1.6357E − 04 1.6394E − 01 7.8800E − 05 1.0695E − 04 3.0691E − 03 1.3682E − 01 3.6527E − 02
Std 6.2600E − 05 1.3341E − 04 6.1309E − 02 6.5100E − 05 1.0095E − 04 2.8218E − 03 2.0698E − 01 1.6353E − 02
F8 Mean −1.2569E + 04 −1.2569E + 04 −7.1073E + 03 −9.3742E + 03 −5.6142E + 03 −1.0050E + 04 −3.7684E + 03 −7.6853E + 03
Std 2.0511E − 02 5.2108E − 01 9.0982E + 02 3.7928E + 03 3.9485E + 02 1.6846E + 03 2.8948E + 02 6.3161E + 02
F9 Mean 0.0000E + 00 0.0000E + 00 5.3927E + 01 0.0000E + 00 1.5400E − 06 0.0000E + 00 3.6516E + 01 1.2767E + 02
Std 0.0000E + 00 0.0000E + 00 1.6886E + 01 0.0000E + 00 1.0800E − 06 0.0000E + 00 3.5214E + 01 3.5868E + 01
F10 Mean 8.8800E − 16 8.8800E − 16 2.5258E + 00 2.1600E − 14 4.2571E − 04 4.3200E − 15 1.4566E + 01 2.5576E + 00
Std 0.0000E + 00 0.0000E + 00 6.8528E − 01 1.1400E − 13 1.8869E − 04 2.7200E − 15 8.3427E + 00 3.3443E + 00
F11 Mean 0.0000E + 00 0.0000E + 00 2.0677E − 02 0.0000E + 00 5.1653E − 04 1.9620E − 02 9.3797E − 01 8.7497E − 01
Std 0.0000E + 00 0.0000E + 00 1.4808E − 02 0.0000E + 00 2.6954E − 03 5.4806E − 02 3.3652E − 01 7.4092E − 02
F12 Mean 2.4700E − 05 5.9758E − 03 7.1903E + 00 3.3600E − 06 7.3782E − 01 1.7457E − 02 1.4353E + 03 2.1818E + 00
Std 5.1900E − 05 6.9167E − 03 2.7304E + 00 3.9400E − 06 2.7918E − 02 1.2428E − 02 7.0295E + 03 1.3736E + 00
F13 Mean 4.6300E − 07 5.4042E − 03 1.2368E + 01 1.4900E − 05 2.9623E + 00 5.1556E − 01 1.8722E + 05 1.4761E − 01
Std 1.4800E − 07 7.9865E − 03 1.2274E + 01 2.0600E − 05 2.0518E − 02 2.3195E − 01 4.3886E + 05 6.2682E − 02
F14 Mean 9.9800E − 01 9.9800E − 01 1.2294E + 00 2.4408E + 00 1.0093E + 01 2.9945E + 00 1.7920E + 00 9.9800E − 01
Std 5.0400E − 16 3.5900E − 13 6.7284E − 01 2.6435E + 00 3.9607E + 00 3.2280E + 00 9.8831E − 01 4.2300E − 11
F15 Mean 3.9234E − 04 5.4854E − 04 2.8300E − 03 4.8202E − 04 7.5731E − 03 8.4669E − 04 1.0574E − 03 5.7644E − 03
Std 1.0289E − 04 2.5100E − 04 5.9501E − 03 1.0743E − 04 1.9781E − 02 6.5602E − 04 3.8453E − 04 1.2715E − 02
F16 Mean −1.0316E + 00 −1.0316E + 00 −1.0316E + 00 −1.0311E + 00 −1.0316E + 00 −1.0316E + 00 −1.0316E + 00 −1.0316E + 00
Std 1.4300E − 13 6.6000E − 10 2.3300E − 12 4.6089E − 04 2.7600E − 11 1.0400E − 09 4.2000E − 05 3.8000E − 07
F17 Mean 3.9789E − 01 3.9789E − 01 3.9789E − 01 3.9808E − 01 4.0051E − 01 3.9789E − 01 3.9921E − 01 3.9789E − 01
Std 2.6700E − 12 3.0000E − 08 1.3400E − 10 2.2131E − 04 1.4391E − 02 6.9400E − 06 1.2200E − 03 1.3300E − 07
F18 Mean 3.9000E + 00 3.0000E + 00 3.0000E + 00 3.0365E + 00 1.2901E + 01 3.0003E + 00 3.0001E + 00 8.4000E + 00
Std 4.9295E + 00 1.8000E − 10 1.5000E − 13 3.6597E − 02 2.1835E + 01 1.5988E − 03 9.1200E − 05 2.0550E + 01
F19 Mean −3.8628E + 00 −3.8628E + 00 −3.8628E + 00 −3.8560E + 00 −3.7416E + 00 −3.8575E + 00 −3.8512E + 00 −3.8628E + 00
Std 4.2800E − 11 8.4700E − 07 1.4600E − 10 7.4968E − 03 5.3652E − 01 5.7697E − 03 8.9408E − 03 1.9300E − 06
F20 Mean −3.2823E + 00 −3.2426E + 00 −3.2259E + 00 −3.2075E + 00 −3.2903E + 00 −3.1996E + 00 −2.9186E + 00 −3.2655E + 00
Std 5.7048E − 02 5.7100E − 02 5.9965E − 02 7.2462E − 02 6.3492E − 02 1.2887E − 01 3.7689E − 01 6.1457E − 02
F21 Mean −1.0153E + 01 −1.0153E + 01 −6.3092E + 00 −1.0142E + 01 −7.4694E + 00 −8.1869E + 00 −2.4287E + 00 −7.0425E + 00
Std 1.0300E − 07 1.9553E − 04 3.5233E + 00 2.6961E − 02 3.0153E + 00 2.6299E + 00 2.0334E + 00 3.0750E + 00
F22 Mean −1.0403E + 01 −1.0403E + 01 −7.8362E + 00 −1.0392E + 01 −7.3418E + 00 −7.6682E + 00 −3.4206E + 00 −8.4065E + 00
Std 1.6600E − 07 3.1185E − 04 3.4923E + 00 1.8669E − 02 3.2433E + 00 3.4333E + 00 1.7953E + 00 2.9406E + 00
F23 Mean −1.0536E + 01 −1.0536E + 01 −9.4298E + 00 −1.0525E + 01 −7.9685E + 00 −7.2480E + 00 −3.6694E + 00 −9.6618E + 00
Std 9.5800E − 08 2.5920E − 04 2.5607E + 00 1.6743E − 02 3.5174E + 00 3.2297E + 00 1.8159E + 00 2.3084E + 00