Table 4 Comparison of optimization capabilities for Benchmark functions.
Function | AO | RIME | GWO | ED | IAO | |||||
|---|---|---|---|---|---|---|---|---|---|---|
Mean | Std | Mean | Std | Mean | Std | Mean | Std | Mean | Std | |
\(f_1\) | 4.3E-33 | 8.5E-33 | 3.8E-01 | 1.4E-01 | 1.1E-58 | 3.5E-58 | 5.2E-06 | 1.1E-05 | 0.0E+00 | 0.0E+00 |
\(f_2\) | 4.8E-23 | 1.2E-22 | 4.3E-01 | 2.8E-01 | 9.6E-35 | 9.9E-35 | 2.8E-03 | 3.3E-03 | 0.0E+00 | 0.0E+00 |
\(f_3\) | 1.3E-03 | 3.2E-03 | 3.6E-02 | 9.6E+01 | 1.9E-14 | 5.7E-14 | 6.8E+02 | 4.1E+02 | 0.0E+00 | 0.0E+00 |
\(f_4\) | 5.2E-05 | 3.5E-05 | 3.4E+00 | 1.6E+00 | 1.9E-14 | 2.2E-14 | 1.4E+01 | 3.5E+00 | 0.0E+00 | 0.0E+00 |
\(f_5\) | 2.7E+01 | 1.3E+01 | 3.6E+02 | 5.9E+02 | 2.7E+01 | 7.5E-01 | 9.0E+01 | 4.2E+01 | 2.6E+01 | 3.6E-01 |
\(f_6\) | 8.2E-05 | 2.5E-04 | 3.9E-01 | 2.1E-01 | 6.4E-01 | 4.0E-01 | 1.3E-05 | 3.4E-05 | 9.8E-07 | 6.7E-07 |
\(f_7\) | 1.4E-03 | 7.1E-04 | 2.0E-02 | 8.1E-03 | 7.8E-04 | 3.5E-04 | 4.5E-02 | 1.9E-02 | 4.9E-05 | 3.6E-05 |
\(f_8\) | -1.1E+04 | 3.2E+02 | -1.1E+04 | 4.6E+02 | -6.0E+03 | 8.6E+02 | -9.9E+03 | 4.0E+02 | -1.2E+04 | 2.4E+02 |
\(f_9\) | 0.0E+00 | 0.0E+00 | 4.8E+01 | 1.0E+01 | 3.1E-01 | 1.7E+00 | 2.5E+01 | 3.8E+00 | 0.0E+00 | 0.0E+00 |
\(f_{10}\) | 2.0E-14 | 9.3E-15 | 1.6E+00 | 5.6E-01 | 1.6E-14 | 4.4E-15 | 2.5E+00 | 6.8E-01 | 4.4E-16 | 3.0E-31 |
\(f_{11}\) | 6.5E-03 | 1.8E-02 | 5.3E-01 | 1.6E-01 | 3.0E-03 | 8.8E-03 | 2.9E-02 | 3.3E-02 | 0.0E+00 | 0.0E+00 |
\(f_{12}\) | 5.6E-04 | 1.7E-03 | 1.4E+00 | 1.2E+00 | 4.3E-02 | 3.0E-02 | 7.6E-02 | 2.5E-01 | 3.1E-05 | 1.2E-04 |
\(f_{13}\) | 1.9E-01 | 2.1E-01 | 5.6E-02 | 2.8E-02 | 5.0E-01 | 2.1E-01 | 2.7E-02 | 5.6E-02 | 1.0E+00 | 5.9E-01 |
\(f_{14}\) | 3.4E+00 | 3.9E+00 | 10.0E-01 | 5.5E-13 | 3.6E+00 | 3.8E+00 | 10.0E-01 | 3.4E-16 | 1.5E+00 | 1.8E+00 |
\(f_{15}\) | 6.4E-03 | 1.3E-02 | 5.4E-03 | 1.3E-02 | 3.0E-03 | 6.9E-03 | 1.0E-03 | 3.1E-04 | 3.9E-04 | 1.3E-04 |
\(f_{16}\) | -1.0E+00 | 0.0E+00 | -1.0E+00 | 1.6E-08 | -1.0E+00 | 4.66E-09 | -1.0E+00 | 0.0E+00 | -1.0E+00 | 0.0E+00 |
\(f_{17}\) | 4.0E-01 | 1.7E-03 | 4.0E-01 | 6.0E-09 | 4.0E-01 | 2.8E-07 | 4.0E-01 | 1.1E-16 | 4.0E-01 | 1.1E-04 |
\(f_{18}\) | 4.8E+00 | 6.9E+00 | 3.0E+00 | 1.4E-07 | 3.0E+00 | 9.5E-06 | 3.0E+00 | 4.5E-16 | 3.0E+00 | 1.3E-08 |
\(f_{19}\) | -2.9E+00 | 1.5E-03 | -3.9E+00 | 1.4E-07 | -3.9E+00 | 2.1E-03 | -3.9E+00 | 2.7E-15 | -3.9E+00 | 3.5E-05 |
\(f_{20}\) | -3.3E+00 | 5.5E-02 | -3.3E+00 | 5.5E-02 | -3.3E+00 | 8.5E-02 | -3.3E+00 | 1.4E-15 | -3.3E+00 | 5.4E-02 |
\(f_{21}\) | -6.3E+00 | 3.2E+00 | -8.5E+00 | 2.4E+00 | -9.7E+00 | 1.6E+00 | -8.6E+00 | 2.2E+00 | -1.0E+01 | 2.1E-02 |
\(f_{22}\) | -5.3E+00 | 3.5E+00 | -9.4E+00 | 2.2E+00 | -1.0E+01 | 3.1E-04 | -8.5E+00 | 2.5E+00 | -1.0E+01 | 1.4E+00 |
\(f_{23}\) | -6.4E+00 | 3.7E+00 | -9.6E+00 | 2.0E+00 | -1.0E+01 | 1.8E+00 | -9.0E+00 | 2.3E+00 | -1.1E+01 | 7.9E-03 |
