Table 13.
Comparison of multi-modal test function
| Algorithms | Parameters | M-modal | |||||
|---|---|---|---|---|---|---|---|
| F8 | F9 | F10 | F11 | F12 | F13 | ||
| GWO [15] | AVG | − 6.1200E+02 | 3.1100E−02 | 1.0600E−14 | 4.4900E−04 | 5.3400E−03 | 6.5400E−02 |
| SD | − 4.0900E+02 | 4.740E+01 | 7.7800E−03 | 6.6600E−04 | 2.0700E−03 | 4.470E−03 | |
| PSO [10] | AVG | − 4.8400E+04 | 4.670E+01 | 2.760E−01 | 9.2200E−04 | 6.9200E−04 | 6.6800E−04 |
| SD | 1.1500E+04 | 1.160E+01 | 5.090E−01 | 7.7200E−04 | 2.6300E−03 | 8.9100E−04 | |
| GSA [4] | AVG | − 2.820E+03 | 2.600E+01 | 6.210E−02 | 2.770E+01 | 1.800E+00 | 8.900E+00 |
| SD | 4.930E+02 | 7.470E+00 | 2.360E−01 | 5.040E+00 | 9.510E−01 | 7.130E+00 | |
| DE [1] | AVG | − 1.110E+04 | 6.920E+01 | 9.700E−08 | 0.000E+00 | 7.900E−15 | 5.100E−14 |
| SD | 5.750E+02 | 3.880E+01 | 4.200E−08 | 0.000E+00 | 8.000E−15 | 4.800E−14 | |
| FEP [91] | AVG | − 1.2600E+03 | 4.6000E−01 | 1.8000E−03 | 1.6000E−03 | 9.2000E−05 | 1.6000E−05 |
| SD | 5.260E+00 | 1.200E−03 | 2.100E−02 | 2.200E−03 | 3.600E−05 | 7.300E−06 | |
| ALO [104] | AVG | − 1.61E+03 | 7.71E−06 | 3.73E−15 | 1.86E−02 | 9.75E−12 | 2.00E−11 |
| SD | 3.14E+02 | 8.45E−06 | 1.50E−15 | 9.55E−03 | 9.33E−12 | 1.13E−11 | |
| SMS [101] | AVG | − 4.21E+00 | 1.33E+00 | 8.88E−06 | 7.06E−01 | 1.23E−01 | 1.35E−02 |
| SD | 9.36E−16 | 3.26E−01 | 8.56E−09 | 9.08E−01 | 4.09E−02 | 2.88E−04 | |
| BA [14] | AVG | − 1.070E+03 | 1.230E+00 | 1.290E−01 | 1.450E+00 | 3.960E−01 | 3.870E−01 |
| SD | 8.580E+02 | 6.860E−01 | 4.330E−02 | 5.700E−01 | 9.930E−01 | 1.220E−01 | |
| CS [96] | AVG | − 2.090E+03 | 1.270E−01 | 8.160E−09 | 1.230E−01 | 5.600E−09 | 4.880E−06 |
| SD | 7.620E−03 | 2.660E−03 | 1.630E−08 | 4.970E−02 | 1.580E−10 | 6.090E−07 | |
| GA [110] | AVG | − 2.090E+03 | 6.590E−01 | 9.560E−01 | 4.880E−01 | 1.110E−01 | 1.290E−01 |
| SD | 2.470E+00 | 8.160E−01 | 8.080E−01 | 2.180E−01 | 2.150E−03 | 6.890E−02 | |
| GOA [42] | AVG | 1.000E+00 | 0.000E+00 | 9.750E−02 | 0.000E+00 | 0.000E+00 | 0.000E+00 |
| SD | 2.000E−04 | 7.000E−04 | 1.000E+00 | 0.000E+00 | 7.000E−04 | 0.000E+00 | |
| MFO [16] | AVG | − 8.500E+03 | 8.460E+01 | 1.260E+00 | 1.910E−02 | 8.940E−01 | 1.160E−01 |
| SD | 7.260E+02 | 1.620E+01 | 7.300E−01 | 2.170E−02 | 8.810E−01 | 1.930E−01 | |
| MVO [6] | AVG | − 1.170E+04 | 1.180E+02 | 4.070E+00 | 9.400E−01 | 2.460E+00 | 2.200E−01 |
| SD | 9.370E+02 | 3.930E+01 | 5.500E+00 | 6.000E−02 | 7.900E−01 | 9.000E−02 | |
| DA [98] | AVG | − 2.860E+03 | 1.600E+01 | 2.310E−01 | 1.930E−01 | 3.110E−02 | 2.200E−03 |
| SD | 3.840E+02 | 9.480E+00 | 4.870E−01 | 7.350E−02 | 9.830E−02 | 4.630E−03 | |
| BDA [98] | AVG | − 9.240E+02 | 1.810E+00 | 3.880E−01 | 1.930E−01 | 1.490E−01 | 3.520E−02 |
| SD | 6.570E+01 | 1.050E+00 | 5.710E−01 | 1.140E−01 | 4.520E−01 | 5.650E−02 | |
| BPSO [107] | AVG | − 9.890E+02 | 4.830E+00 | 2.150E+00 | 4.770E−01 | 4.070E−01 | 3.070E−01 |
| SD | 1.670E+01 | 1.550E+00 | 5.410E−01 | 1.290E−01 | 2.310E−01 | 2.420E−01 | |
| BGSA [100] | AVG | − 8.610E+02 | 1.030E+01 | 2.790E+00 | 7.890E−01 | 9.530E+00 | 2.220E+03 |
| SD | 8.060E+01 | 3.730E+00 | 1.190E+00 | 2.510E−01 | 6.510E+00 | 5.660E+03 | |
| SCA [108] | AVG | 1.000E+00 | 0.000E+00 | 3.800E−01 | 0.000E+00 | 0.000E+00 | 0.000E+00 |
| SD | 3.600E−03 | 7.300E−01 | 1.000E+00 | 5.100E−03 | 0.000E+00 | 0.000E+00 | |
| SSA [109] | AVG | 5.570E−02 | 0.000E+00 | 1.950E−01 | 0.000E+00 | 1.420E−01 | 8.320E−02 |
| SD | 8.090E−01 | 0.000E+00 | 1.530E−01 | 6.510E−02 | 5.570E−01 | 7.060E−01 | |
| WOA [105] | AVG | − 5.080E+03 | 0.000E+00 | 7.400E+00 | 2.890E−04 | 3.400E−01 | 1.890E+00 |
| SD | 6.960E+02 | 0.000E+00 | 9.900E+00 | 1.590E−03 | 2.150E−01 | 2.660E−01 | |
| CSMA | AVG | − 12,569.1 | 0 | 8.88E−16 | 0 | 0.003937 | 0.00664 |
| SD | 0.319584 | 0 | 0 | 0 | 0.006237 | 0.00989 | |
Bold values indicate the results of the Chaotic variant of the Slime Mould Algorithm