Table 3 Results of HAOAROA compared to AOA and ROA on benchmark functions.
Function | Algorithm | Best value | Worst value | Avg. value | Median value | STD |
|---|---|---|---|---|---|---|
\(\:{f}_{1}\left(x\right)\) | HAOAROA | 0 | 0 | 0 | 0 | 0 |
AOA | 1.23E-10 | 5.68E-08 | 3.46E-09 | 2.35E-09 | 1.23E-09 | |
ROA | 2.35E-09 | 1.23E-06 | 7.89E-08 | 6.79E-08 | 4.57E-08 | |
\(\:{f}_{2}\left(x\right)\) | HAOAROA | 0 | 0 | 0 | 0 | 0 |
AOA | 2.57E-11 | 8.91E-09 | 4.57E-10 | 3.46E-10 | 1.79E-10 | |
ROA | 4.68E-10 | 2.35E-08 | 1.23E-09 | 9.01E-10 | 3.46E-09 | |
\(\:{f}_{3}\left(x\right)\) | HAOAROA | 0 | 0 | 0 | 0 | 0 |
AOA | 4.57E-08 | 9.88E-06 | 5.68E-07 | 4.57E-07 | 2.35E-07 | |
ROA | 9.88E-07 | 1.23E-04 | 1.57E-06 | 8.90E-07 | 7.89E-07 | |
\(\:{f}_{4}\left(x\right)\) | HAOAROA | 0 | 0 | 0 | 0 | 0 |
AOA | 3.46E-07 | 7.65E-05 | 1.23E-06 | 8.90E-07 | 4.57E-07 | |
ROA | 6.54E-06 | 2.35E-04 | 5.68E-06 | 3.46E-06 | 1.23E-06 | |
\(\:{f}_{5}\left(x\right)\) | HAOAROA | 0 | 0 | 0 | 0 | 0 |
AOA | 1.23E-05 | 5.68E-03 | 3.46E-04 | 2.35E-04 | 1.23E-03 | |
ROA | 3.46E-04 | 1.23E-02 | 9.88E-04 | 7.65E-04 | 3.46E-03 | |
\(\:{f}_{6}\left(x\right)\) | HAOAROA | 0 | 0 | 0 | 0 | 0 |
AOA | 1.23E-08 | 4.57E-06 | 2.35E-07 | 1.23E-07 | 5.68E-08 | |
ROA | 2.35E-07 | 9.88E-05 | 1.57E-06 | 1.23E-06 | 2.35E-07 | |
\(\:{f}_{7}\left(x\right)\) | HAOAROA | 0 | 0 | 0 | 0 | 0 |
AOA | 1.23E-06 | 3.46E-04 | 1.57E-05 | 9.01E-06 | 2.35E-05 | |
ROA | 1.57E-05 | 5.68E-03 | 2.35E-04 | 1.23E-04 | 4.57E-04 | |
\(\:{f}_{8}\left(x\right)\) | HAOAROA | 0 | 0 | 0 | 0 | 0 |
AOA | 2.35E-06 | 4.57E-04 | 1.23E-05 | 6.79E-06 | 2.35E-05 | |
ROA | 5.68E-05 | 2.35E-03 | 1.23E-04 | 9.01E-05 | 3.46E-04 | |
\(\:{f}_{9}\left(x\right)\) | HAOAROA | 0 | 0 | 0 | 0 | 0 |
AOA | 1.23E-03 | 7.65E-02 | 2.35E-03 | 1.23E-03 | 5.68E-03 | |
ROA | 3.46E-03 | 1.23E-01 | 4.57E-03 | 2.35E-03 | 1.23E-02 |
